Chapter 6 Exercises

Work these with the chapter's habit of mind: run every risk through exposure → hazard → controls → frequency × severity, and never confuse the peril that causes a loss with the hazard that makes it more likely or more severe. Items marked with a dagger (†) have worked solutions in Appendix: Answers to Selected Exercises; the rest are for discussion or self-test. Section references like (§6.3) point you back to the relevant part of the chapter. Every dollar figure here is a constructed teaching example.

A. Recall and definitions

  1. † Distinguish pure risk from speculative risk, and explain in one sentence why insurance addresses only the first. (§6.1)
  2. Define peril and hazard in your own words, and give one example of each drawn from a metal-fabrication plant. (§6.2)
  3. † Name the four families of hazard and give a one-line example of each. (§6.2)
  4. Write the relationship that connects frequency, severity, and expected loss, and state in words what each term means. (§6.3)
  5. Define the exposure unit and state the typical exposure base for commercial property, workers' compensation, general liability, and commercial auto. (§6.4)
  6. What is risk classification, and why does the chapter call it "the underwriter's core cure for adverse selection"? (§6.5)
  7. State the underwriter's core mental move as a sequence, and explain what the controls step adds that risk description alone does not. (§6.6)

B. Peril vs. hazard, and the four families

  1. † For each item, say whether it is a peril or a hazard, and if a hazard, which of the four families: (a) a kitchen fire; (b) oil-soaked rags stored next to a furnace; (c) a jurisdiction famous for runaway jury verdicts; (d) an owner whose failing business is worth more burned than sold; (e) a newly-insured driver who stops doing brake inspections; (f) a hailstorm. (§6.2)
  2. Explain why two physically identical buildings, both exposed to the identical peril of fire, can be a good risk and a terrible one. What accounts for the entire difference? (§6.2)
  3. † Give an example of a legal hazard that would make the same trucking fleet a materially worse risk in one state than in another, with nothing physical about the fleet changed. Why does the chapter treat legal hazard as a peer of the older three families? (§6.2)
  4. A loss-control report on a warehouse notes "poor housekeeping, blocked sprinkler heads, and a propped-open fire door." Classify each finding by hazard family, and say for each whether it primarily raises the frequency of a fire loss, the severity, or both. (§6.2, §6.3)
  5. Why is moral hazard described as the most dangerous family even though it is often the least visible? What does it do that the other families do not? (§6.2)

C. Frequency and severity

  1. † A delivery fleet averages 4 collision claims a year at an average cost of \$18,000 per claim. (a) What is the expected annual collision loss? (b) If a safety program cuts the frequency to 2.5 claims a year with no change in average severity, what is the new expected loss, and by what percentage did it fall? (§6.3)
  2. Two accounts each carry an expected annual loss of \$120,000. Account R is 48 claims of \$2,500; Account S is one claim of \$1,200,000 expected roughly every ten years. (a) Which is primarily a housekeeping/operations problem and which is a limits/catastrophe problem? (b) Name one underwriting tool you would reach for in each case. (§6.3)
  3. † Explain why a pricing model estimates frequency and severity separately rather than modeling the total loss directly. What is different about the shape of the two distributions? (§6.3)
  4. The chapter distinguishes expected severity from maximum (probable) severity. For a coastal commercial property, which one drives the everyday premium, and which one drives how much reinsurance and capital must stand behind the policy? Why are they so different for this risk? (§6.3)
  5. A homeowners book shows frequency flat but severity rising sharply over three years. Give two plausible real-world drivers of rising severity with flat frequency, and explain why "raise the deductible a little" is an incomplete response. (§6.3)

D. Exposure and the exposure base

  1. † Explain the three properties of a good exposure base (proportional to loss, practical to measure, hard to manipulate), and show how payroll satisfies all three as the base for workers' compensation. (§6.4)
  2. An insured proposes to insure a 50,000-square-foot fabrication plant for a \$9M building value. Using a rough construction cost you can defend for industrial/joisted-masonry construction, sanity-check whether that value is plausible, and explain what the coinsurance mechanism (owned by Chapter 12) would do at a partial loss if the building is in fact under-valued. (§6.4)
  3. † "A million dollars of value in one building and a million dollars spread across fifty buildings in fifty towns are the same exposure." Attack or defend this claim using the independence idea from Chapter 1, and say which measurement — total value or accumulation — each statement gets right. (§6.4, and Ch. 1)
  4. Why does general liability sometimes rate on sales, sometimes on payroll, and sometimes on area? Give one type of business for which each base would best track the third-party-injury exposure. (§6.4)

E. Identification, classification, and the red flag

  1. Walk the identification loop (exposure → perils → hazards → frequency × severity) on a single exposure: a restaurant's commercial kitchen. List at least three perils, three hazards (naming families), and say which dimension of loss each hazard chiefly drives. (§6.5, §6.6)
  2. † (find the red flag) A submission for a small electronics warehouse arrives with: values increased 60% over last year; the owner's financials show the business is deeply unprofitable; an unusually high coverage limit requested on "stock"; and a cover note emphasizing how eager the insured is to bind before month-end. Identify the hazard family these facts point to, name the specific red flags, and say what you would do before quoting. (§6.2, §6.5; previews Ch. 33)
  3. † (underwrite this submission — risk classification) David Okafor [constructed], 45, applies for \$1M term life. Total cholesterol mildly elevated; BMI 28; excellent blood pressure; confirmed non-smoker; active recreational cyclist; father had a heart attack at 58. A naive point-counting system flags two negatives (cholesterol, BMI) and offers a substandard rate. Argue, using whole-person classification, whether David should plausibly be standard, near-preferred, or preferred — and explain what the box-counting system missed about the BMI in particular. (No need to set a final class; that is Chapter 17.) (§6.5)
  4. Explain why charging every applicant in a class the same rate only works if the class members truly have similar expected loss. What goes wrong (name the concept from Chapter 1) if you lump dissimilar risks into one class at one price? (§6.5, and Ch. 1)

F. The underwriter's mindset and insurability

  1. † (underwrite this submission) Run exposure → hazard → controls on Harbor Steel's commercial auto line only (12-unit flatbed/delivery fleet, regional radius, two minor prior claims). List the exposure, at least three hazards by family, and at least three controls you could require — then say in one sentence what the residual risk you would actually price looks like. (§6.6, The Underwriting File)
  2. The chapter argues that the exposure → hazard → controls sequence "organizes judgment; it does not replace it." Explain what the frame guarantees and what it cannot do, and why two competent underwriters can grade the same risk differently. (§6.6)
  3. † Apply the six insurability criteria from Chapter 1 to Harbor Steel one by one, and identify the single criterion that is genuinely under strain. Then explain why the chapter says insurability is "a function of the risk plus the terms, the price, and the machinery" rather than a yes/no property of the risk. (§6.7, and Ch. 1)
  4. Describe the over-confident accept trap in your own words. Why is pricing a catastrophe-exposed risk for its comfortable average year a mistake that may not reveal itself for years? (§6.7)

G. Memo, ethics, and the Underwriting File

  1. † (write the memo) In no more than 200 words, write the "risk inventory summary" paragraph you would place at the top of the Harbor Steel file: name the exposures by line, the one or two hazards that most drive each, and the controls you will require — and end with the one-sentence verdict the chapter models ("controllable, at the right price and with the right requirements"). Do not set a price or a final decision; that is later chapters. (§6.6, The Underwriting File)
  2. (ethics dilemma) Your carrier's predictive classifier reliably charges higher auto premiums in certain ZIP codes. An analyst shows you that, after controlling for driving record and vehicle, the ZIP-code factor still adds price — and that those ZIP codes correlate strongly with a protected class. The factor "improves the model's accuracy." Lay out the tension between actuarial fairness (price reflects measured risk) and the legal/ethical line against unfair discrimination, name what a proxy is, and state what you would escalate and to whom. (Do not resolve it glibly.) (§6.5; previews Ch. 4 and Ch. 35)
  3. (Underwriting-File extension) The risk inventory you built deliberately left the moral-hazard judgment "open." Explain why this chapter cannot close it, name the two later instruments (by chapter) that will, and describe one specific thing you would want each to confirm before you would be comfortable binding Harbor Steel. (§6.2, The Underwriting File; previews Ch. 9 and Ch. 33)
  4. † A junior colleague says, "Harbor Steel had two fires and sits in a hurricane zone — that's an easy decline." Using everything in this chapter, write the two-or-three-sentence reply that reframes the account from "decline" to "writable with the right price, terms, and reinsurance," and name the specific insurability criterion their reasoning ignored. (§6.7)