Chapter 1 Exercises

Work these with the chapter's habits of mind: ask of every risk what could go wrong, how likely, and how bad, and of every insurance arrangement what holds the pool together and what could poison it. 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 (§1.4) point you back to the relevant part of the chapter.

A. Recall and definitions

  1. † Define insurance in one sentence, and name the three features the chapter pulls out of that definition (transfer, pooling, promise). (§1.1)
  2. In your own words, explain why insurance can have genuine value to a policyholder even though the policyholder pays in more, on average, than they expect to collect. Use the word variance. (§1.1)
  3. State the law of large numbers in plain language, as it applies to an insurer. (§1.2)
  4. † List the six characteristics of an ideally insurable risk. For each, give a one-line reason it matters. (§1.3)
  5. Define adverse selection and explain, in one sentence, why it is called the "enemy" of the pool. (§1.4)
  6. Distinguish moral hazard from morale hazard. Which one involves intent? (§1.5)
  7. Name the seven functions of the insurance value chain in order, and say in a phrase what each contributes. (§1.6)

B. Risk pooling and the law of large numbers

  1. † An insurer covers 50,000 warehouses. Each has a 1-in-2,000 chance of a \$1,000,000 total loss in a year, and the losses are independent. (a) What is the expected number of losses per year? (b) What is the total expected loss? (c) What is the pure premium per warehouse, before expenses and profit? (§1.2)
  2. Two insurers each expect a 4% annual loss frequency. Insurer X writes 2,000 policies; Insurer Y writes 2,000,000. Explain which insurer's actual loss ratio will land closer to 4% next year, and why that makes Y's book easier to price. (§1.2)
  3. † Explain why "doubling the size of a homogeneous, independent book reduces relative volatility but not absolute volatility." Why does the relative figure matter more to a pricing actuary? (§1.2)
  4. An insurer writes earthquake coverage for 800 buildings, all within five miles of the same fault. Has it built a pool the law of large numbers will stabilize? Identify precisely which assumption is violated. (§1.2, §1.3)

C. Insurable risk

  1. † A would-be insured asks you to cover the risk that their new restaurant won't attract enough customers to be profitable. Which insurability criterion does this fail most clearly, and what is the category name for this kind of risk? (§1.3)
  2. Explain why a building's thirty-year-old roof "wearing out" is not, by itself, an insurable event, while "a windstorm tears the roof off next March" is. Which criterion separates them? (§1.3)
  3. Of the six insurability criteria, which one does catastrophe risk (hurricane, earthquake, wildfire) violate most directly? Name two parts of the industry's machinery, introduced elsewhere in the book, that exist to make catastrophe writable anyway. (§1.3, §1.6)
  4. Give one example each of a risk that fails the "definite and measurable loss" criterion and one that fails the "economically feasible premium" criterion. (§1.3)

D. Adverse selection

  1. † A new online insurer offers a single flat life-insurance price to all applicants and advertises heavily on websites people visit after a serious medical diagnosis. Predict, step by step, what happens to its pool and its price, and name the spiral. (§1.4)
  2. Explain the analogy between Akerlof's "market for lemons" and adverse selection in insurance. Who holds the private information in each case? (§1.4)
  3. "Underwriting is the cure for adverse selection." List four specific underwriting tools named in the chapter and say, for each, how it corrects the information imbalance. (§1.4)
  4. † A friend argues that the fairest insurance system would charge everyone the same price regardless of their risk. Using adverse selection, explain to them what would happen to such a system — and then state the strongest counter-argument from the other side of the fairness debate. (§1.4; preview of Ch. 35)

E. Moral and morale hazard

  1. For each of the following, identify whether it is primarily moral hazard or morale hazard, and name one policy feature that would push back on it: (a) a struggling owner whose warehouse is worth more burned than sold; (b) a newly-insured driver who stops locking the car; (c) a fully-insured business that cancels its planned sprinkler upgrade. (§1.5)
  2. † Explain how a deductible does two jobs at once — one financial, one behavioral. Why does the behavioral job matter to the quality of the insurer's whole book? (§1.5)
  3. The chapter claims an insurer that "pays claims quickly and generously, with no attention to loss prevention," can make its own book worse over time. Explain the mechanism. (§1.5)

F. The value chain and the underwriter

  1. Place the underwriter precisely within the value chain. Why does the chapter call the underwriting decision "the gate the whole chain depends on"? (§1.6, §1.7)
  2. † The combined ratio combines the loss ratio and the expense ratio. Explain why a combined ratio of 103% means the insurer lost money on underwriting, and why "we'll make it up on volume" is a dangerous response. (§1.6)
  3. The chapter argues that underwriting is "judgment, not data entry," yet also that some underwriting is rightly being automated. Reconcile these two claims. Which kinds of risk fall on each side? (§1.7)

G. The Underwriting File

  1. † Open the Harbor Steel file. Write, in your own words, the single question the file exists to answer, and list the three things this chapter says you should notice about the account without yet trying to decide it. (§1.7, The Underwriting File)
  2. The prior carrier is non-renewing Harbor Steel. The chapter warns you to treat that fact as "information to weigh, not simply to trust." Give two different reasons a carrier might non-renew a perfectly writable account, and one reason the non-renewal might be a genuine red flag. (The Underwriting File)
  3. Identify which of the six insurability criteria (§1.3) the Harbor Steel account most clearly strains, and explain in two or three sentences why that straining is what makes it an interesting account rather than an automatic decline. (§1.3, The Underwriting File)