Chapter 14 Exercises

Work these with the chapter's habits of mind: a personal-auto premium is not one number but the sum of several priced coverage parts, and almost every rating factor is a proxy for a loss you cannot measure directly. For every factor, ask what loss mechanism is this standing in for, what can it not see, and may I legally use it here? 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 (§14.3) point you back to the relevant part of the chapter. All dollar figures are illustrative teaching values.

A. Recall and definitions

  1. † Name the four principal coverage parts of the personal-auto policy (PAP) and say in a phrase what each one pays for. Which is the part the state requires, and which is "first-party" rather than "third-party"? (§14.1)
  2. Define rating territory and list four distinct loss drivers it is a proxy for. (§14.2)
  3. In one sentence each, define driver class, vehicle symbol, and nonstandard auto. (§14.2, §14.6)
  4. † Distinguish telematics from usage-based insurance (UBI). Which is the data and which is the product? (§14.4)
  5. The chapter argues the driving record is "a real factor, but a comparatively weak one." Give the two reasons it is a weak predictor of next year's loss. (§14.2)
  6. What is a credit-based insurance score, and how does it differ from the FICO score a lender uses? (§14.3)

B. The coverage parts and what drives them

  1. For each of the following, state which coverage part of the PAP responds and whether it is first-party or third-party: (a) the insured rear-ends another car and injures its driver; (b) hail dents the insured's own roof; (c) an uninsured driver runs a light and injures the insured; (d) the insured's own car is stolen. (§14.1)
  2. † Explain why a young driver in a cheap, old car and a careful retiree in a new luxury SUV are "mirror-image" risks in terms of which coverage parts dominate their premium. Which part dominates each, and why? (§14.1)
  3. An applicant complains: "My premium went up and I didn't even have an accident." Give three distinct, legitimate reasons a renewal premium can rise with no change in the insured's own driving. (§14.1, §14.7)
  4. Map each coverage part to whether its losses are mostly high-frequency/low-severity or low-frequency/ high-severity: comprehensive glass claims; a serious bodily-injury liability claim; small collision claims. Why does this matter for which factors price each part? (§14.1; Ch. 6)

C. Rating factors — applied reasoning

  1. † Why is multivariate rating (e.g., a GLM) necessary when two factors — young driver and high- performance vehicle — are correlated? What specific error does a one-factor-at-a-time analysis make? (§14.2; Ch. 32)
  2. Rank these factors from generally stronger to generally weaker as predictors of personal-auto loss, and justify your ranking: a single old speeding ticket; the rating territory; a four-month coverage lapse; the credit-based insurance score (assume permitted). (§14.2, §14.3)
  3. A broker insists a particular relativity "is obviously too high — no factor should cost that much." Using the chapter's argument about how relativities are estimated, explain why this univariate intuition is usually the thing that is wrong. (§14.2)
  4. Explain the loss mechanism behind the prior-insurance lapse factor. Give one behavioral and one selection reason a lapse correlates with higher future loss. (§14.2)

D. Underwrite this submission

  1. † Two applicants in the same state both want standard auto with comprehensive and collision, and both have clean driving records. Applicant A: 52, six-year-old mid-size sedan, low-density suburban territory, 8,000 commute miles, twenty years continuous coverage at \$250K/\$500K limits. Applicant B: 24, two-year-old high-performance coupe, dense urban high-theft territory, 18,000 miles, a four-month coverage lapse last year, prior limits at the state minimum. (a) Which is the higher expected loss, and on which specific factors? (b) Are both writable in the standard market? (c) What does neither application reveal that only telematics could? (§14.2, §14.4)
  2. A 23-year-old applicant is quoted a high premium driven mostly by the age factor, but offers to enroll in your telematics program and, over the monitoring period, demonstrates 5,500 careful daytime miles a year. As the underwriter, how should this change your view of the risk, and what is the limit of the conclusion you can draw from a monitored window? (§14.4)
  3. † An applicant has a DUI from six years ago and a clean record since, a current job, continuous prior coverage, and a modest vehicle. A second applicant has three at-fault accidents in two years and a current coverage lapse. Both fall in the "nonstandard" bucket. Explain why pricing them the same is an underwriting error, and what adverse selection does to you if you do. (§14.6)

E. Price this risk

  1. † A personal-auto rating plan has a base rate of \$800 (for the liability + physical-damage package on one vehicle). The filed relativities for a given applicant are: driver-class factor 1.45, vehicle-symbol factor 1.30, territory factor 1.20, annual-mileage factor 0.95, and a multi-policy (account) credit of 0.90. Relativities are multiplicative. (a) Compute the indicated premium. (b) Which single factor contributes the most to the price, and what loss mechanism is it pricing? (§14.2)
  2. Using the same base rate of \$800, a second applicant has relativities 0.85 (mature, clean driver class), 0.90 (low-symbol vehicle), 0.80 (low-cost rural territory), 1.00 (mileage), and 0.90 (multi- policy). (a) Compute this premium. (b) Express the difference between this applicant and the one in Exercise 18 as a ratio, and explain in plain terms why two drivers with the same clean record can differ this much. (§14.2)
  3. † A personal-auto segment posts, for one year (all illustrative): earned premium \$10,000,000; incurred losses \$7,200,000; loss-adjustment expense \$600,000; other expenses \$2,600,000. (a) Compute the loss ratio, the expense ratio, and the combined ratio. (b) Is the segment profitable on underwriting? (c) If the target combined ratio is 98% at the same expense level, roughly how many points must the loss ratio improve — and name one force that is simultaneously pushing it the other way. (§14.7; Ch. 3)
  4. A carrier's filed plan would price a household at \$1,640, but the underwriter, because the owner is a valued commercial client, manually discounts it to \$1,300. Explain what is wrong with this — and name the legal concept (from Chapter 4) it violates. (§14.7, The Underwriting File; Ch. 4)

F. Find the red flag

  1. † Review this telematics-program design and find the fairness red flag: the carrier surcharges heavily for "hard braking" events, applies the surcharge uniformly nationwide, and markets the program as "objective, behavior-based pricing free of bias." What is the problem, and what is the name (Chapter 35) for it? (§14.4; Ch. 35)
  2. An underwriter in a state that prohibits credit in auto rating notices that a competitor's prices track credit-like patterns and concludes "credit must be junk — see, you can rate fine without it." Identify the two distinct errors in this reasoning. (§14.3, §14.5)
  3. A rating engine returns a price for an applicant in State X that includes an occupation factor and a gender factor. Before you bind, what is the one question you must ask about each factor that is not "is the price right?" — and why can the answer affect the carrier's license? (§14.5)

G. Write the memo / explain the decision

  1. † Write a short (one- to two-paragraph) explanation to an applicant who has just received an adverse-action notice because their credit-based insurance score raised their premium. Explain, in plain and non-defensive language, what the notice means, that credit was used because it is permitted in your state and predicts insurance loss, and what an "extraordinary life event" provision would let them do. (§14.3)
  2. Draft a brief internal note to your manager recommending whether to launch a telematics-based UBI program for your standard book. State two underwriting benefits, two limitations or risks (include at least one fairness or privacy concern), and the adverse-selection consequence of not offering it while competitors do. (§14.4)
  3. A regulator's market-conduct examiner asks you to explain why your personal-auto rates rose 9% this year. Write the two- or three-sentence answer a disciplined underwriter gives — grounded in loss trend and rate adequacy, not in growth targets. (§14.7; Ch. 11)

H. Ethics and fairness

  1. † The credit-based insurance score is predictive and, in many states, permitted — yet it falls hardest on lower-income and, through history, minority households. State the strongest case for using it (the actuarial-fairness argument) and the strongest case against (the social-fairness argument) without resolving the tension. Then say what your actual duty as an underwriter is, given that the law has drawn a line. (§14.3, §14.5; Ch. 35)
  2. Several states run low-cost auto programs for low-income drivers and price the residual market deliberately high. Explain how these two facts together express the "insurance serves a social function" theme — and why they do not change the underwriting math on any individual risk. (§14.6; Ch. 1)
  3. A colleague argues that because insurance "must discriminate by risk," any factor that predicts loss is automatically fair to use. Explain why "predictive" and "fair to use" are not the same thing, using territory or credit as your example. (§14.3, §14.5; Ch. 35)

I. The Underwriting File extension

  1. † The broker proposes account rounding: writing the Harbor Steel owner's personal auto alongside the commercial program. (a) Explain how the personal auto is underwritten differently from the commercial fleet (Chapter 23) — "classify and rate the household" versus "assess and structure the operation." (b) Explain precisely why you must charge the household its filed, risk-based price even though the owner is a valued commercial client, and what the personal umbrella's underlying-limit requirement (Chapter 16) has to do with this placement. (§14.2, The Underwriting File)
  2. The owner's household includes a young adult driver away at college. Explain how this single fact flows through the driver-class, use/mileage, and territory factors of the personal-auto rate — and why a telematics option might particularly benefit this driver if your state permits it. (§14.2, §14.4, The Underwriting File)