Chapter 11 Exercises

Work these with the chapter's central habit of mind: a premium is built from nameable parts, and every modification to it should be defensible — to your manager, to the broker, and to the regulator who may one day ask you to justify 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 (§11.4) point you back to the relevant part of the chapter. Every dollar figure here is a constructed teaching example — real rates depend on filed plans, jurisdiction, and the specific risk.

A. Recall and definitions

  1. † Name the three blocks that compose a premium and say, in one phrase each, what each block pays for. Which block is typically the smallest? (§11.1)
  2. Distinguish a manual (class) rate, a base rate, and a loss cost. Which one contains no expense or profit load? (§11.2)
  3. † Define a rating factor (relativity). What does a factor of 1.00 mean? A factor of 1.25? A factor of 0.90? (§11.3)
  4. In one sentence each, distinguish experience rating from schedule rating. Which is retrospective and mechanical, and which is prospective and judgmental? (§11.4, §11.5)
  5. Define rate adequacy and state the three-word statutory standard a filed rate must satisfy (the rate must not be , , or ___). (§11.7, §11.2)
  6. What is a loss cost multiplier (LCM), and what two things does it gross the loss cost up for? (§11.2)
  7. † Define retrospective rating and explain in one sentence how it differs structurally from a prospective (manual/experience/schedule) plan. (§11.6)
  8. What is a minimum premium, and which of the three premium blocks explains why it has to exist? (§11.6, §11.1)

B. Building the premium

  1. † A class of buildings has a pure premium of \$3.20 per \$1,000 of value. The insurer's expense load is 28% of premium and its target profit and contingencies load is 6% of premium. (a) What is the permissible loss ratio? (b) What indicated rate makes the pure premium fill exactly that permissible loss ratio? (Hint: rate = pure premium ÷ permissible loss ratio.) (§11.1)
  2. An ISO loss cost for a class is \$2.50 per \$1,000 of value. The insurer's loss cost multiplier is 1.60. What manual rate does the carrier charge, and how much of that rate is loss versus expense-and-profit? (§11.2)
  3. † Two insurers price the same risk from the same \$2.50 loss cost. Insurer A's LCM is 1.45; Insurer B's is 1.70. (a) What does each charge? (b) Give the single most likely reason A can charge less than B on identical risk, and explain why it is not that A sees the risk as safer. (§11.2)
  4. Build a rate from the following relativities applied to a base rate of \$4.00 per \$1,000: construction 1.10, protection class 1.05, occupancy hazard 1.25, sprinkler credit 0.88. What is the building rate per \$1,000, and on a \$15M building, the building premium? Show the chain. (§11.3)
  5. † A junior underwriter is handed an NCCI workers'-comp loss cost of \$1.40 per \$100 of payroll and quotes a rate of \$1.40 per \$100. Explain precisely what is wrong, what the rate is missing, and what the account's first-year combined ratio looks like before any claim is filed. (§11.2, §11.1)

C. Rating factors and relativities

  1. A relativity of 1.40 is sometimes misread by newcomers as "this risk is 40% likely to have a loss." Correct the misreading: what does a 1.40 relativity actually say, and what two underlying drivers can raise it? (§11.3)
  2. † Explain the flaw in deriving relativities one factor at a time (univariate analysis) when risk characteristics are correlated. Give an example using construction and protection class, and name the modern technique (from a later chapter) that fixes it. (§11.3; preview of Ch. 32)
  3. A loss-control inspector tells you the occupancy factor for a class is high because the class has fires more often (a frequency story), not because its fires are bigger (a severity story). Why does that distinction matter for the loss-control recommendation even though both raise the same rating factor? (§11.3; Ch. 9)

D. Experience rating

  1. † Compute a credibility-weighted loss estimate. A risk's own three-year loss rate is \$1.10 per \$100 of payroll; the class loss rate is \$0.75; the credibility weight Z assigned to the risk's own experience is 0.35. (a) What is the modified estimate? (b) Is it a debit or a credit relative to the class? (c) If the risk were much larger, so Z = 0.70, what would the modified estimate become, and why has it moved? (§11.4)
  2. An account had one clean year immediately following three bad years. A colleague wants to grant it a large experience credit on the strength of the clean year. Using credibility, explain why one clean year is weak evidence, and what the disciplined response is. (§11.4)
  3. † Explain, beyond accuracy of price, why experience rating reduces moral and morale hazard. Who bears the cost of a loss next year under experience rating, and how does that change the insured's behavior this year? (§11.4; Ch. 1)
  4. The workers'-comp X-mod is the canonical experience-rating device. Without redefining the X-mod (Chapter 22 owns it), explain in two sentences how its design embodies the credibility principle from Chapter 10 — i.e., why a larger employer's mod responds more to its own losses than a smaller employer's. (§11.4; Ch. 10)

E. Schedule rating

  1. † Underwrite this submission. You are schedule-rating a small woodworking shop. Inspection notes: (i) an owner who personally runs a documented daily clean-up and tool-maintenance program; (ii) a dust- collection system that is well maintained; (iii) combustible sawdust nonetheless accumulating in one back room; (iv) no formal employee safety training. Build a schedule-rating worksheet: assign a credit or debit to each category with a one-line documented basis, and state whether the net modification is a credit or a debit. (§11.5)
  2. Find the red flag. Review this schedule-rating file entry: "Management credit 10% — long relationship with the broker; we want to keep the account." Identify exactly what is wrong, which compliance rule it violates, and rewrite the entry so that, if a 10% management credit is genuinely warranted, it would survive a market-conduct audit. (§11.5)
  3. † Explain why an account can simultaneously carry a debit experience modification and a credit schedule modification without contradiction. Use Harbor Steel as your example. (§11.4, §11.5)
  4. A broker pushes you to grant a hot-work-program schedule credit on a fabricator before the program is installed, "because they've promised to put it in." Explain why a promised-but-unverified control cannot yet be a schedule credit, and what underwriting device (from a later chapter) is the correct way to give the insured the benefit of the program once it exists. (§11.5; preview of Ch. 13)

F. Loss-sensitive plans and minimums

  1. † Price this risk. A large, financially strong manufacturer with substantial, stable loss volume asks whether a guaranteed-cost (fixed prospective) program or a retrospective-rating plan is better for it. Lay out the trade-off in terms of expected cost versus volatility of cost, and state the single most important question you must answer about the insured before recommending a retro plan. (§11.6)
  2. Under a retrospective plan, an insured has a low-loss year. Does its final premium move toward the minimum or the maximum? Now a catastrophic-loss year: where does the final premium land, and who is protected by the maximum? (§11.6)
  3. A tiny account's fully rated premium calculates to \$140, but the insurer's minimum premium for the line is \$500. The risk is genuinely excellent. What does the account pay, and why is charging the minimum not a case of unfair discrimination against a good risk? (§11.6, §11.1)

G. Rate adequacy, ethics, and the cycle

  1. † Ethics / discipline dilemma. It is a soft market. Your production manager is pressing you to hit a growth number; a strong broker has an account the incumbent is renewing 20% below your indicated rate. The account looks clean — no losses in three years. Write a short (150–200 word) statement of how you would respond, what you would and would not do to the rate, and how you would defend the decision if you lose the account to a competitor. Reference rate adequacy and the delayed-loss problem. (§11.7)
  2. Explain the sentence "the punishment for inadequate pricing is delayed by two or three years." Why does that delay make rate adequacy uniquely hard to enforce compared with pricing discipline in an ordinary (non-insurance) business? (§11.7)
  3. † Write the memo. A line underwriter has quoted Harbor Steel's property at a net schedule debit. The broker has come back arguing the debit is "punitive" and the account should get a credit because management is improving. Draft a 150–250 word response to the broker that (a) explains, in risk-based terms, why the roof condition and hot-work history justify a debit; (b) acknowledges the genuine credits available; and (c) states what the insured must do for the contingent credits to apply. Keep it firm, fair, and relationship-preserving. (§11.5, §11.7, The Underwriting File)
  4. The chapter argues that charging an adequate rate is, in the deepest sense, an ethical act, not merely a profit-seeking one. Reconstruct that argument in three or four sentences, connecting rate adequacy to the insurer's solvency and to the claimants who depend on the carrier still existing. (§11.7; Ch. 1)
  5. Describe the underwriting cycle as a repeated process of forgetting and relearning rate adequacy. What does an underwriter who "prices through the cycle" do differently in a soft market versus a hard one, and why is being whipsawed by the cycle "exactly backwards"? (§11.7; Ch. 3)

H. The Underwriting File (extension)

  1. † Underwriting-File extension. Lay out, in order, the three pricing steps you applied to Harbor Steel's property line in this chapter: (1) the manual rate from the class and its relativities, (2) the experience-rating effect, and (3) the net schedule modification. For each step, state in one sentence what it contributed to the indicated price and why. Then state what the chapter explicitly says pricing does not settle (and which chapters settle it). (§11.3, §11.4, §11.5, The Underwriting File)
  2. Harbor Steel's two fires are, on the property side, "thin and shock-driven." Explain why this makes them low-credibility evidence about future frequency but still material to the underwriting — i.e., what they credibly establish about severity and hazard, and how that flows into schedule rating rather than experience rating. (§11.4, §11.5, The Underwriting File; Ch. 10)
  3. The hot-work-program credit on Harbor Steel is described as "verification-contingent." Explain in your own words why the credit cannot be applied today, what would make it applicable, and how this connects to the subjectivities the decision chapter will attach. (§11.5, The Underwriting File; preview of Ch. 13)