Chapter 27 Exercises

Work these the way a treaty underwriter and a primary underwriter would together: always ask who keeps this dollar and who pays it when the loss comes. Keep the tower diagram (§27.4) and the gross-versus-net table (§27.5) beside you. 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 (§27.4) point back to the chapter. All figures are illustrative teaching numbers.

A. Recall and definitions

  1. † Define reinsurance in one sentence, and name the three jobs it does for a primary insurer. (§27.1)
  2. Who is the ceding company, and why does it remain liable to its own policyholder even after it has reinsured the risk? (§27.1)
  3. Distinguish treaty from facultative reinsurance in terms of scope, obligation, and timing. (§27.2)
  4. † Distinguish quota share from surplus share. For each, state the single problem it is best at solving. (§27.3)
  5. Define excess of loss (XOL) and explain what "\$4M xs \$1M" means in plain language. (§27.4)
  6. What is catastrophe XOL, and how does the event it responds to differ from the risk a per-risk XOL responds to? (§27.4)
  7. Define retrocession and ceding commission in one sentence each. (§27.7, §27.3)
  8. In one sentence each, distinguish a risk's gross position from its net position. (§27.5)

B. Proportional reinsurance — the math

  1. † A 25% quota-share treaty covers a property book. (a) On a risk with a \$2,000,000 limit, how much does the cedent retain and how much does the reinsurer take? (b) A \$600,000 loss occurs on that risk — who pays what? (c) The original premium for the risk was \$8,000; how is it split? (§27.3)
  2. A surplus-share treaty has a \$1,000,000 retention and provides 4 lines. (a) What is the total capacity (retention + treaty)? (b) For a risk with a \$4,000,000 limit, how much does the cedent retain and how much is ceded, and what is the cession percentage? (c) A \$1,000,000 loss occurs on that \$4M risk — who pays what? (§27.3)
  3. † Using the same \$1M-retention, 4-line surplus-share treaty: a risk comes in at a \$6,000,000 limit. How much can the treaty take, and what happens to the part it cannot? Name two ways the cedent can place the remainder. (§27.3)
  4. A reinsurer pays a 32% ceding commission on a quota share. The cedent cedes \$5,000,000 of premium to the reinsurer. (a) How much ceding commission does the cedent receive? (b) Explain, in one sentence, what that payment is reimbursing the cedent for. (§27.3)
  5. Explain why quota share relieves a young insurer's surplus strain but does not solve its large-line problem, while surplus share does the reverse emphasis. Use a one-line numerical illustration for each. (§27.3)

C. Non-proportional reinsurance — read the tower

  1. † A cedent's per-risk tower is: retention \$1M; layer 1 = \$4M xs \$1M; layer 2 = \$5M xs \$5M; layer 3 = \$10M xs \$10M. For each of the following single losses, state exactly who pays what: (a) \$700,000; (b) \$3,000,000; (c) \$7,500,000; (d) \$22,000,000. (§27.4)
  2. Explain reinstatement on an XOL layer, and why "running out of reinstatements" is especially dangerous on a catastrophe XOL during an active hurricane season. (§27.4)
  3. An underwriter buys only a high-attaching XOL layer (say \$10M xs \$10M) and no lower cover. Against what kind of loss year is the cedent well protected, and against what kind is it dangerously exposed? Use the frequency-versus-severity language of Chapter 6. (§27.4; Ch. 6)
  4. † Draw (in text) a three-layer reinsurance tower of your own design for a cedent with a \$2M retention and \$30M of total program. Label each layer "limit xs attachment" and show where a \$18M loss is paid. (§27.4)

D. Net vs. gross — the underwriter's lens

  1. † Your company writes a \$15,000,000 property limit. It retains \$5,000,000 net and cedes the rest via surplus share. (a) A \$15,000,000 total loss occurs — what does the company pay gross and what does it pay net? (b) If the surplus-share treaty pays a 30% ceding commission on the ceded premium, in which direction does that move the company's net expense ratio? (§27.5)
  2. Explain, in your own words, the statement: "Your capacity, your appetite, and ultimately your pen are governed by your net retention, not your gross limit." (§27.5)
  3. † A coastal warehouse account is priced at a gross rate that comfortably exceeds its gross expected loss, and the underwriter calls it "clearly profitable." Explain two reasons the account might still be unprofitable on a net basis, and state what the price must be adequate against instead. (§27.5)
  4. Reinsurance changes the combined ratio in opposite directions in a catastrophe year versus a quiet year. Explain both effects, and what a well-bought program should do to the volatility of the combined ratio across the cycle. (§27.5; Ch. 3)

E. Underwrite this submission

  1. † (Underwrite this submission.) A broker offers your company a \$25,000,000 property line on a single large risk. Your per-risk surplus-share treaty provides capacity up to \$20,000,000 (retention \$5M plus 3 lines). The account is otherwise attractive and in appetite. State (a) whether you can bind the full \$25M on the treaty alone, (b) what you must do about the \$5M excess, (c) how you would protect the company from binding the gross limit before that cover is confirmed, and (d) the one term from Chapter 13 you would attach to the quote. (§27.2, §27.5)
  2. (Underwrite this submission.) Two property submissions arrive the same morning. Risk A is a \$3M limit in an inland, low-catastrophe county. Risk B is a \$3M limit in the same named-windstorm zone where your company already has heavy coastal accumulation. Both are priced identically gross. Explain why B may be the worse net risk even at the same gross price, and what reinsurance cost makes the difference. (§27.5; preview of Ch. 29)

F. Price this risk

  1. † (Price this risk.) You are setting the net economics of a single catastrophe-exposed account. The gross premium is \$60,000. The account's allocated share of the catastrophe-treaty cost is \$14,000, and a facultative placement on the over-treaty slice costs \$9,000. Surplus-share cession costs \$10,000 of premium but returns \$3,000 of ceding commission. (a) Estimate the net premium the company keeps. (b) If the company's net expected loss on what it retains is \$22,000, comment on whether the account looks adequate on a net basis. (All figures illustrative.) (§27.5)
  2. (Price this risk.) A cedent is deciding between a 20% quota share and a 40% quota share on a book whose expected loss ratio is 60% and whose acquisition + overhead expenses run 30% of premium. The reinsurer offers a 33% ceding commission either way. Qualitatively, what happens to the cedent's retained premium, retained expected loss, and surplus strain as it moves from 20% to 40%? When would the larger cession be the right call? (§27.3)

G. Find the red flag

  1. † (Find the red flag.) A reinsurance broker pitches your company a deeply discounted catastrophe cover from a reinsurer you have not heard of, domiciled offshore, unrated, posting no collateral, at a price well below the rest of the market. Identify the red flag, name the concept from §27.6 at stake, and state what you would require before relying on the cover. (§27.6; Ch. 4)
  2. (Find the red flag.) Under a facultative-obligatory treaty, you notice over a year that the cedent's underwriters have ceded a markedly worse slice of business to the reinsurer than they kept net. Name the problem (and the Chapter 1 concept behind it), and explain why fac-oblig treaties are especially exposed to it. (§27.2; Ch. 1)
  3. (Find the red flag.) A reinsurer discovers it is buying retrocession from a chain of counterparties who, several steps removed, are reinsuring its own original cession. Name the phenomenon, the real historical episode that exemplifies it, and the underwriting discipline that prevents it. (§27.7)

H. Memo and communication

  1. (Write the memo.) Write a short internal memo (150–250 words) to your underwriting manager explaining why a \$20M catastrophe-exposed account that is "profitable gross" requires a higher price than its gross expected loss would suggest. Use the terms net retention, cat XOL, and ceding commission correctly, and end with your recommended action. (§27.4, §27.5)
  2. † (Write the explanation.) A new analyst on your team says, "If we've reinsured the risk, why do we care how strong the reinsurer is — it's their problem now." Write a three-to-four-sentence reply that corrects the misconception using privity, collectability, and credit for reinsurance. (§27.1, §27.6)

I. Ethics and judgment

  1. (Ethics dilemma.) Your company can write significantly more coastal premium next year if it relies on a cheaper, lower-rated reinsurer for its catastrophe cover. The extra premium would help you hit your growth target and bonus. The cheaper reinsurer is plausibly fine — but in a true 1-in-100 event, its ability to pay is genuinely less certain than the incumbent's. Lay out the competing considerations (growth and compensation vs. the policyholders' security and the company's solvency), and state and defend your recommendation. Which of the book's six themes are in tension here? (§27.6; Ch. 1, §1.1)
  2. (Judgment.) The chapter argues that "passing on risk is not the same as making it disappear." Construct an argument for why a primary underwriter should still decline a risk they could fully reinsure, and a counter-argument for writing it. Where do you come down, and why? (§27.7)

J. The Underwriting File

  1. † (Underwriting-File extension.) Take Harbor Steel's \$20M building limit and your company's \$5M net retention with a surplus-share treaty above it. (a) Show the gross-versus-net split of a \$20M total fire loss. (b) State whether a facultative placement is or is not needed, and on what fact that depends. (c) Name the one subjectivity (Chapter 13) you would attach if facultative cover were required. (§27.5, The Underwriting File)
  2. (Underwriting-File extension.) Harbor Steel sits in a named-windstorm zone. Explain, in your own words, why its catastrophe exposure is ceded through the cat XOL treaty rather than risk-by-risk, and why the account's net price must carry a slice of the cat-treaty cost even though the 5% named-storm wind deductible already shifts the first layer of a wind loss to the insured. (§27.4, The Underwriting File)
  3. (Underwriting-File extension; looking ahead.) The File's running disposition says the catastrophe exposure is "ceded to the cat XOL treaty; net per-risk line within retention." Name the three questions this chapter explicitly leaves to Chapters 28, 29, and 30, and say in one phrase what each will settle. (The Underwriting File)