Chapter 29 Exercises

Work these with the chapter's central habit of mind: stop asking "is this risk any good?" and start asking "what is this risk doing to my book?" For every aggregate, ask what holds it together and what could make its pieces lose all at once. 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 (§29.4) point you back to the relevant part of the chapter. All dollar figures are illustrative teaching numbers.

A. Recall and definitions

  1. † Define a book of business in one sentence, and name three properties a book has that no single account has. (§29.1)
  2. Explain in your own words why diversification reduces a book's volatility but not the expected loss of any single risk in it. (§29.2)
  3. Name the four axes along which insurance books diversify, and state for each the correlation it is meant to break. (§29.2)
  4. † Define concentration risk and accumulation. How are the two related — which is the danger and which is the mechanism that builds it? (§29.3)
  5. List the four flavors of accumulation the chapter names (peril-zone, industry/class, counterparty, clash), with a one-line example of each. (§29.3)
  6. Define portfolio segmentation and name at least four dimensions along which a book can meaningfully be sliced. (§29.4)
  7. Define the retention ratio and explain why a portfolio manager reads it for quality, not just level. (§29.4)
  8. † What is the new-business penalty, and why does new business almost always run a worse loss ratio than seasoned renewal business? (§29.4)
  9. List the five questions a serious underwriting plan and budget answers, and say why an undifferentiated "grow 10%" target is dangerous. (§29.5)
  10. Distinguish a soft market from a hard market in terms of capacity, price, and terms, and state in one sentence how a disciplined portfolio manager steers through each. (§29.6)

B. Diversification and correlation

  1. † A regional carrier writes 1,200 commercial property policies, none larger than \$5M, spread across eight industries — but all within a single 60-mile coastal strip. Is this book diversified? Explain which axis is strong, which is fatally weak, and what single event undoes the apparent spread. (§29.2, §29.3)
  2. Explain why "more accounts" is not the same as "more diversification." Use the law of large numbers' word independent in your answer. (§29.2, §29.3)
  3. Two accounts cross your desk at the same price and the same quality. One is a Mountain West property; one is the tenth warehouse in a Gulf zone where your book is already heavy. Argue that they are not equally valuable to the book, and explain how a portfolio manager might reflect that difference in pricing or appetite. (§29.2)
  4. † A model tells you your two largest lines are "uncorrelated" because their historical losses have never moved together. Give two concrete scenarios in which they could lose together anyway, and explain why the model could not see it. (§29.2, the Model-vs-Judgment callout)

C. Concentration and accumulation

  1. Explain, using the chapter's image, why "a book of a thousand homes in the same flood zone is a single bet wearing a thousand costumes." What is the management instrument that prevents this? (§29.3)
  2. † Describe counterparty accumulation in three of its forms (reinsurer, large insured, broker) and explain why each is a portfolio exposure even though no individual policy looks risky. (§29.3)
  3. Connect accumulation to capital. Using Chapter 28's ideas, explain why a concentrated coastal book is expensive every year — before any storm arrives. (§29.3; Chapter 28)
  4. A colleague says, "We don't have a concentration problem — no single account is more than 2% of our premium." Explain why this reassurance can be completely wrong, and what number they should be looking at instead. (§29.3)

D. Reading the book (the price-this/segment-this skill)

  1. † A book has a blended loss ratio of 72%. Segmented, it shows: light manufacturing \$14.0M at 58%; metal fabrication \$9.0M at 71%; coastal property \$11.0M at 66% (growing 18%); habitational \$6.0M at 112% (growing 22%). (a) Which segment is the profit engine and which is bleeding? (b) Which segment is the accumulation worry, and why is its growth rate part of the problem? (c) State one management action for each of the two problem segments. (§29.4)
  2. † A segment shows a falling loss ratio and a falling retention ratio at the same time. Explain why this can be a danger sign rather than good news, and name the Chapter 1 concept at work. (§29.4; Chapter 1)
  3. A book is growing 20% in a segment where the loss ratio is also climbing. The sales team is delighted. Write two sentences explaining to them, in plain language, why fast growth plus a rising loss ratio is a warning, not a triumph. (§29.4, §29.6)
  4. "Read three numbers together, never one alone." Take a single segment and invent a small set of figures in which loss ratio looks fine but the combination of retention and new-business share reveals a deteriorating book. Show your numbers and your reasoning. (§29.4)

E. The plan, the cycle, and steering

  1. † A soft market arrives: a competitor cuts rates 15% and your retention starts to slide. Your manager wants to "hold our growth number." Lay out the case for disciplined shrinkage instead — what happens to the book if you follow the market down, and on what timeline does the cost appear? (§29.6; Chapters 3, 11)
  2. Explain why a portfolio manager cannot steer the cycle using the loss ratio alone. Name four leading indicators that move before the loss ratio, and say what each warns of. (§29.4, §29.6)
  3. The chapter calls the cycle's lag its "cruelest feature." Explain the lag and why it causes even experienced managers to grow exactly the wrong business at exactly the wrong time. (§29.6)
  4. † Your underwriting plan reads "grow the book 10%." Rewrite it as a segmented plan for a book with a profitable manufacturing core, an accumulating coastal segment, and a bleeding habitational segment — specifying direction (grow/hold/shrink) and one reason for each segment. (§29.5)

F. Find the red flag

  1. A unit reports a banner quarter: premium up 25%, a quote-to-bind win rate that has doubled, retention at an all-time high, and an early loss ratio right on plan. Identify the red flags hiding inside this "good news," and explain what is most likely actually happening to the book. (§29.4, §29.6)
  2. † A renewal book has held its premium flat for three years in a softening market while every competitor cut price. Retention is high. The manager is proud of the stability. What is the worst-case interpretation of "high retention in a soft market," and what one cut of the data would confirm or refute it? (§29.4)

G. Memo and judgment

  1. † Write a short internal memo (150–250 words) from a portfolio manager to a line underwriter explaining why a sound, adequately-priced coastal account is being declined for portfolio reasons, and how to communicate the decline to the broker without damaging the relationship. (§29.7; Chapter 39)
  2. Write the portfolio-appetite paragraph for a coastal-exposed, mid-market commercial book: state what the book wants more of, less of, and where it is full, in the form a referral grid could enforce. (§29.7)
  3. Draft three portfolio referral triggers (distinct from authority triggers) that would route an account to a manager before binding, and for each, name the book-level danger it guards against. (§29.7)

H. Ethics

  1. The chapter argues that portfolio discipline is "a fiduciary obligation, not just a profit discipline." Explain how over-concentrating a coastal book can fail the very policyholders it concentrates — and tie your answer to the book's social-function theme. (§29.7)
  2. † A profitable, fast-growing segment turns out to be growing because your price is the cheapest in the market — you are winning the business everyone else priced higher for a reason. Is it ethical to keep writing it at that price to make your growth plan? Argue both sides, then state what a disciplined manager does and why. (§29.4, §29.6)

I. The Underwriting File extension

  1. † Harbor Steel has cleared every per-risk gate — graded and controllable (Chapter 9), priced (Chapter 11), termed (Chapter 12), modified to a quote-with-conditions (Chapter 13), its catastrophe exposure ceded to the cat XOL treaty (Chapter 27), and capital-adequate (Chapter 28). Apply the portfolio gate: list the three concentrations a manager must check (coastal-zone, industry-class, broker), and for each, state the question that decides whether Harbor Steel "earns its place" in the book. (§29.7)
  2. The Harbor Steel portfolio disposition is "fits appetite if the coastal zone has aggregate room." Explain why this chapter cannot settle whether the zone in fact has room, which chapter does, and why that ordering is correct. (§29.7; Chapter 30)
  3. Suppose the Port Hadley zone is already at 95% of its aggregate cap. Walk through what a portfolio manager could do to write Harbor Steel anyway without breaching the cap — naming at least two levers (terms, reinsurance, shedding other zone business) and the trade-off each carries. (§29.7; Chapters 12, 27)