Chapter 28 Quiz

Twenty questions — fifteen multiple choice and five short answer — covering surplus, leverage, RBC, Solvency II, ERM and the ORSA, the cost of capital, and rating-agency models. Answers are in the collapsed block at the bottom. All dollar figures are illustrative.

Multiple choice

1. Policyholder surplus is best defined as: - A) the total premium an insurer collects in a year - B) the money set aside for claims that have happened but are not yet paid - C) an insurer's assets minus its liabilities — the cushion that absorbs worse-than-expected losses - D) the portion of premium an insurer has not yet earned

2. Loss reserves pay for __; policyholder surplus pays for ____. - A) expected losses; losses worse than expected - B) losses worse than expected; expected losses - C) expenses; losses - D) reinsurance premiums; investment losses

3. A carrier holds \$500M of surplus and writes \$1,000M of net written premium. Its premium-to-surplus ratio is: - A) 0.5 to 1 - B) 1 to 1 - C) 2 to 1 - D) 5 to 1

4. The premium-to-surplus ratio's chief weakness as a risk measure is that it: - A) is too slow to calculate - B) counts premium volume rather than the riskiness of the business - C) ignores investment income - D) cannot be computed for mutual insurers

5. The RBC formula combines its risk charges using a covariance ("square-root") adjustment rather than a simple sum because: - A) regulators want the number to look smaller - B) the risks are assumed to be largely independent, so they are unlikely to all go wrong at once - C) addition is mathematically impossible for capital charges - D) it makes catastrophe risk easier to ignore

6. An RBC ratio is calculated as: - A) total adjusted capital ÷ the Authorized Control Level requirement - B) net premium ÷ surplus - C) losses ÷ premium - D) surplus ÷ total assets

7. A carrier reports an RBC ratio of 180%. This means it is: - A) in the "no action" zone with a comfortable margin - B) in the Company Action Level zone and must file a plan to restore capital - C) in Mandatory Control and must be seized - D) insolvent

8. Which RBC risk charge most directly embodies Chapter 27's warning that reinsurance only helps if the reinsurer can pay? - A) asset risk - B) reserve risk - C) credit risk (including reinsurance recoverables) - D) premium risk

9. Solvency II's Solvency Capital Requirement (SCR) is calibrated to allow an insurer to survive, roughly: - A) any conceivable loss with certainty - B) a 1-in-200-year loss over a one-year horizon (99.5% confidence) - C) a 1-in-10-year loss - D) the average loss year

10. Which is a true difference between U.S. RBC and Solvency II? - A) RBC permits approved internal models for the requirement; Solvency II does not - B) Solvency II is a factor formula; RBC is market-consistent - C) Solvency II uses market-consistent valuation and permits approved internal models; RBC is a factor-based formula on statutory values - D) they are identical in approach

11. Enterprise risk management (ERM) is best described as: - A) a single department that handles insurance claims - B) managing each risk type separately in its own silo - C) identifying, aggregating, and managing all of an organization's material risks together as one portfolio, governed at the top - D) the same thing as buying reinsurance

12. The ORSA is: - A) a regulator's formula applied to the insurer - B) the insurer's own forward-looking assessment of all its material risks and whether its capital is and will remain adequate, filed with its regulator - C) a rating agency's published score - D) a type of reinsurance treaty

13. Two accounts each run a 95% combined ratio, but the coastal account ties up three times the capital of the inland account. On a cost-of-capital basis: - A) they create identical value - B) the coastal account creates more value because it earns more premium - C) the inland account can create value while the coastal account destroys it - D) neither account can ever create value

14. For most carriers, the capital constraint that actually governs how much catastrophe business an underwriter can write is usually: - A) the RBC Mandatory Control Level - B) the rating-agency capital model - C) the premium-to-surplus ratio alone - D) the unearned premium reserve

15. "Economic profit" on an account is best expressed as: - A) premium minus losses - B) the combined ratio - C) underwriting profit minus the cost of the capital the risk consumes - D) investment income minus expenses

Short answer

16. Explain why an insurer that runs a combined ratio above 100% year after year is doing more than losing money — what specific resource is it burning, and why does that threaten its ability to write future business? (§28.1)

17. State the five RBC action levels in order and explain why the design makes intervention escalate before a company actually fails rather than after. (§28.3)

18. Chapter 1 said the law of large numbers depends on losses being independent. Explain how that same independence assumption appears inside the RBC covariance adjustment, and describe one scenario in which relying on it causes RBC to understate the capital truly needed. (§28.3; Ch. 1)

19. Using the cost of capital, explain why a catastrophe-exposed account must be priced to a lower combined ratio than an economically equivalent inland account in order to create the same value for the company. (§28.6)

20. Your CUO says the company "can't write more of this coastal book," yet the company's RBC ratio is a healthy 250%. Reconcile these: which capital authority is the CUO most likely protecting, and why does it bind tighter than the regulator's number? (§28.7)

Answer key (click to expand) **1.** C — Surplus is assets minus liabilities, the cushion for worse-than-expected losses. (§28.1) **2.** A — Reserves cover *expected* losses on business written; surplus covers losses *worse* than expected. (§28.1) **3.** C — \$1,000M ÷ \$500M = 2 to 1. (§28.2) **4.** B — It measures premium volume, not the riskiness (e.g., catastrophe concentration) of the book. (§28.2) **5.** B — The risks are assumed largely independent, so the formula does not require capital for them all to fail simultaneously. (§28.3) **6.** A — Total adjusted capital divided by the Authorized Control Level requirement. (§28.3) **7.** B — 150%–200% is the Company Action Level zone; the insurer must file a plan to restore capital. Note that "180%" is above the seizure level but still in an action zone. (§28.3) **8.** C — Credit risk, which explicitly includes reinsurance recoverables. (§28.3; Ch. 27) **9.** B — A 1-in-200-year loss over one year, i.e., 99.5% confidence. (§28.4) **10.** C — Solvency II is market-consistent and permits approved internal models; RBC is a factor-based formula on statutory book values. (§28.4) **11.** C — Aggregating and managing *all* material risks together as a single portfolio at the top of the firm. (§28.5) **12.** B — The insurer's *own* forward-looking risk-and-solvency assessment, filed with the regulator. (§28.5) **13.** C — The capital-light inland account can earn its capital cost; the capital-heavy coastal account at the same combined ratio may not, destroying value. (§28.6) **14.** B — The rating-agency capital model, which typically demands more capital than the RBC floor and governs the carrier's effective capacity. (§28.7) **15.** C — Underwriting profit minus the cost of the capital the risk ties up. (§28.6) **16.** Underwriting losses consume **policyholder surplus** — the capital that backs every promise. Because surplus is the raw material that lets a carrier write business (the premium-to-surplus and rating-agency constraints are both expressed against it), burning surplus shrinks the company's *capacity* to write future business. "Make it up on volume" is self-defeating: more volume requires more surplus, and the losses are destroying it. (§28.1) **17.** Order: ≥200% no action; 150–200% Company Action Level (file a plan); 100–150% Regulatory Action Level (examination and corrective orders); 70–100% Authorized Control Level (regulator *may* seize); <70% Mandatory Control Level (regulator *must* seize). The thresholds are set above zero capital so the regulator gains authority while the company is *weakening but not yet failed* — there is still something left to protect for policyholders. (§28.3) **18.** RBC combines its risk charges as a square root of the sum of squares, which mathematically *assumes* the charges (asset, credit, reserve, premium) are largely uncorrelated — the same independence assumption that lets the law of large numbers stabilize a pool. When risks become correlated — e.g., a financial crisis that simultaneously depresses asset values *and* impairs reinsurers' ability to pay (2008), or a single hurricane that the formula treats as one independent risk but that hits a whole coastal book — the true required capital exceeds what the adjusted formula reports, so RBC understates the danger. (§28.3; Ch. 1) **19.** Capital has a cost. A catastrophe-exposed account ties up far more surplus than an inland one, so its capital cost per premium dollar is higher. Economic profit = underwriting profit − capital cost; to reach the same economic profit as an inland account, the coastal account needs a larger *underwriting* profit to offset its larger capital cost — i.e., a lower combined ratio (a richer margin / a higher price). Pricing it to the same combined ratio as the inland account leaves it destroying value. (§28.6) **20.** The CUO is almost certainly protecting the **rating-agency capital model**, not the regulatory RBC floor (250% is well clear of any action level). The rating agency demands more capital than the regulator to support the company's *rating*, and writing more cat-exposed business would force the company to hold still more capital to keep that rating — or risk a downgrade, which shrinks the flow of business that replenishes capital (a slow death spiral). The market, not the law, makes the rating a gating credential, so the rating-agency constraint binds tightest. (§28.7)