Actuarial Notes

Earthquake Exposure Risk Margin

Study guide: Exam 6C

The Earthquake Exposure Risk Margin is the MCT requirement that an insurer hold financial resources sufficient to meet its earthquake exposure at a prescribed return period — under OSFI's guidance, the 1-in-500 year PML. Earthquake is treated separately from other catastrophe perils because Canada's exposure is concentrated, severe, and capable of failing multiple insurers at once.

\text{Requirement} = \text{PML}_{1/500} - \text{Reinsurance} - \text{Other resources}

  • Why earthquake is singled out. Canadian earthquake exposure concentrates in two zones — coastal British Columbia and the Quebec City–Montreal–Ottawa corridor — so a single event would strike a large share of the industry simultaneously. It is the archetypal Concentration Risk and the scenario most likely to exhaust PACICC's capacity.
  • What counts as financial resources: capital and surplus, reinsurance (with registration and collateral rules applying), any earthquake reserve or premium reserve accumulated, and capital markets instruments such as catastrophe bonds where they genuinely respond.
  • PML data quality is explicitly a supervisory matter. OSFI expects documented exposure data, model validation, an understanding of model limitations, and a stated basis for the selected PML — see Model Risk. An insurer that cannot demonstrate the quality of its exposure data cannot demonstrate its PML.
  • The earthquake exposure requirement is separate from the ordinary insurance risk margin, because ordinary factors applied to liabilities capture the expected cost of business as usual, not a tail event that has not occurred.
  • Take-up is a policy problem beside the capital one. Earthquake insurance penetration in high-hazard Canadian regions is low, so a major event would produce large uninsured losses and heavy pressure for government assistance — the same coverage-gap structure as Flood Insurance.
  • Reinstatement and the second event. A programme adequate for one event may be exhausted for the aftershock; OSFI expects insurers to consider it, and FCT scenarios frequently test a second event.

Meeting the Requirement An insurer's 1-in-500 earthquake PML is \$520 million. Its reinsurance programme covers \$40 million to \$420 million with one reinstatement. It holds an earthquake reserve of \$25 million and capital available of \$310 million.

Does it meet the requirement, and what would improve the position?

Answer Net retained exposure at the 1-in-500 level:

\begin{align*}
\text{Retention} &= \$40\text{M} \\
\text{Above the programme} &= \$520\text{M} - \$420\text{M} = \$100\text{M} \\[4pt]
\text{Net} &= \$140\text{M}
\end{align*}

Resources available: the \$25 million earthquake reserve plus capital. The retained \$140 million is covered by \$310 million of capital available, so the requirement is met in the narrow sense.

But look at what it leaves. After the event, capital available falls to roughly \$310 - \$140 + \$25 = \$195 million before tax effects. If the base solvency buffer is \$185 million, the MCT ratio falls from 168\% to about 105\% — barely above the minimum, and in the aftermath of a catastrophe that has also damaged the insurer's operations and its market.

What would improve it, in order of effectiveness:

  1. Extend the programme above \$420 million. The \$100 million of unprotected exposure above the top of the tower is the single largest item, and top-layer capacity is the cheapest part of a catastrophe programme per dollar of limit.
  2. Reduce the exposure. Underwriting action in the highest-hazard postal codes, or higher earthquake deductibles, lowers the PML itself — the only remedy that does not depend on someone else paying.
  3. Verify the reinstatement. One reinstatement covers a second event, but the reinstatement premium is payable at the worst possible moment and should be in the cash flow scenario.
  4. Raise the internal target so that the post-event ratio lands above the supervisory target rather than above the minimum.

And test the PML itself. A \$520 million figure from one model with imperfect exposure data could plausibly be \$650 million, at which point the retained loss is \$270 million and the insurer does not survive in any meaningful sense. That sensitivity, not the point estimate, is what the board needs to see.