Catastrophe reinsurance
A Socratic walk-through of catastrophe reinsurance — reasoned out one step at a time, not lectured.
The question we started with
THE QUESTION #Why does an insurer holding a million policies across a whole country still need to buy insurance for itself?
An insurer with a million householders has done what insurance is supposed to do: assembled a pool large enough that the average is predictable. Then it buys cover for itself, at considerable expense. If pooling works, what is left to insure? And if it does not work at that scale, what could a second insurer do that the first could not?
How pooling makes an average predictable, and why correlation puts a floor under that, is worked through under insurance pooling; take that floor as given. The fixed point of difference: pooling explains why the tail cannot be diversified away, and this is about the structure and price of what the insurer does instead.
Reasoning it through
REASONING #Start with the shape of the loss. In an ordinary year a national household book produces a scatter of unrelated fires, burst pipes and burglaries — numerous, independent, comfortably covered by premium. Now add a windstorm crossing the country. It does not visit a random four percent of the book; it visits everyone in its path at once. So the annual loss distribution is not a bell around an average but a well-behaved body with a long thin tail, and the tail is one event repeated across a million correlated policies.
The body is fundable from premium; the tail is not. So the insurer must hold something against the tail, and there are only two candidates: its own capital, or somebody else's promise.
Why not simply hold the capital? Because capital is not free. To survive a one-in-two-hundred-year event — roughly what European solvency rules require — the insurer must keep equity on the balance sheet every year against an event that by construction almost never happens, and shareholders demand a return on it whether it is used or not. Reserving with owned capital means renting money at an equity rate for a purpose idle 199 years in 200.
Reinsurance is the alternative: rent the capacity rather than own the capital. That only helps if the reinsurer holds the same buffer more cheaply, so ask why it could. Here is the only genuine efficiency in the arrangement. A Japanese earthquake, a Florida hurricane and a European windstorm are, as far as anyone can tell, causally unrelated, so a reinsurer writing all three holds one pool of capital against all of them. The same capital does duty several times over: the averaging that failed within one country's book works again across perils.
The cover is not a blanket policy but a tower of layers, each with an attachment point and a limit. Suppose an insurer retains the first 200 million of any event, then buys 200 million of cover above 200, 600 above 400, and 1,000 above 1,000. A 2,000 million storm is paid 200 by the insurer, 200 by the first layer, 600 by the second and 1,000 by the third — adding, as it must, to 2,000. Why slice it? The layers are wildly different products: the bottom is hit often and prices near its expected loss, the top almost never, and its price is dominated by something else.
That something else is the cost of capital, and a rough derivation makes the market legible. Take a remote layer whose expected annual loss is 1% of its limit. The reinsurer must post capital against the full limit, because when the layer goes it goes entirely. If investors require 8% on that capital, the premium must cover 1% of expected loss plus about 8% of capital cost — a rate on line near 9%, roughly nine times expected loss. The buyer is paying mostly for the standing readiness of capital, not for the expected claim.
Which suggests a test. If the mechanism is capital scarcity rather than changed loss expectations, a hurricane season that destroys reinsurers' capital should raise the price of European windstorm cover too, though nothing about European storms has changed. The refuting observation: if remote-layer prices moved only with revisions to their own peril's loss model and stayed flat when unrelated events consumed industry capital, the capital-cost account would be wrong. My recollection is that prices do move across perils after big capital events.
The analogy
THE ANALOGY #Think of a town's fire brigade. The station is manned all year for a fire that may not come, and the town pays for that readiness rather than for the water. One village cannot justify a station, so several share one, relying on being unlikely to burn on the same night — and when they all burn together, the shared station is exactly as overwhelmed as a village station would have been.
a brigade's cost is wages and equipment that exist whether or not there is a fire, whereas a reinsurer's readiness is capital that could be earning elsewhere, so its price rises and falls with how much capital the market happens to hold — which has no counterpart in a fire station's payroll.
Clarifying the model
THE MODEL #Two honest qualifications, on the mechanism and on the price.
On the mechanism: reinsurance does not make catastrophe risk smaller. It relocates it, and that only helps if the receiving balance sheet is genuinely diversified against the peril. If several insurers cede the same regional exposure to the same few reinsurers, the concentration reappears at the top of the chain, invisible to each buyer — and retrocession, reinsurers reinsuring each other, has historically routed exposure in circles until nobody could say who held it. Catastrophe bonds address this: they are collateralised, so the money is posted in advance, and their investors hold nothing else exposed to hurricanes, so they demand a smaller premium for the correlation than a reinsurer does. The price of that cheapness is basis risk — an index-triggered bond pays on the measured event, not on your actual claims.
On the price: not all of the multiple over expected loss is cost of capital. Reinsurance runs a pronounced cycle — after a large event capital withdraws, capacity is scarce, and rates rise far beyond any revision to the loss estimate; as capital returns they erode below what the risk warrants. The hard phase is rent extraction, plainly, and the buyer pays because solvency rules and its own board require the cover with no option to go without for a year.
A picture of it
THE PICTURE #How to readThe band on the left is one 2,000 million storm, and the widths are money, so the picture is to scale. It splits into the four slices the contracts define — the retention, then the three layers of the tower above: Layer 1 is 200 million of cover above the first 200, Layer 2 is 600 above 400, Layer 3 is 1,000 above 1,000. Follow each slice right to see who pays. Only the thinnest band comes from the insurer's own capital; the middle two are met by reinsurers pooling this peril against unrelated ones; the largest is met by capital markets through a collateralised bond. The point is the mismatch between how rarely that top layer is touched and how much it carries when it is.
What became clearer
WHAT CLEARED #An insurer buys insurance because its million policies are diversified against each other and not against the peril, so the tail of its loss distribution is one event, not a thousand. What it buys is not risk reduction but capital: the readiness of somebody else's balance sheet, rented in layers and priced overwhelmingly by the cost of holding money idle rather than by the expected claim. That is why a remote layer can cost many times its expected loss without anyone being cheated — and why the price can double after a hurricane on the other side of the world, which is not cost at all.
Where to go next
ONWARD #- How catastrophe models estimate a one-in-two-hundred-year loss when the record contains nothing like it.
Key terms
TERMS #| Term | What it means |
|---|---|
| Excess-of-loss layer | cover of a stated limit above a stated attachment point, written "limit xs attachment". |
| Basis risk | the gap between what an index-triggered contract pays and what the buyer actually lost. |
Every term the collection defines is gathered in the glossary.