The reinsurer the state stands behind

The French natural catastrophe regime would not hold without a third tier few practitioners can describe, and which explains why insurers accept a compulsory cover they cannot rate. That tier is a public reinsurance, carried by a fund whose commitments the state guarantees. It is not compulsory, it is offered, and most of the market uses it, which is enough to make it the keystone of the scheme.

The first mechanism is a proportional cession. The insurer cedes a share of its natural catastrophe premiums and, in the same proportion, a share of its losses. This quota share does what all proportional treaties do: it reduces net burden and volatility in the same measure, without deforming the distribution. It does not protect against the extreme event, it shares everything in the same proportions, and that is why it is not enough.

The second mechanism is the one that counts in rare years: an annual excess of loss protection, a stop-loss, which takes over when the year's net burden exceeds a threshold defined as a percentage of retained premiums. It is this second tier that makes the regime bearable for medium-sized insurers, because it turns a burden with no known bound into a burden bounded for the year. Without it, a regional company could not carry a compulsory cover whose exposure is concentrated on its own territory.

The third element is the state guarantee, and one must be precise about what it does. It decides nothing about a loss: neither the order, nor the criterion, nor the deductible, which belong to other mechanisms already studied. Nor does it set the surcharge. What it does is narrower and more fundamental: it removes, at the extreme of the distribution, the risk that the reinsurer itself defaults. A private reinsurer, however large, has a limit; a reinsurer backed by the state guarantee has none, and that is the only difference, but it bears exactly on the part of the distribution where other solutions stop responding.

From this follows a reading rule that holds for all the technical work of a French insurer on these perils: gross and net tell two different stories, and confusing them leads to two opposite errors. Reasoning on gross alone overstates the volatility actually carried, and leads to declining business the structure would absorb. Reasoning on net alone removes from view the portfolio's real exposure, and lets a concentration grow whose size nobody measures any more, until the day the structure changes.

The temptation this architecture creates must be named explicitly, because it is comfortable and it argues well. Since a public mechanism guarantees the extreme, why measure finely an exposure whose tail is taken. The answer comes in three points. The terms of the cession and the threshold of the protection are not carved in stone: they change, and a house that has never measured its gross will not be able to say what a change costs it. The part under the threshold, that of medium and repeated events, remains entirely with the insurer, and that is where most financial years are decided. Finally, an exposure one does not measure cannot be steered, and steering is what separates an insured house from a covered one.

In practice, the useful skill is not reciting mechanisms but being able to say, in front of a figure, on which side of the structure it sits. Is a modeled loss presented to a committee gross or net of the proportional cession. Is the annual protection taken into account or not. Is the threshold expressed as an amount or as a percentage of retained premiums, in which case it moves with the portfolio without anyone having decided it. Three questions, and a table that does not allow them to be answered is not a steering table.