Excess of Loss Reinsurance

Excess of loss reinsurance (often shortened to XoL) is non-proportional reinsurance in which the reinsurer pays the part of a loss that exceeds an amount retained by the ceding insurer, up to an agreed limit. A layer described as "$40 million excess of $10 million" means the insurer keeps the first $10 million of each qualifying loss and the reinsurer pays up to $40 million above that, so the cover is exhausted at $50 million.

Unlike quota share reinsurance, premiums are not shared in proportion to the underlying policies; the reinsurer charges a price for the layer based on how likely and how large the losses reaching it are expected to be. Excess of loss is usually written as treaty reinsurance but can also cover a single risk as excess facultative reinsurance. It is the main tool insurers use against large individual claims and natural catastrophes.

Think of a family that agrees with a wealthy relative: the family pays every household repair bill up to $1,000 itself, and the relative pays anything above $1,000 on a single bill, up to $5,000. In return, the family pays the relative a fixed amount every year, whether or not any big bill turns up.

Small leaks and broken handles never trouble the relative. Only the rare burst boiler or collapsed ceiling does. The family gets peace of mind about the expensive surprises, and the relative earns a steady fee for standing behind them. That is the core of excess of loss: the insurer handles the everyday claims and pays a reinsurer to step in only when a claim, or a disaster, is unusually large.

• Per-risk excess of loss. Responds to a large loss on any one insured risk, such as a fire destroying a single factory.
• Catastrophe excess of loss. Responds to the total of many losses caused by one event, such as a hurricane or earthquake. An hours clause defines the event, for example all windstorm losses within 72 consecutive hours.
• Per-occurrence casualty and clash covers. Protect liability writers when one incident triggers claims under several policies at once.
• Aggregate excess of loss. Responds when the total of losses over a period exceeds a threshold; when that threshold is set as a loss ratio, the cover is called stop-loss reinsurance.

Mutual marine liability insurers offer a well-known example: the clubs providing P&I insurance pool large claims among themselves and buy a shared excess of loss programme above that pool.

Insurers buy excess of loss cover in stacked layers that together form a tower. A catastrophe programme might run $50 million excess of $25 million, then $100 million excess of $75 million, then $150 million excess of $175 million, each layer placed with a different panel of reinsurers. Lower layers are hit more often and cost more per dollar of cover; upper layers are rarely touched and cost less.

Once a layer pays out, its limit is used up for the year unless the contract allows reinstatements. A reinstatement restores the limit, usually for an extra premium calculated in proportion to the amount of cover used, so the insurer stays protected against a second event.

For a single loss $L$, retention $R$ and limit $M$, the reinsurer's payment is:

The price of a layer is often quoted as a rate on line:

• $L$ is the insurer's gross loss from the risk or event.
• $R$ is the retention, the amount the insurer keeps.
• $M$ is the limit of the layer.

Take a layer of $40 million excess of $10 million. A $30 million loss produces a recovery of $20 million; a $70 million loss produces the full $40 million, leaving the insurer with $30 million. If the layer costs $6 million, the rate on line is 6 ÷ 40, or 15%, which means the premium equals the cover in roughly 6.7 years without losses (the payback period, 1 ÷ 0.15).

Reinsurers price lower layers mainly from experience, adjusting past losses for inflation and growth (the burning cost method). Higher catastrophe layers depend on catastrophe models, because the losses that reach them are rare and have fat tails that historical data understate. Insurers often compare a programme's protection with internal measures similar to value at risk, such as the size of loss expected once in 100 or 250 years.

Since the 1990s, part of the catastrophe excess of loss market has moved into insurance-linked securities. In a catastrophe bond, a special purpose vehicle issues notes to investors and holds the proceeds in collateral; if a defined disaster occurs, the investors lose principal and the money pays the sponsor's claims. This is a form of securitization of insurance risk. Industry loss warranties and parametric covers, which pay on a measured index such as wind speed, work in a similar way to a weather derivative.

These instruments attract investors because natural catastrophe losses are largely unrelated to equity and bond markets, which adds diversification to their portfolios. For the insurer, a fully collateralised cover reduces counterparty risk compared with relying on a rated reinsurer's promise. Supervisors recognise excess of loss protection in regulatory capital calculations, particularly for catastrophe risk, and expect insurers to show that their underwriting appetite and reinsurance purchases are consistent with board-approved risk limits.

• National Association of Insurance Commissioners (NAIC)
• International Association of Insurance Supervisors (IAIS)