Non-Proportional CoversCore

Excess of Loss

Q: Under a $10M xs $5M cover, a $4.2M loss produces a recovery of:

Nil — The loss never reaches the $5M attachment, so the cedent retains all of it. Excess-of-loss covers are silent below the attachment point.

Q: Which risk does an excess-of-loss treaty deliberately NOT address?

A high frequency of small attritional claims — Attritional frequency sits entirely below the attachment and is retained. If frequency is the problem, quota share or an aggregate cover is the answer.

XoL / non-proportional

The reinsurer pays only the part of a loss that exceeds an agreed amount, up to an agreed limit.

Open the interactive version → definition, quiz, structure diagram and progress tracking

Definition

Excess of loss reinsurance responds only when a loss breaches an agreed threshold. Premium bears no fixed relation to the exposure ceded — it is priced from the cedent's loss experience and exposure profile. Written as "limit excess of attachment", so "$20M xs $5M" means the reinsurer pays from $5M up to $25M.

Three families: per risk (one policy, one loss), per occurrence / catastrophe (many policies, one event), and aggregate (many losses, one year).
Protects severity, not frequency: a book of small attritional claims is entirely retained.
The cedent keeps the premium on the business but pays a separate, generally much smaller, reinsurance premium.

Recovery = min( max(UNL − Attachment, 0), Limit )

Losses below the attachment and above attachment + limit are retained in full.

Worked example

Under a $20M xs $5M per-risk cover: a $3M loss produces no recovery; a $12M loss recovers $7M; a $30M loss recovers the full $20M and leaves the cedent with $10M.

The structure diagram for this term is in the interactive version.

Scenario · figures in USD

Four losses against one layer of $20M xs $5M

Ridgeway Property buys a per-risk layer of $20M excess of $5M. Four losses hit the book during the year.

Loss 1 — $3.0M	Cedent $3.0M · reinsurer nil
Loss 2 — $8.5M	Cedent $5.0M · reinsurer $3.5M
Loss 3 — $12.0M	Cedent $5.0M · reinsurer $7.0M
Loss 4 — $30.0M	Cedent $10.0M · reinsurer $20.0M
Total gross losses	$53.5M
Total recovered	$30.5M
Total retained	$23.0M

So whatLoss 4 is the instructive one: the cedent pays $5M below the layer and $5M above it. Excess-of-loss protects a slice, not a total.

Check your understanding

Under a $10M xs $5M cover, a $4.2M loss produces a recovery of:

Nil. The loss never reaches the $5M attachment, so the cedent retains all of it. Excess-of-loss covers are silent below the attachment point.

Which risk does an excess-of-loss treaty deliberately NOT address?

A high frequency of small attritional claims. Attritional frequency sits entirely below the attachment and is retained. If frequency is the problem, quota share or an aggregate cover is the answer.

Word problem

Fairmont Casualty buys $40M xs $10M per occurrence, and pays $2.4M for it. During the year it suffers occurrence losses of $6M, $18M, $55M and $9M. Calculate total recoveries, total retention, and whether the cover paid for itself.

Show a hint

Apply the formula loss by loss, then compare recoveries with the $2.4M premium.

Reveal the worked answer

$6M → below the $10M attachment → recovery nil, cedent $6M
$18M → recovery $18M − $10M = $8M, cedent $10M
$55M → exceeds the $50M exhaustion point → recovery $40M (full limit), cedent $10M + $5M = $15M
$9M → below attachment → recovery nil, cedent $9M
Total recoveries = 0 + 8 + 40 + 0 = $48M
Total gross = $88M; total retained = $88M − $48M = $40M

Recoveries $48M against a $2.4M premium — a 20:1 return in this particular year. The cedent still retains $40M, including $15M on the single $55M occurrence. Note that two of the four losses returned nothing: an attachment point is a choice about which losses you intend to feel.