Proportional CoversApplied

Surplus Share

Q: A 6-line surplus with a $2.5M line provides how much treaty capacity?

$15M — 6 lines × $2.5M = $15M of treaty capacity, on top of the $2.5M retained line, giving $17.5M of gross capacity.

Variable proportional cession

The cedent keeps one "line" and cedes the surplus above it — so the cession percentage moves with the size of the risk.

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

Definition

A surplus treaty lets the cedent retain a chosen amount — its line — on each risk and cede the surplus above it. Capacity is expressed in multiples of that line: a "9-line surplus" with a $2M line provides $18M of automatic capacity. Unlike quota share, the cession percentage varies risk by risk, which lets the cedent keep 100% of the small business it likes.

Homogenises the net account: whatever the sum insured, net exposure never exceeds one line.
Cedes proportionately more of the large risks, so it is more selective — and therefore more expensive in commission terms — than quota share.
Administration is heavier: every risk needs its own cession calculation and entry on the bordereau.

Cession % = (Sum insured − Retained line) ÷ Sum insured

Capped at the treaty's capacity: line × number of lines.

Worked example

With a $2M line and 9 lines of capacity, a $10M risk is retained 20% and ceded 80%; a $2M risk is retained in full; a $25M risk exceeds the $20M gross capacity and needs facultative support.

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

Scenario · figures in USD

One line, three very different cessions

Argyle Fire operates a 9-line surplus with a $2M line — $18M of treaty capacity, $20M of gross capacity in total.

Risk A — SI $2M	Retain $2M (100%) · cede nil
Risk B — SI $10M	Retain $2M (20%) · cede $8M (80%)
Risk C — SI $20M	Retain $2M (10%) · cede $18M (90%)
Risk D — SI $25M	Treaty capacity exhausted — $5M facultative needed
Maximum net loss on any single risk	$2M
Premium on Risk C at 0.15% rate	$30,000 · $3,000 retained

So whatEvery risk in the portfolio, from a $2M shop to a $20M factory, leaves the same $2M of exposure on the cedent's books. That uniformity is the entire point of a surplus treaty.

Check your understanding

A 6-line surplus with a $2.5M line provides how much treaty capacity?

$15M. 6 lines × $2.5M = $15M of treaty capacity, on top of the $2.5M retained line, giving $17.5M of gross capacity.

Compared with quota share, a surplus treaty is generally:

More selective, because the cedent keeps whole the risks it likes. The cedent chooses its line and keeps small risks entirely. That anti-selection is real, and reinsurers price for it with lower commissions than a comparable quota share.

Word problem

Vantage Fire runs a 5-line surplus with a $3M line. It writes a factory with a $15M sum insured at a premium of $150,000. A fire causes a $6M loss. Calculate the cession, the premium split and the loss split.

Show a hint

Retention percentage is the line divided by the sum insured — then apply it to everything.

Reveal the worked answer

Treaty capacity = 5 × $3M = $15M; gross capacity $18M, so the risk fits
Retained = $3M of $15M = 20%; ceded = $12M = 80%
Premium retained = 20% × $150,000 = $30,000; ceded = $120,000
Loss retained = 20% × $6M = $1.2M
Loss ceded = 80% × $6M = $4.8M

Cedent: $3M line, $30,000 premium, $1.2M of the loss. Surplus reinsurers: $12M, $120,000 premium, $4.8M of the loss. Had the same $6M loss struck a $3M risk instead, the cedent would have paid all of it — the treaty only responds where there is a surplus to cede.