Economics & ClaimsApplied

Reinstatement

Q: A layer of $30M xs $20M has two reinstatements. What is its aggregate exposure?

$90M — The original limit plus two reinstatements gives three full limits: 3 × $30M = $90M in the aggregate.

Q: "Pro rata as to amount and time" means the reinstatement premium is scaled by:

The limit used and the unexpired portion of the period — Both factors apply. A loss in month eleven restores cover for only one remaining month, so the cedent pays roughly one-twelfth of the amount-based figure.

Restoring the limit

Putting the cover back after a loss has eaten into it — and paying for the privilege.

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

Definition

A reinstatement restores an excess-of-loss layer's limit after it has been reduced by a loss. The contract states how many reinstatements are available and at what cost. "One reinstatement at 100%" means the limit can be restored once, for an additional premium equal to the original — so the layer's aggregate exposure is twice its limit.

Pro rata as to amount: you pay only for the portion of limit actually restored.
Pro rata as to time: you also pay only for the unexpired part of the year. Many cat covers are "pro rata as to amount only" — time is not discounted.
Reinstatement premium is normally deducted from the loss payment, so it never becomes a separate cash call at the worst possible moment.

Reinstatement premium = Layer premium × (Recovery ÷ Limit) × Reinstatement %

Multiply by the unexpired fraction of the year if the cover is also pro rata as to time.

Worked example

A $20M xs $10M layer costs $4M with one reinstatement at 100%, pro rata as to amount. A $12M recovery uses 60% of the limit and triggers $2.4M of reinstatement premium.

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

Scenario · figures in USD

Two losses, one reinstatement

Layer: $20M xs $10M. Annual premium $4M. One reinstatement at 100%, pro rata as to amount only. Two separate occurrences hit during the year: $22M and $18M.

Occurrence 1 — $22M	Cedent $10M · recovery $12M
Reinstatement premium: $4M × 12/20	$2.40M
Occurrence 2 — $18M	Cedent $10M · recovery $8M
Reinstatement premium: $4M × 8/20	$1.60M
Total recoveries	$20M
Total premium paid ($4M + $4M)	$8M
Aggregate limit under the layer	$40M
Limit still available	$20M

So whatThe two reinstatement premiums add up to exactly one full annual premium — because exactly one full limit was reinstated. Net of reinstatement cost the cedent recovered $12M for an $8M spend.

Check your understanding

A layer of $30M xs $20M has two reinstatements. What is its aggregate exposure?

$90M. The original limit plus two reinstatements gives three full limits: 3 × $30M = $90M in the aggregate.

"Pro rata as to amount and time" means the reinstatement premium is scaled by:

The limit used and the unexpired portion of the period. Both factors apply. A loss in month eleven restores cover for only one remaining month, so the cedent pays roughly one-twelfth of the amount-based figure.

Word problem

A cat layer of $50M xs $25M costs $6M and carries one reinstatement at 100%, pro rata as to amount and time. A hurricane on 1 October (with three months of the year left) causes a $60M loss. Calculate the recovery, the reinstatement premium and the remaining limit.

Show a hint

Recovery first, then the amount fraction, then the time fraction of 3/12.

Reveal the worked answer

Recovery = $60M − $25M = $35M (within the $50M limit)
Proportion of limit used = $35M ÷ $50M = 70%
Unexpired period = 3 months ÷ 12 = 25%
Reinstatement premium = $6M × 70% × 25% × 100% = $1.05M
Net cash to the cedent = $35M − $1.05M = $33.95M
Limit reinstated to $50M, with the reinstatement now used up

Recovery $35M, reinstatement premium $1.05M, net $33.95M, and the full $50M limit is back in force for the last quarter. Had the wording been "amount only", the reinstatement premium would have been $4.2M — four times as much for identical cover. Read the time clause before you buy.

Related terms

Part of the Treaty Reinsurance guide, where this term is explained alongside every other treaty metric.