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.