Facultative Versus Treaty Recoveries

Why the Coverage Scope Matters

Two reinsurance contracts can use similar recovery formulas but protect different sets of risks. A facultative placement is negotiated for a particular risk or policy. A treaty applies to a defined portfolio, subject to the treaty’s eligibility rules and terms. Correctly identifying the scope is essential: it determines whether a loss is eligible for recovery before attachment points, participation percentages, and limits are applied.

The contract wording controls. In the examples below, every covered loss amount and allocation order is specified so that the calculations illustrate the stated terms, not a universal rule about how contracts operate. This distinction is especially important where facultative coverage and treaty coverage appear in the same program.

Definition: Facultative reinsurance is coverage negotiated for an individually identified risk or policy. The reinsurer considers that risk specifically, and coverage applies only as provided by the placement. Treaty reinsurance covers a defined class or portfolio of risks according to agreed eligibility terms, usually without separate negotiation of each qualifying risk. A facultative contract or treaty may be proportional or nonproportional; “facultative” and “treaty” describe the scope of coverage, not the recovery formula.

Scope First, Recovery Formula Second

For a facultative placement, begin by identifying the particular risk, policy, or portion of a risk that the placement names. Then determine the covered loss basis, the reinsurer’s participation, and any retention, attachment, or limit. A placement may cover a proportional share of covered loss or may protect a specified excess layer.

For a treaty, first test whether the risk belongs to the defined portfolio and satisfies its eligibility conditions. If it does, apply the treaty’s recovery terms. A treaty can, for example, cede a percentage of eligible losses or cover losses above a per-risk retention. A risk-specific exclusion or limit can change the result even when the rest of the portfolio is covered.

For an excess-of-loss layer attaching at $A$ with a limit $C$ above that attachment, the covered layer amount on a qualifying loss $L$ is:

\min\bigl(\max(L-A,0),C\bigr).

If the reinsurer participates at share $p$, the recovery is $p$ times that layer amount. This assumes the loss $L$ is already measured on the contract’s stated basis, the layer has no remaining aggregate restriction, and no other contract term changes the recovery.

Identify scope.
Decide whether the contract is specific to the individual risk or applies to a qualifying portfolio. Check that the loss is within the stated coverage.

Determine the subject loss.
Use the loss amount and basis specified in the contract. Do not silently substitute gross policy loss for loss after a retention or another recovery.

Apply participation and layer terms.
For proportional coverage, apply the stated share to the eligible loss. For excess-of-loss coverage, calculate the layer amount, then apply any participation percentage.

Reconcile the allocation.
Check that recoveries do not exceed covered loss, participation, or available limits, and that ceded plus retained loss equals the subject loss being allocated.

Worked Allocations

Worked Example: A Facultative Share on One Specified Risk

A hypothetical insurer buys facultative proportional coverage on one commercial refrigeration risk. The placement names that risk and reimburses 75% of its covered loss, applied to no more than the first $800,000 of covered loss. A covered claim on the named risk is $920,000. Find the recovery and the insurer’s retained loss. Assume there are no other recoveries or adjustments.

Method. This is facultative because the placement names one particular risk. The stated $800,000 cap applies to the loss amount to which the 75% share is applied.

First identify the covered amount subject to the share:

\min(\$920{,}000,\$800{,}000)=\$800{,}000.

The reinsurer’s recovery is:

0.75(\$800{,}000)=\$600{,}000.

The insurer retains the part of the covered amount not ceded, plus the loss above the cap:

0.25(\$800{,}000)+(\$920{,}000-\$800{,}000) =\$200{,}000+\$120{,}000 =\$320{,}000.

Check: the recovery and retention sum to the claim, since $\$600{,}000+\$320{,}000=\$920{,}000$. The common mistake is to apply 75% to the entire claim, producing an incorrect recovery of $690,000; the placement caps the amount subject to the share at $800,000.

Worked Example: A Treaty Share with an Ineligible Risk

A hypothetical insurer has a treaty that automatically covers eligible household-equipment policies and cedes 35% of each eligible covered loss. The treaty excludes a separately defined class of industrial equipment. There are no per-policy limits or other recoveries. Three claims are $360,000 on eligible policy A, $540,000 on eligible policy B, and $500,000 on an excluded industrial-equipment policy C. Calculate the treaty recovery and the insurer’s net loss across all three claims.

Method. This is treaty coverage because it applies automatically to a defined class of qualifying policies. Policy C is not eligible, so its loss is not included in the treaty calculation.

For policy A, the recovery is $0.35(\$360{,}000)=\$126{,}000$, leaving $\$360{,}000-\$126{,}000=\$234{,}000$ net.

For policy B, the recovery is $0.35(\$540{,}000)=\$189{,}000$, leaving $\$540{,}000-\$189{,}000=\$351{,}000$ net.

Policy C is excluded, so its recovery is $0 and its full $500,000 loss remains with the insurer. The total treaty recovery is:

\$126{,}000+\$189{,}000+\$0=\$315{,}000.

The gross total is $\$360{,}000+\$540{,}000+\$500{,}000=\$1{,}400{,}000$. Therefore the insurer’s net loss is:

\$1{,}400{,}000-\$315{,}000=\$1{,}085{,}000.

Check: the net amounts also sum to $\$234{,}000+\$351{,}000+\$500{,}000=\$1{,}085{,}000$. The trap is to apply the 35% share to all three claims just because they belong to the same insurer. Treaty eligibility, not ownership by the insurer, determines which losses enter the calculation.

Worked Example: A Treaty Layer with Facultative Coverage for an Excluded Risk

A hypothetical insurer has a treaty covering each qualifying risk for $250,000 excess of a $100,000 per-risk retention, at 100% participation. A separate risk, C, is specifically excluded from the treaty. The insurer has a facultative placement on risk C covering 80% of the layer from $150,000 to $550,000 of covered loss; thus the maximum layer amount before participation is $400,000. The covered losses are $460,000 on treaty-eligible risk A, $170,000 on treaty-eligible risk B, and $700,000 on excluded risk C. Assume each contract applies only as stated, with no other recoveries or limits.

Method. Calculate the treaty separately for A and B. Do not apply it to C, even though C has a large loss. Then calculate the facultative recovery on C’s specifically covered layer.

For risk A, the loss above the treaty retention is $\$460{,}000-\$100{,}000=\$360{,}000$. The treaty limit is $250,000, so the treaty recovery is $\min(\$360{,}000,\$250{,}000)=\$250{,}000$. Risk A’s net loss is $\$460{,}000-\$250{,}000=\$210{,}000$.

For risk B, the loss above the retention is $\$170{,}000-\$100{,}000=\$70{,}000$. This is below the $250,000 limit, so the treaty recovery is $70,000. Risk B’s net loss is $\$170{,}000-\$70{,}000=\$100{,}000$.

Risk C is excluded from the treaty, so its treaty recovery is $0. Under the facultative placement, the loss within the specified layer is:

\min\bigl(\max(\$700{,}000-\$150{,}000,0),\$400{,}000\bigr) =\min(\$550{,}000,\$400{,}000) =\$400{,}000.

The facultative recovery is $0.80(\$400{,}000)=\$320{,}000$, leaving risk C with $\$700{,}000-\$320{,}000=\$380{,}000$ net.

Total ceded loss is $\$250{,}000+\$70{,}000+\$320{,}000=\$640{,}000$. Total gross loss is $\$460{,}000+\$170{,}000+\$700{,}000=\$1{,}330{,}000$, so total net loss is $\$1{,}330{,}000-\$640{,}000=\$690{,}000$. The net amounts check: $\$210{,}000+\$100{,}000+\$380{,}000=\$690{,}000$.

Common mistake avoided: putting C into the treaty layer because its loss exceeds the treaty retention. Attachment does not establish eligibility; C is excluded by the treaty’s scope. Its recovery comes only from the facultative placement.

Why the Layer Formula Works

The excess-of-loss expression follows from the layer’s boundaries. A loss at or below attachment $A$ produces no layer loss, which is represented by $\max(L-A,0)$. For a loss above $A$, the amount reaching the layer is $L-A$, but the layer cannot pay more than its limit $C$. Taking the minimum of those two amounts gives the covered layer amount. If the reinsurer takes only share $p$, its recovery is:

R=p\min\bigl(\max(L-A,0),C\bigr).

This formula applies only after confirming that the risk and loss qualify for the contract, and it assumes the stated layer has available capacity. It does not determine whether a risk is covered, how a contract defines its subject loss, or whether another agreement applies first. Those questions must be resolved from the stated terms before calculating $R$.

Common Traps and Practical Checks

Confusing scope with structure. A facultative placement is not necessarily excess-of-loss, and a treaty is not necessarily proportional. Identify the scope and the recovery structure separately.
Applying treaty terms to every risk in the insurer’s book. A treaty only responds to risks meeting its eligibility conditions. Apply exclusions before the recovery formula.
Ignoring participation. If a reinsurer takes 80% of a layer, the recovery is 80% of the covered layer amount, not the entire layer.
Applying a share beyond its stated cap. Check whether a limit caps the underlying amount subject to a proportional share or caps the reinsurance payment itself; those are different terms.
Failing to reconcile. For a simple allocation with no other adjustments, ceded loss plus retained loss should equal the loss being allocated.

For exam-style problems, a reliable sequence is to identify the covered risk, write the subject loss, calculate the covered amount under the stated terms, apply participation, and then reconcile the result. These distinctions and allocation techniques are aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.

Check Your Understanding

For each problem, identify the relevant coverage scope before calculating. Assume there are no other recoveries or adjustments unless stated.

A facultative placement names one risk and pays 60% of its covered loss, with no separate cap. The risk has a covered loss of $250,000. Find the recovery and retained loss. (Answer: Recovery $150,000; retained loss $100,000.)
A treaty cedes 25% of eligible covered losses. Eligible risks have losses of $120,000 and $80,000; a third risk has a $40,000 loss but is excluded. Find total recovery and total net loss. (Answer: Recovery $50,000; net loss $190,000.)
A treaty covers a qualifying risk for $150,000 excess of $50,000, at 80% participation. The qualifying loss is $260,000. Find the recovery and retained loss. (Answer: Recovery $120,000; retained loss $140,000.)
A facultative placement on a named risk covers 70% of a $300,000 layer excess of $100,000. The covered loss is $510,000. Find the recovery and retained loss. (Answer: Recovery $210,000; retained loss $300,000.)
A treaty covers eligible risks for $200,000 excess of $100,000 at 100%. Risk A is eligible and has a $360,000 loss. Risk B has a $500,000 loss but is excluded from the treaty; a facultative placement on B covers 50% of the first $300,000 above $100,000. Find the total recovery and total net loss. (Answer: Total recovery $350,000; total net loss $510,000.)

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