Why the Reinsurance Structure Matters
Reinsurance transfers some of an insurer’s risk to another insurer, the reinsurer. Two broad structures answer different questions. Proportional reinsurance shares covered premiums and losses according to a fixed fraction. Nonproportional reinsurance responds when a loss, or a group of losses, exceeds a specified threshold. Recognizing which structure applies is essential before calculating either party’s share.
The distinction is not simply that one arrangement has a percentage and the other has a dollar amount. A proportional contract links the reinsurer’s share of covered losses to the same fixed proportion across the relevant business. A nonproportional contract instead makes its recovery depend on whether losses cross a retention or aggregate threshold, and by how much. Its premium is set separately under the contract; it is not mechanically the same fraction of each covered loss.
Two Different Ways to Transfer Risk
Let \(c\) be the reinsurer’s fixed share, where \(0\leq c\leq1\). For a covered premium \(P\) and covered loss \(L\), the basic proportional allocation is \(cP\) of premium and \(cL\) of loss to the reinsurer. The primary insurer retains the balance, \((1-c)P\) and \((1-c)L\). These expressions describe the basic allocation; actual contracts may specify commissions, expenses, exclusions, or other adjustments.
For nonproportional cover, define a retention as the amount of covered loss that remains with the primary insurer before the reinsurance recovery begins. A contract may also cap the reinsurer’s payment. A per-risk or per-occurrence retention applies at the unit specified in the contract. An aggregate threshold instead applies to losses accumulated over a defined period. The contract wording determines which losses count and how the threshold is applied.
The following comparison emphasizes the central distinction. It does not replace the contract terms, which determine exactly what is covered.
| Feature | Proportional structure | Nonproportional structure |
|---|---|---|
| Loss transfer | A fixed fraction of each covered loss | Losses above a stated retention or threshold, subject to contract terms |
| Premium treatment | A corresponding fixed fraction of covered premium is ceded | Reinsurance premium is specified separately; it is not automatically a fixed share of each loss |
| What determines recovery? | The covered loss and the agreed share | The size and applicable level of loss relative to the threshold |
| Typical purpose | Share results across a defined block of business | Protect against losses exceeding a specified amount |
Proportional Allocation in a Simple Portfolio
A proportional arrangement provides a consistent allocation for each covered loss, regardless of whether the loss is small or large. A fixed fraction of a loss is transferred; there is no loss threshold that must first be crossed. This feature can make proportional structures useful for sharing the experience of a defined portfolio. The calculation below uses a hypothetical arrangement with no commission or other adjustment.
Worked Example: Allocating Premium and Claims Proportionally
A hypothetical insurer cedes 30% of a covered portfolio under a proportional agreement. During the period, covered premium is $600,000 and two covered claims are $80,000 and $120,000. Calculate the reinsurer’s and primary insurer’s premium and loss shares. Assume the agreed fraction applies to all stated amounts, with no commission or other adjustment.
Method. Apply the fixed fraction \(c=0.30\) separately to the covered premium and to each covered loss.
Premium allocation. The reinsurer receives \(0.30\times \$600{,}000=\$180{,}000\). The primary insurer retains \((1-0.30)\times \$600{,}000=0.70\times \$600{,}000=\$420{,}000\). The shares reconcile: \(\$180{,}000+\$420{,}000=\$600{,}000\).
First claim. The reinsurer pays \(0.30\times \$80{,}000=\$24{,}000\). The primary insurer pays \(0.70\times \$80{,}000=\$56{,}000\). These add to the $80,000 claim.
Second claim. The reinsurer pays \(0.30\times \$120{,}000=\$36{,}000\). The primary insurer pays \(0.70\times \$120{,}000=\$84{,}000\). These add to the $120,000 claim.
Check. Total claims are \(\$80{,}000+\$120{,}000=\$200{,}000\). The reinsurer pays \(\$24{,}000+\$36{,}000=\$60{,}000\), and the primary insurer pays \(\$56{,}000+\$84{,}000=\$140{,}000\). Their total is $200,000, and the reinsurer’s $60,000 is 30% of total claims. The common mistake avoided is applying the cession fraction to premium but not to each covered claim.
Threshold-Based Recoveries
A nonproportional recovery is driven by the amount of loss above the contract’s threshold, not by a fixed fraction of the entire loss. For a simple excess layer, let \(r\) be the retention and \(m\) be the maximum recovery. If \(L\) is the covered loss, the recovery is zero when \(L\leq r\). Above the retention, the recovery grows with the excess, until it reaches the cap \(m\). This is a basic model of a contract whose recovery cannot exceed the stated cap.
The formula follows directly from the contract conditions. If \(L\leq r\), then \(L-r\leq0\), so \(\max(L-r,0)=0\). If \(r<L<r+m\), the excess \(L-r\) is positive but below the cap, so the recovery is \(L-r\). If \(L\geq r+m\), the excess is at least \(m\), so the maximum recovery is \(m\). Thus the formula handles losses below, within, and above the covered layer without assigning a recovery to the portion below the retention.
A threshold can also apply to an accumulated total over a stated period. In a simple annual aggregate arrangement with threshold \(A\) and maximum recovery \(M\), let \(T\) be the covered losses accumulated during that period. The recovery is \(\min(\max(T-A,0),M)\). Unlike a per-risk or per-occurrence threshold, this calculation is based on the period’s total, not on each individual loss in isolation.
Worked Example: A Per-Risk Retention and Recovery Cap
A hypothetical insurer has a per-risk agreement with a $100,000 retention and a maximum recovery of $150,000 for any one covered risk. Three covered risks produce losses of $65,000, $145,000, and $280,000. Calculate the reinsurance recovery and primary insurer’s retained loss for each risk. Assume there are no other recoveries.
Method. Apply \(R=\min(\max(L-r,0),m)\) separately to each risk, with \(r=\$100{,}000\) and \(m=\$150{,}000\).
Risk 1. The loss is $65,000, below the retention. The amount above the retention is \(\max(\$65{,}000-\$100{,}000,0)=\$0\). Recovery is \(\min(\$0,\$150{,}000)=\$0\). The primary insurer retains \(\$65{,}000-\$0=\$65{,}000\).
Risk 2. The excess over the retention is \(\$145{,}000-\$100{,}000=\$45{,}000\). This is below the $150,000 cap, so recovery is \(\min(\$45{,}000,\$150{,}000)=\$45{,}000\). The primary insurer retains \(\$145{,}000-\$45{,}000=\$100{,}000\).
Risk 3. The excess is \(\$280{,}000-\$100{,}000=\$180{,}000\), which exceeds the cap. Recovery is \(\min(\$180{,}000,\$150{,}000)=\$150{,}000\). The primary insurer retains \(\$280{,}000-\$150{,}000=\$130{,}000\).
Check. The three recoveries total \(\$0+\$45{,}000+\$150{,}000=\$195{,}000\). The insurer’s retained losses total \(\$65{,}000+\$100{,}000+\$130{,}000=\$295{,}000\). Together they equal total losses of \(\$65{,}000+\$145{,}000+\$280{,}000=\$490{,}000\). The common mistake avoided is treating the cap as the total loss limit rather than as the maximum reinsurance recovery.
Worked Example: An Annual Aggregate Threshold
A hypothetical insurer buys annual aggregate protection. The reinsurer pays covered annual losses above $1,000,000, up to a maximum recovery of $300,000. Covered losses during the year are $400,000, $350,000, and $500,000. Calculate the annual recovery and the insurer’s retained total. Assume all three amounts count toward the same annual total.
Method. First aggregate the covered losses, then apply the annual threshold and recovery cap.
The covered annual total is \(\$400{,}000+\$350{,}000+\$500{,}000=\$1{,}250{,}000\). The amount above the $1,000,000 threshold is \(\max(\$1{,}250{,}000-\$1{,}000{,}000,0)=\$250{,}000\). This is less than the $300,000 maximum recovery, so the recovery is \(\min(\$250{,}000,\$300{,}000)=\$250{,}000\).
The insurer retains \(\$1{,}250{,}000-\$250{,}000=\$1{,}000{,}000\) of covered annual losses. Check: retained losses plus recovery equal \(\$1{,}000{,}000+\$250{,}000=\$1{,}250{,}000\), the original total. The common mistake avoided is applying the annual threshold separately to each loss: the agreement in this example applies to the annual aggregate.
Choosing the Correct Calculation
Before calculating a recovery, identify both the structure and the unit to which it applies. The same list of losses can produce different recoveries depending on whether the contract uses a fixed share, a per-risk retention, a per-occurrence retention, or an annual aggregate threshold. For threshold-based cover, the contract’s wording determines how losses are grouped; do not assume that separate claims, risks, or occurrences can be combined.
Look for a fixed fraction of premiums and losses, or for language that makes recovery depend on a retention or aggregate threshold.
Determine whether the contract applies to each risk, each occurrence, or a defined accumulation period.
For proportional cover, apply the fixed share. For nonproportional cover, find the covered excess over the applicable threshold and respect any recovery cap.
Check that the primary insurer’s retained loss plus the reinsurer’s recovery equals the covered gross loss, subject to any other contract adjustments.
A frequent exam trap is to see a percentage in a contract description and assume that every percentage represents a proportional share. A premium rate, a commission, and a fixed fraction of covered losses serve different purposes. Conversely, a nonproportional treaty still has a premium, but that premium is not necessarily calculated as the same percentage of each loss. Read what the percentage applies to, then identify whether recovery depends on a share or on crossing a threshold.
These distinctions are aligned with the SOA Exam FAM (Fundamentals of Actuarial Mathematics) syllabus. They also matter in practice because they determine which loss amounts are transferred, how the primary insurer’s retained exposure is calculated, and what information is needed to assess the reinsurance protection.
Check Your Understanding
For each hypothetical arrangement, identify the applicable structure and calculate the requested amounts. Unless stated otherwise, assume no commissions, exclusions, or other recoveries.
- A primary insurer cedes 20% of covered premium and losses. Covered premium is $250,000 and a covered claim is $90,000. Find the reinsurer’s premium and claim shares, and the primary insurer’s retained claim. (Answer: reinsurer premium $50,000; reinsurer claim $18,000; primary claim $72,000.)
- A per-risk agreement has a $75,000 retention and a maximum recovery of $100,000. A covered risk produces a $210,000 loss. Find the recovery and primary insurer’s retained loss. (Answer: recovery $100,000; retained loss $110,000.)
- An annual aggregate agreement has a $600,000 threshold and a $250,000 maximum recovery. The covered losses for the year are $240,000, $190,000, and $310,000. Find the annual recovery and retained total. (Answer: recovery $140,000; retained total $600,000.)
- Compare two hypothetical arrangements for a $50,000 covered loss and $12,000 covered premium. Under Arrangement A, the reinsurer has a 40% proportional share. Under Arrangement B, a nonproportional per-loss cover has a $40,000 retention and no recovery cap. Find Arrangement A’s premium and loss shares, and Arrangement B’s loss recovery. (Answer: Arrangement A reinsurer premium $4,800 and loss share $20,000; Arrangement B recovery $10,000.)
- A per-risk layer has a $100,000 retention and an $80,000 maximum recovery. Two separate covered risks have losses of $130,000 and $260,000. Calculate each recovery, the total recovery, and the primary insurer’s combined retained loss. (Answer: recoveries $30,000 and $80,000; total recovery $110,000; combined retained loss $280,000.)