Why Ceding Commissions Matter
A quota share treaty transfers an agreed proportion of covered premiums and losses from a cedent to a reinsurer. The cedent may also receive a ceding commission from the reinsurer. This commission reduces the premium cash ultimately remitted to the reinsurer, but it does not change the agreed share of losses transferred.
The calculation is straightforward once the contractual base is clear: determine the premium subject to the treaty, apply the quota share percentage, and then apply the commission rate to the ceded premium. The treaty wording matters because it specifies whether the commission is based on written premium, earned premium, or another defined amount. The examples below use fixed commission rates and state the settlement basis explicitly.
These equations assume a fixed quota share percentage and a fixed commission rate, with no additional adjustments or settlement items. If a treaty defines a limit, cap, sliding-scale commission, or different premium base, the contract terms must be reflected before applying the calculation. The examples here use the stated effective quota share share and commission terms only.
Premium and Loss Flows Are Separate
The commission changes the premium settlement. It is not an additional loss recovery and does not alter the quota share percentage applied to claims. If the cedent transfers a proportion \(q\) of covered losses, it continues to retain proportion \(1-q\), whether or not it receives a commission.
| Item | Calculation | Meaning |
|---|---|---|
| Ceded premium | \(qP\) | Premium allocated to the reinsurer before commission |
| Ceding commission | \(cqP\) | Amount allowed back to the cedent |
| Net premium remittance | \(qP-cqP=(1-c)qP\) | Premium cash paid by the cedent to the reinsurer |
| Premium remaining with cedent | \(P-(1-c)qP\) | Gross premium less the net remittance |
| Ceded loss | \(qL\) | Reinsurer’s share of covered loss \(L\) |
| Retained loss | \((1-q)L\) | Cedent’s share of covered loss \(L\) |
The premium remaining with the cedent has an equivalent decomposition:
The cedent therefore keeps its unceded share of premium, \((1-q)P\), plus the commission, \(cqP\). This identity is a useful reconciliation check. It also makes clear that a commission can cause the cedent to retain more premium than its simple unceded share, without increasing the cedent’s share of losses.
Deriving the Net Remittance Formula
The commission is defined as a percentage of ceded premium, not automatically as a percentage of all gross premium. First the treaty allocates \(qP\) of the premium to the reinsurer. The reinsurer then allows the cedent \(c\) of that amount back as commission. Subtracting the allowance from the ceded premium gives the cash remittance:
The quota share allocates \(qP\) to the reinsurer before commission.
The commission is \(c(qP)=cqP\), because its base is ceded premium.
The cedent remits \(qP-cqP=qP(1-c)\) to the reinsurer.
This derivation requires the stated assumption that the commission rate applies to ceded premium on the same settlement basis as \(P\). If the contract instead defines a different commission base, the second step must use that base. The formula also does not discount cash flows; if settlement timing and interest are material, the payments must be valued at a common date using the applicable interest assumptions.
Worked Example: Fixed Commission on Written Premium
A hypothetical property insurer enters a quota share treaty with a 40% quota share and a 25% ceding commission on ceded written premium. It writes $1,200,000 of eligible premium during the year. Covered losses are $700,000. Calculate the commission, the cedent’s net remittance, the premium remaining with the cedent, and each party’s loss share.
Assumptions and method. The commission base is written premium; the quota share and commission rates are fixed. All amounts are deterministic contractual totals. There is no mortality model or stochastic loss distribution, and no interest or discounting is applied. Apply the quota share first, then the commission to ceded premium.
Step 1: Ceded premium. With \(P=\$1{,}200{,}000\) and \(q=0.40\), ceded premium is \(0.40\times \$1{,}200{,}000=\$480{,}000\).
Step 2: Commission. The commission rate applies to the $480,000 ceded premium, so commission is \(0.25\times \$480{,}000=\$120{,}000\).
Step 3: Net remittance. The cedent pays the reinsurer \(\$480{,}000-\$120{,}000=\$360{,}000\).
Step 4: Premium remaining with the cedent. The cedent retains \(\$1{,}200{,}000-\$360{,}000=\$840{,}000\). The reconciliation is \((1-0.40)\times \$1{,}200{,}000+\$120{,}000=\$720{,}000+\$120{,}000=\$840{,}000\).
Step 5: Loss allocation. The reinsurer’s loss share is \(0.40\times \$700{,}000=\$280{,}000\). The cedent’s retained loss is \(0.60\times \$700{,}000=\$420{,}000\). These sum to $700,000, as required.
Check and common mistake. The cedent’s premium balance, $840,000, equals its 60% unceded premium share plus the commission. A common error is to calculate the commission as 25% of all $1,200,000, producing $300,000. That uses the wrong base: the contract applies 25% to the $480,000 ceded premium, so the correct commission is $120,000.
Premium Settlement and Underwriting Results
A net remittance can also be used to calculate a simplified underwriting balance for the reinsurance transaction. Before expenses and other contract provisions, the reinsurer’s premium less its ceded claims is \((1-c)qP-qL\). The cedent’s premium remaining after remittance less its retained claims is \(P-(1-c)qP-(1-q)L\). These are not complete measures of profitability: they omit expenses, timing differences, reserve changes, taxes, and any other treaty terms.
Worked Example: Reconciling Both Parties’ Premium and Loss Shares
A hypothetical commercial insurer has $860,000 of eligible premium and $510,000 of covered losses under a 35% quota share treaty. The treaty pays a 30% commission on ceded earned premium. Assume the $860,000 is already the earned-premium amount for the settlement period. Calculate the net premium remittance, the loss shares, and each party’s simplified underwriting balance before expenses.
Assumptions and method. The fixed commission applies to the stated earned premium ceded under the treaty. The premium and loss totals are deterministic; no mortality model or stochastic distribution is assumed. There is no interest or discounting. Calculate ceded premium and commission first, then allocate losses using the quota share alone.
Step 1: Ceded earned premium. \(0.35\times \$860{,}000=\$301{,}000\).
Step 2: Commission and remittance. The commission is \(0.30\times \$301{,}000=\$90{,}300\). Thus the net remittance is \(\$301{,}000-\$90{,}300=\$210{,}700\).
Step 3: Premium remaining with the cedent. The cedent retains \(\$860{,}000-\$210{,}700=\$649{,}300\). Equivalently, the unceded premium is \(0.65\times \$860{,}000=\$559{,}000\), and \(\$559{,}000+\$90{,}300=\$649{,}300\).
Step 4: Loss allocation. Ceded losses are \(0.35\times \$510{,}000=\$178{,}500\). Retained losses are \(0.65\times \$510{,}000=\$331{,}500\). Together these equal $510,000.
Step 5: Simplified balances. The reinsurer’s balance before expenses is \(\$210{,}700-\$178{,}500=\$32{,}200\). The cedent’s balance before expenses is \(\$649{,}300-\$331{,}500=\$317{,}800\). Their sum is $350,000, which equals gross premium less gross losses: \(\$860{,}000-\$510{,}000=\$350{,}000\).
Check and common mistake. The combined balance reconciles because the commission is an internal transfer between the parties: it reduces the reinsurer’s net premium by exactly the amount it adds to the cedent’s premium balance. Do not subtract the commission from ceded losses. The loss allocation remains $178,500 to the reinsurer and $331,500 to the cedent under the stated 35% quota share.
Written Premium, Earned Premium, and Settlement Basis
Written premium and earned premium are not interchangeable. Written premium generally relates to policies issued or premiums booked during a period. Earned premium reflects the portion attributed to coverage already provided during that period. A treaty may specify which amount determines ceded premium and commission, and its accounting or settlement provisions may involve timing that differs from the simplified calculations here.
For a commission stated on earned premium, determine the earned amount first. Then apply the quota share and commission rate. Applying the rate to written premium instead can overstate the commission when some premium remains unearned. Conversely, if the treaty expressly bases commission on written premium, do not replace that contractual basis with earned premium.
Worked Example: Commission on Earned Rather Than Written Premium
A hypothetical specialty insurer writes $900,000 of premium under a quota share treaty. At year-end, 20% of that written premium remains unearned. The quota share is 50%, and the commission is 27.5% of ceded earned premium. The period’s covered incurred losses are $400,000. Assume the treaty settles the stated earned premium without discounting. Find the correct commission and remittance, and compare them with the result from mistakenly using written premium.
Assumptions and method. The 20% unearned portion applies to the written premium stated, so the remaining 80% is earned. The commission is explicitly based on ceded earned premium. Amounts are deterministic, with no mortality model or stochastic distribution and no interest or discounting.
Step 1: Earned premium. Unearned premium is \(0.20\times \$900{,}000=\$180{,}000\). Earned premium is \(\$900{,}000-\$180{,}000=\$720{,}000\).
Step 2: Ceded earned premium. Applying the 50% quota share gives \(0.50\times \$720{,}000=\$360{,}000\).
Step 3: Commission and net remittance. Commission is \(0.275\times \$360{,}000=\$99{,}000\). The cedent remits \(\$360{,}000-\$99{,}000=\$261{,}000\).
Step 4: Loss shares. Ceded losses are \(0.50\times \$400{,}000=\$200{,}000\), and retained losses are also $200,000. Commission does not change either amount.
Step 5: Quantify the wrong-basis result. If written premium were incorrectly used, ceded premium would be \(0.50\times \$900{,}000=\$450{,}000\), and the calculated commission would be \(0.275\times \$450{,}000=\$123{,}750\). This is $24,750 greater than the correct $99,000 commission. The incorrect amount uses premium that the problem states is unearned.
Check and common mistake. The correct remittance is \(\$360{,}000-\$99{,}000=\$261{,}000\), not a remittance calculated from the $450,000 written-premium cession. The key is to follow the stated earned-premium commission base before applying the commission percentage.
Exam Traps and Practical Checks
When a problem gives several premium amounts or describes a commission allowance, establish the base and the cash-flow direction before calculating. A short written flow can prevent a sign or base error:
- Label the base. Confirm whether the commission applies to ceded written premium, ceded earned premium, or another contractually specified amount.
- Apply the quota share before the commission. Under the fixed-rate assumption, commission is \(c\) times ceded premium, not necessarily \(c\) times gross premium.
- Keep direction clear. The reinsurer allows the commission to the cedent, so the allowance is subtracted from the ceded premium to obtain the cedent’s net payment.
- Allocate losses independently. Use the quota share percentage for ceded and retained losses; do not reduce a loss allocation by the commission.
- Reconcile the cash flows. The cedent’s retained premium should equal gross premium less net remittance, or equivalently unceded premium plus commission.
A ceding commission can affect the simplified underwriting balance of each party, but it does not alone establish whether the treaty is profitable or adequate. Such conclusions require additional information about expenses, loss development, timing, and other contractual features. The calculations in this tutorial isolate the premium transfer and its relationship to the quota share loss allocation.
Check Your Understanding
For each problem, use the stated commission base and keep the premium settlement separate from the loss allocation.
- A hypothetical insurer has $640,000 of eligible written premium under a 25% quota share with a 32% commission on ceded written premium. Covered losses are $280,000. Find the commission, net remittance, and ceded losses. (Answer: Commission $51,200; net remittance $108,800; ceded losses $70,000.)
- A hypothetical treaty covers $1,500,000 of earned premium at a 40% quota share and a 22% commission on ceded earned premium. Covered losses are $900,000. Find the cedent’s premium balance after remittance and its retained losses. (Answer: Premium balance $1,032,000; retained losses $540,000.)
- A hypothetical insurer reports $780,000 of earned premium, a 30% quota share, and a 35% commission on ceded earned premium. Gross covered losses are $500,000. Find the ceded premium, commission, net remittance, and cedent’s premium balance. (Answer: Ceded premium $234,000; commission $81,900; net remittance $152,100; cedent’s premium balance $627,900.)
- A hypothetical insurer cedes 50% of $2,400,000 of eligible premium. The reinsurer is to receive a net premium remittance of $780,000 after a commission applied to ceded premium. Find the commission rate and, if covered losses are $1,000,000, the ceded loss. (Answer: Commission rate 35%; ceded loss $500,000.)
- A hypothetical treaty has $1,200,000 of written premium, of which 25% is unearned at year-end. Its 50% quota share pays a 30% commission on ceded earned premium. Covered losses are $640,000. Find the earned premium, commission, net remittance, and cedent’s retained loss. (Answer: Earned premium $900,000; commission $135,000; net remittance $315,000; retained loss $320,000.)