Quota Share Recoveries and Ceding Commissions

How Quota Share Reinsurance Allocates Premium and Loss

A quota share treaty transfers a fixed percentage of specified premiums and losses from the cedant to the reinsurer. The percentage is applied proportionally to the amounts that satisfy the treaty’s definitions; it is not a retention that changes with claim size. When the participation percentage changes across policy cohorts or periods, each premium and loss must be assigned to the applicable percentage before the results are combined.

A ceding commission is a payment from the reinsurer to the cedant, commonly calculated as a percentage of ceded premium. It compensates the cedant for some expenses or other agreed amounts. It changes the premium cash settlement between the parties, but it does not change the amount of loss ceded under the treaty.

Definition: Let $P$ be gross subject premium, $L$ be gross subject loss, $q$ be the quota share percentage ceded to the reinsurer, and $k$ be the ceding commission rate on ceded premium. For a single quota share percentage and commission rate: $$ \text{ceded premium}=qP,\qquad \text{retained premium}=(1-q)P $$ $$ \text{ceded loss}=qL,\qquad \text{net loss}=(1-q)L $$ $$ \text{ceding commission}=kqP,\qquad \text{net premium remitted to reinsurer}=(1-k)qP $$ Here, “net loss” means the cedant’s share of the covered loss after the quota share recovery. The treaty’s actual definitions determine which premiums and losses are subject to cession. The loss amount $L$ in these formulas is therefore the treaty-covered loss amount, not automatically an amount before policy deductibles, limits, or other applicable terms.

The quota share percentage is a proportion, so $q=0.40$ means 40% is ceded and 60% is retained. A ceding commission rate of $k=0.25$ means that the reinsurer returns 25% of ceded premium to the cedant. It does not mean that the cedant recovers only 75% of ceded losses.

Why the Proportional Formulas Hold

The allocation follows directly from the meaning of a quota share: the reinsurer takes the same proportion $q$ of each covered premium and loss amount. For a premium amount $P$, the ceded part is $qP$. The two parties’ shares must add back to the whole premium, so the cedant retains $P-qP=(1-q)P$. The same reasoning applies to covered losses.

The commission is calculated separately. If it is $k$ times ceded premium, it equals $k(qP)$. The reinsurer initially receives ceded premium $qP$, then pays the commission $kqP$ to the cedant. Its premium cash receipt after commission is therefore $qP-kqP=(1-k)qP$. This derivation also shows why commission should not be subtracted from the ceded loss recovery.

Assumptions and limits: These formulas assume that the stated premium and loss amounts are measured on the treaty’s applicable basis and that the quota share applies uniformly to those amounts. They do not determine whether a particular policy, claim, expense, or premium is treaty-subject; that depends on the treaty wording. If a commission has a sliding scale, profit condition, or another adjustment, use the commission provision actually specified rather than assuming a fixed rate $k$.

Worked Calculations for One Quota Share

Worked Example: Separating Loss Recovery From Commission

A hypothetical insurer has $2,400,000 of subject premium and $1,560,000 of subject loss under a treaty ceding 40% of both. The reinsurer pays a ceding commission equal to 25% of ceded premium. Calculate ceded and retained premium, the commission, the net premium remittance, ceded loss, and net loss.

Model and assumptions. This is a deterministic proportional allocation; no probability distribution or stochastic parameters are assumed. There is no interest adjustment because the amounts are compared on the same accounting basis and valuation date. The stated premium and loss are fully subject to the treaty, with $q=0.40$ and $k=0.25$.

Step 1: Allocate premium. Ceded premium is $0.40\times \$2{,}400{,}000=\$960{,}000$. Retained premium is $0.60\times \$2{,}400{,}000=\$1{,}440{,}000$. The check is $\$960{,}000+\$1{,}440{,}000=\$2{,}400{,}000$.

Step 2: Calculate commission and net premium remittance. The commission is $0.25\times \$960{,}000=\$240{,}000$. The cedant remits $\$960{,}000-\$240{,}000=\$720{,}000$ to the reinsurer after commission. Equivalently, $0.75\times \$960{,}000=\$720{,}000$.

Step 3: Allocate loss. Ceded loss is $0.40\times \$1{,}560{,}000=\$624{,}000$. Net loss is $0.60\times \$1{,}560{,}000=\$936{,}000$. The check is $\$624{,}000+\$936{,}000=\$1{,}560{,}000$.

Method and trap avoided. Apply the quota share to premium and loss separately, then calculate commission from ceded premium. The commission is not a reduction to the $624,000 loss recovery.

Changing Participation Percentages

A treaty may have one participation percentage for one cohort and a different percentage for another. The relevant cohort may be defined by policy effective date, underwriting year, or another contract term. Apply the percentage that governs each amount under the treaty; do not assign a new percentage to an old cohort simply because the treaty later changes.

For cohorts indexed by $j$, let $P_j$ and $L_j$ be the subject premium and loss for cohort $j$, and let $q_j$ be its applicable quota share percentage. If the commission rate is $k_j$, calculate each cohort separately and then sum:

\text{total ceded premium}=\sum_j q_jP_j,\qquad \text{total ceded loss}=\sum_j q_jL_j $$ $$ \text{total commission}=\sum_j k_jq_jP_j,\qquad \text{total net loss}=\sum_j(1-q_j)L_j

A single overall percentage can summarize the allocation only if it is weighted using the relevant base. The premium-weighted percentage is $\sum_j q_jP_j/\sum_j P_j$; the loss-weighted percentage is $\sum_j q_jL_j/\sum_j L_j$. Those percentages need not be equal. In particular, a premium-weighted percentage cannot generally be used to allocate losses.

Worked Example: A Treaty Share Changes for a New Cohort

A hypothetical treaty cedes 30% for one cohort and 50% for a later cohort. The first cohort has $1,200,000 of subject premium and $750,000 of subject loss; the later cohort has $800,000 of subject premium and $900,000 of subject loss. A 22% ceding commission applies to both cohorts. Calculate the total ceded premium, commission, net premium remittance, ceded loss, and net loss.

Model and assumptions. Treat each cohort’s values as deterministic treaty-subject amounts, with $q_1=0.30$, $q_2=0.50$, and $k=0.22$. No probability distribution or interest adjustment is assumed; amounts are on the same accounting basis. The cohort assignment is given and no other treaty adjustment applies.

Step 1: Ceded premium by cohort. For the first cohort, $0.30\times \$1{,}200{,}000=\$360{,}000$. For the later cohort, $0.50\times \$800{,}000=\$400{,}000$. Total ceded premium is $\$360{,}000+\$400{,}000=\$760{,}000$. Total gross premium is $\$2{,}000{,}000$, so retained premium is $\$2{,}000{,}000-\$760{,}000=\$1{,}240{,}000$.

Step 2: Commission and remittance. The commission is $0.22\times \$760{,}000=\$167{,}200$. Net premium remitted to the reinsurer is $\$760{,}000-\$167{,}200=\$592{,}800$.

Step 3: Ceded and net losses. The first cohort’s ceded loss is $0.30\times \$750{,}000=\$225{,}000$. The later cohort’s ceded loss is $0.50\times \$900{,}000=\$450{,}000$. Total ceded loss is $\$675{,}000$. Total gross loss is $\$750{,}000+\$900{,}000=\$1{,}650{,}000$, so net loss is $\$1{,}650{,}000-\$675{,}000=\$975{,}000$.

Check and trap avoided. Ceded and net losses add to $\$675{,}000+\$975{,}000=\$1{,}650{,}000$. A simple average participation of 40% would incorrectly produce $\$800{,}000$ of ceded premium. The correct premium-weighted share is $\$760{,}000/\$2{,}000{,}000=38\%$, because the cohorts have different premium amounts.

Reconciling the Parties’ Amounts

The same allocation can be viewed from the cedant’s and reinsurer’s sides. Before other expenses and adjustments, the cedant’s underwriting result on the covered business is retained premium plus commission income less net loss. The reinsurer’s corresponding result is premium received after commission less ceded loss. Adding these results should recover the original gross premium less original gross loss.

\bigl[(1-q)P+kqP-(1-q)L\bigr] +\bigl[(1-k)qP-qL\bigr]=P-L

This identity holds because $(1-q)P+kqP+(1-k)qP=P$, while $(1-q)L+qL=L$. It is a useful reconciliation check, not a claim that either party’s final operating profit equals this amount: other expenses, investment income, taxes, and treaty adjustments are outside the calculation.

Worked Example: Reconciling Two Cohorts With Different Shares

A hypothetical insurer has two treaty cohorts. Cohort A has $1,500,000 of subject premium and $1,100,000 of subject loss, with 25% ceded. Cohort B has $2,000,000 of subject premium and $1,400,000 of subject loss, with 60% ceded. The commission is 20% of ceded premium for both cohorts. Calculate the ceded and retained amounts, then reconcile the combined results for both parties.

Model and assumptions. Use deterministic proportional allocations with $q_A=0.25$, $q_B=0.60$, and $k=0.20$. No probability distribution or interest adjustment is assumed. All stated premiums and losses are subject to the treaty, and no expenses other than the commission are included in the reconciliation.

Step 1: Ceded premium. Cohort A cedes $0.25\times \$1{,}500{,}000=\$375{,}000$. Cohort B cedes $0.60\times \$2{,}000{,}000=\$1{,}200{,}000$. Total ceded premium is $\$1{,}575{,}000$; total gross premium is $\$3{,}500{,}000$, so retained premium is $\$1{,}925{,}000$.

Step 2: Commission and premium cash flow. Total commission is $0.20\times \$1{,}575{,}000=\$315{,}000$. The reinsurer receives $\$1{,}575{,}000-\$315{,}000=\$1{,}260{,}000$ after commission.

Step 3: Ceded and net loss. Cohort A cedes $0.25\times \$1{,}100{,}000=\$275{,}000$ of loss. Cohort B cedes $0.60\times \$1{,}400{,}000=\$840{,}000$. Total ceded loss is $\$1{,}115{,}000$. Gross loss is $\$2{,}500{,}000$, leaving net loss of $\$2{,}500{,}000-\$1{,}115{,}000=\$1{,}385{,}000$.

Step 4: Reconcile results. The cedant’s result before other expenses is $\$1{,}925{,}000+\$315{,}000-\$1{,}385{,}000=\$855{,}000$. The reinsurer’s result before other expenses is $\$1{,}260{,}000-\$1{,}115{,}000=\$145{,}000$. Together they equal $\$855{,}000+\$145{,}000=\$1{,}000{,}000$, which matches gross premium less gross loss: $\$3{,}500{,}000-\$2{,}500{,}000=\$1{,}000{,}000$.

Method and check. Calculate each cohort using its own share before combining results. The premium and loss allocations both reconcile to their gross totals, and the two parties’ results reconcile to the gross underwriting margin.

Common Mistakes and Practical Checks

Using one unweighted average share. If cohorts differ in size, an arithmetic average of their percentages does not generally produce the correct ceded premium or loss. Apply each share to its own base and then sum.
Using the premium-weighted share for losses. Losses can be distributed differently across cohorts than premiums. Allocate losses using the loss cohort’s applicable share.
Subtracting commission from the recovery. A ceding commission changes the premium settlement; it does not reduce the contractual quota share of covered losses.
Applying a change to the wrong cohort. A change in participation generally applies according to the treaty’s specified effective date or cohort definition, not simply the date a premium or claim is paid.
Applying the share to the wrong amount. Confirm that premium and loss bases match the treaty wording. A gross policy amount may not be the treaty-subject amount if policy terms or treaty definitions first change what is covered.

For a calculation with changing participation percentages, a reliable process is to identify the treaty-subject premium and loss by cohort, attach the applicable percentage and commission rate to each cohort, calculate each item separately, and then sum. Finally, check that ceded plus retained premium equals gross subject premium, ceded plus net loss equals gross subject loss, and commission is calculated on the stated ceded-premium base.

The proportional allocation and commission calculations taught here are aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.

Check Your Understanding

For each hypothetical situation, identify the applicable share for each cohort before combining the amounts. Report dollar amounts to the cent.

A treaty cedes 37.5% of $640,000 subject premium and $416,000 subject loss. The commission is 20% of ceded premium. Find ceded premium, commission, net premium remitted, ceded loss, and net loss. (Answer: ceded premium $240,000; commission $48,000; net premium remitted $192,000; ceded loss $156,000; net loss $260,000.)
A hypothetical treaty cedes 20% of an earlier cohort with $900,000 premium and $360,000 loss, and 50% of a later cohort with $600,000 premium and $480,000 loss. A 15% commission applies to all ceded premium. Find total ceded premium, commission, net premium remitted, ceded loss, and net loss. (Answer: ceded premium $480,000; commission $72,000; net premium remitted $408,000; ceded loss $312,000; net loss $528,000.)
A treaty cedes 30% of a cohort with $2,400,000 premium and $1,200,000 loss, and 65% of another cohort with $1,600,000 premium and $1,100,000 loss. The commission is 22%. Find the premium-weighted quota share, total commission, net premium remitted, total ceded loss, and total net loss. (Answer: premium-weighted share 44.0%; commission $387,200; net premium remitted $1,372,800; ceded loss $1,075,000; net loss $1,225,000.)
A hypothetical treaty cedes 10% of a cohort with $500,000 premium and $200,000 loss, and 50% of a cohort with $1,500,000 premium and $800,000 loss. The commission is 25%. Calculate ceded premium and loss by cohort, the commission and net premium remitted, and total net loss. Explain why the premium-weighted share cannot be used for the loss allocation. (Answer: ceded premium $800,000; ceded loss $420,000; commission $200,000; net premium remitted $600,000; net loss $580,000; premium-weighted share 40% differs from loss-weighted share 42%.)

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