Ceding Commissions Under Quota Share Treaties

Why the Ceding Commission Matters

Under a quota share treaty, the cedant transfers an agreed proportion of covered premiums and claims to the reinsurer. The reinsurer may also pay the cedant a ceding commission, calculated as a stated proportion of ceded premium. This allowance reduces the cedant’s cash outflow for reinsurance and contributes to its retained underwriting result.

The commission is not a change to the quota share percentage: premium and claim allocations still follow the treaty’s cession share. It is a separate payment calculated from the ceded premium. Keeping those steps distinct is essential when calculating both the net premium outflow and the cedant’s underwriting result.

Definition: Let $G$ be the cedant’s gross covered premium, $L$ its gross covered claims, $q$ the quota share ceded to the reinsurer, $k$ the ceding commission rate applied to ceded premium, and $E$ the cedant’s own expenses. Assume $0\leq q\leq1$, $0\leq k\leq1$, and that premiums, claims, and expenses are measured on a consistent basis for the same treaty period. The ceded premium is $qG$, and the ceding commission is $kqG$. The cedant retains proportion $1-q$ of both premium and covered claims.

Calculating the Commission and Net Premium Outflow

The commission rate applies to the ceded premium, not automatically to the cedant’s gross premium. First calculate the ceded share of gross premium; then apply the commission rate to that amount. The cedant’s net premium outflow to the reinsurer is the ceded premium less the commission allowance.

\begin{aligned} \text{Ceded premium} &= qG,\\ \text{Ceding commission} &= k(qG)=kqG,\\ \text{Net premium outflow} &= qG-kqG=qG(1-k). \end{aligned}

“Net premium outflow” here means the ceded premium payment after subtracting the commission. It does not include claim recoveries, the cedant’s retained claims, or its own expenses. A commission rate of 20% means that the cedant receives 20% of ceded premium back as an allowance; it does not mean that the cedant pays only 20% of ceded premium.

Worked Example: Calculating the Commission and Net Outflow

A hypothetical insurer has gross covered premium of $480,000 under a quota share treaty that cedes 35% of premium. The reinsurer pays a ceding commission equal to 20% of ceded premium. Find the ceded premium, commission, and net premium outflow. No probability distribution is assumed; the figures are stated totals.

Method. Calculate the ceded premium first, and apply the commission rate to that ceded amount. This avoids applying the commission rate directly to gross premium.

Ceded premium. The cession share is $q=0.35$, so

0.35\times \$480{,}000=\$168{,}000.

Commission. The commission rate is $k=0.20$, so

0.20\times \$168{,}000=\$33{,}600.

Net premium outflow. Subtract the commission from the ceded premium:

\$168{,}000-\$33{,}600=\$134{,}400.

Check. The cedant pays 80% of ceded premium after the 20% allowance: $0.80\times \$168{,}000=\$134{,}400$. The result agrees.

Retained Underwriting Result

To calculate the cedant’s underwriting result, first allocate covered claims using the same quota share as premiums. The cedant retains $(1-q)L$ of gross covered claims, while the reinsurer’s share is $qL$. The commission is then included as income to the cedant, and the cedant’s own expenses are deducted.

\begin{aligned} \text{Retained premium} &= (1-q)G,\\ \text{Retained covered claims} &= (1-q)L,\\ \text{Retained underwriting result} &=(1-q)G+kqG-(1-q)L-E. \end{aligned}

A positive result is an underwriting gain under the items included in this calculation; a negative result is an underwriting loss. The result does not include investment income, taxes, or any other items unless the problem supplies them and asks that they be included.

Equivalent formula: When the same quota share $q$ applies to gross covered premium and gross covered claims, the retained underwriting result can also be written as

$$ (1-q)(G-L)+kqG-E. $$

This form separates the cedant’s share of gross underwriting margin, $(1-q)(G-L)$, from the commission income $kqG$ and its own expenses $E$. It is a useful independent check on a calculation made from retained premium and retained claims.

Why the Result Formula Holds

The formula follows by adding the cedant’s retained premium and commission, then subtracting its retained covered claims and its own expenses. The key allocation assumption is that the same quota share applies to both premium and claims.

Start with the cedant’s premium share.
The cedant retains $G-qG=(1-q)G$ of gross covered premium. It also receives a commission of $kqG$.

Subtract its covered claims share.
The cedant retains $L-qL=(1-q)L$ of gross covered claims. Subtract this amount and the cedant’s own expenses $E$.

Combine and factor.
The result is $(1-q)G+kqG-(1-q)L-E$. Group the retained premium and claim terms to obtain $(1-q)(G-L)+kqG-E$.

\begin{aligned} \text{Result} &=(1-q)G+kqG-(1-q)L-E\\ &=(1-q)(G-L)+kqG-E. \end{aligned}

The commission term remains $kqG$ in the equivalent formula: the commission is calculated on ceded premium, even though the gross underwriting margin is multiplied by the retained share.

Worked Example: Calculating a Retained Result

A hypothetical insurer has $700,000 of gross covered premium and $610,000 of gross covered claims. It cedes 40% of each under a quota share treaty. The commission is 18% of ceded premium, and the insurer’s own expenses are $26,000. Find the commission, net premium outflow, and retained underwriting result. No probability distribution is assumed; the figures are stated totals.

Method. Allocate premium and claims using $q=0.40$, calculate the commission on ceded premium, and then calculate the result from the cedant’s retained amounts. Check it using the equivalent gross-margin formula.

Ceded premium and commission.

\begin{aligned} qG&=0.40\times \$700{,}000=\$280{,}000,\\ kqG&=0.18\times \$280{,}000=\$50{,}400. \end{aligned}

Net premium outflow.

\$280{,}000-\$50{,}400=\$229{,}600.

Retained premium and claims. The retained share is $1-0.40=0.60$:

\begin{aligned} \text{Retained premium}&=0.60\times \$700{,}000=\$420{,}000,\\ \text{Retained claims}&=0.60\times \$610{,}000=\$366{,}000. \end{aligned}

Retained result. Add the commission to retained premium, then subtract retained claims and own expenses:

\$420{,}000+\$50{,}400-\$366{,}000-\$26{,}000=\$78{,}400.

Check. The gross underwriting margin is $\$700{,}000-\$610{,}000=\$90{,}000$. The cedant’s share is $0.60\times \$90{,}000=\$54{,}000$. Adding commission and subtracting expenses gives $\$54{,}000+\$50{,}400-\$26{,}000=\$78{,}400$, as calculated above.

Common mistake avoided. Applying 18% to the entire $700,000 gross premium would incorrectly produce a $126,000 commission. The correct base is the $280,000 ceded premium, giving a $50,400 commission.

Worked Example: Finding a Break-Even Commission Rate

A hypothetical treaty covers $640,000 of gross premium and $700,000 of gross covered claims. The quota share is 30%, and the cedant has $20,000 of its own expenses. Find (a) the net premium outflow and retained result if the commission rate is 25%, and (b) the commission rate that would make the retained result exactly zero. No probability distribution is assumed; the figures are stated totals.

Method. For part (a), calculate the commission and result from the allocated amounts. For part (b), set the equivalent result formula equal to zero and solve for the commission rate.

Ceded premium.

0.30\times \$640{,}000=\$192{,}000.

Part (a): commission and net outflow. At $k=0.25$, the commission is $0.25\times \$192{,}000=\$48{,}000$. Thus the net premium outflow is $\$192{,}000-\$48{,}000=\$144{,}000$.

Part (a): retained result. The retained share is $1-0.30=0.70$. Retained premium is $0.70\times \$640{,}000=\$448{,}000$, and retained claims are $0.70\times \$700{,}000=\$490{,}000$. Therefore,

\$448{,}000+\$48{,}000-\$490{,}000-\$20{,}000=-\$14{,}000.

The retained underwriting result is a loss of $14,000.

Part (b): break-even rate. The gross underwriting margin is $\$640{,}000-\$700{,}000=-\$60{,}000$. Using the equivalent result formula, set the result to zero:

\begin{aligned} 0&=0.70(-\$60{,}000)+k(\$192{,}000)-\$20{,}000,\\ 0&=-\$42{,}000+k(\$192{,}000)-\$20{,}000,\\ \$62{,}000&=k(\$192{,}000),\\ k&=\frac{\$62{,}000}{\$192{,}000}=0.322916\ldots. \end{aligned}

The break-even commission rate is approximately 32.29%, rounded to two decimal places. At this rate the commission is $62,000, and $-\$42,000+\$62,000-\$20,000=\$0$, which checks the answer. This rate is based on the $192,000 ceded premium, not on gross premium.

Common Mistakes and Treaty Assumptions

The calculations above assume the commission is a stated percentage of the ceded premium for the same period as the premium and claims used in the result. They also assume the same quota share applies to covered premium and claims. If a problem states a different commission base, a different cession for some business, or a different accounting period, use those stated terms rather than applying these formulas unchanged.

Using gross premium as the commission base. Calculate $qG$ first; the commission is $kqG$, unless the treaty explicitly defines another base.
Subtracting the commission from retained premium. The commission is received by the cedant, so it is added when calculating retained underwriting result. It is subtracted from ceded premium only when calculating the cedant’s net premium outflow.
Allocating claims incorrectly. The cedant retains $(1-q)L$, not $qL$. The latter is the reinsurer’s share of covered claims.
Counting the commission twice. In the retained-result calculation, either add $kqG$ as commission income or calculate from the net premium outflow and other cash flows consistently. Do not subtract the commission from ceded premium and then add it again as a separate receipt in the same accounting expression.
Mixing scopes or periods. Use premium, claims, commission, and expenses that relate to the same covered business and period, unless the problem explicitly requires a reconciliation between different bases.

A reliable exam calculation labels each amount before combining it: ceded premium, commission, net premium outflow, retained premium, retained claims, and own expenses. The labels make it easier to detect a reversed share or an incorrect sign.

The commission does not alter the treaty’s premium or claim cession percentages. It changes the cedant’s financial result through a separate allowance based on ceded premium. The treatment of ceding commissions and quota share results is aligned with the SOA Exam FAM (Fundamentals of Actuarial Mathematics) syllabus.

Check Your Understanding

For each problem, use the stated quota share and commission terms. Amounts are hypothetical, and no probability distribution is assumed.

A cedant has gross covered premium of $360,000. It cedes 25% and receives a commission of 16% of ceded premium. Find the commission and net premium outflow. (Answer: commission $14,400; net premium outflow $75,600)
A hypothetical treaty cedes 35% of $800,000 gross premium and 35% of $860,000 gross covered claims. The commission is 20% of ceded premium, and the cedant has $30,000 of its own expenses. Find the retained underwriting result. (Answer: a loss of $13,000)
Gross premium is $500,000, gross covered claims are $560,000, the quota share is 40%, and the cedant’s own expenses are $8,000. What commission rate on ceded premium makes the retained underwriting result zero? (Answer: 22%)
A cedant has $1,100,000 of gross premium, $900,000 of gross covered claims, a 30% quota share, and $25,000 of own expenses. Compare the net premium outflow and retained result at commission rates of 10% and 14%. (Answer: at 10%, outflow $297,000 and result $148,000; at 14%, outflow $283,800 and result $161,200)
A treaty cedes 20% of $420,000 gross premium and $500,000 gross covered claims. The commission is 25% of ceded premium, and the cedant’s own expenses are $11,000. Find the commission, net premium outflow, and retained underwriting result. (Answer: commission $21,000; net premium outflow $63,000; retained result a loss of $54,000)

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