Start Here: 5 Things You MUST Know
Pro rata (proportional) reinsurance shares premiums AND losses in the same percentage. If the reinsurer takes 40% of premium, it pays 40% of every loss.
Excess of loss (non-proportional) only kicks in when a loss exceeds a threshold. The reinsurer charges a flat premium, NOT a proportional share.
Quota share = fixed % on ALL policies. Surplus share = variable % based on each policy's size vs. the insurer's retention ("line").
Three types of XOL: per risk (one building), per occurrence/cat (one event, many policies), and aggregate stop loss (whole year).
Most insurers use BOTH pro rata and excess of loss in layers. A complete reinsurance program stacks multiple treaties for protection at every level.
How Reinsurance Agreements Actually Work
Part 1 covered why insurers use reinsurance and where it comes from. Now we get into the mechanics: how do the dollars actually flow? There are two fundamentally different approaches. In pro rata reinsurance, the insurer and reinsurer split premiums and losses in the same proportion — like business partners sharing revenue and expenses. In excess of loss reinsurance, the reinsurer only pays when losses blow past a set threshold — more like buying a deductible for the insurer itself.
Exam Alert!
This is THE most math-heavy reinsurance topic. Expect calculation questions: "Given a 40% quota share, what does the reinsurer pay on a $200,000 loss?" Be ready to calculate ceding commissions, surplus share percentages, and excess of loss payments. Know the formulas cold.
1. Pro Rata (Proportional) Reinsurance
The Core Idea
The insurer and reinsurer share premiums AND losses in a pre-agreed proportion. If the reinsurer takes 40% of the premium, it also pays 40% of every loss. Think of it as a partnership where both sides share the revenue and the costs in the same ratio.
Ceding Commission
In pro rata treaties, the reinsurer pays a ceding commission back to the primary insurer. Why? Because the insurer did all the work — marketing, underwriting, issuing the policy, handling claims. The ceding commission reimburses the insurer for those acquisition costs. It typically ranges from 25% to 40% of ceded premium.
1A. Quota Share Treaty
Definition: A fixed percentage split applied to ALL policies in the treaty. Every policy, every premium, every loss — same percentage, no exceptions. The insurer cannot cherry-pick which risks to cede.
Worked Example: 40% Quota Share with 30% Ceding Commission
The Setup: ABC Insurance writes a commercial property policy with a $100,000 premium. They have a 40% quota share treaty. The reinsurer pays a 30% ceding commission on ceded premium.
What Happens: A fire causes an $80,000 loss.
Reinsurer (40%)
- Receives premium: 40% x $100,000 = $40,000
- Pays loss: 40% x $80,000 = $32,000
- Pays ceding commission: 30% x $40,000 = $12,000
- Net: $40,000 - $32,000 - $12,000 = -$4,000
Ceding Insurer (60%)
- Keeps premium: 60% x $100,000 = $60,000
- Pays loss: 60% x $80,000 = $48,000
- Receives ceding commission: +$12,000
- Net: $60,000 - $48,000 + $12,000 = +$24,000
Why did the reinsurer lose money here? This was a bad risk (80% loss ratio). On profitable policies with low losses, the reinsurer comes out ahead. Over thousands of policies, the math works in the reinsurer's favor — that is the law of large numbers.
Advantages
- Simple — one percentage for everything
- Predictable — cash flows are easy to forecast
- Surplus relief — immediately reduces net liabilities on the balance sheet
- Great for new insurers — limits exposure while building a book of business
Disadvantages
- Gives away profit on good risks — even the most profitable policies get ceded at 40%
- No selectivity — cannot keep more of the best risks
- Expensive over time — as the book matures and profitability improves, the insurer may want to retain more
1B. Surplus Share Treaty
Definition: The percentage ceded varies from policy to policy based on each policy's insured value relative to the insurer's retention (called a "line"). Small policies may not be ceded at all. Large ones are ceded heavily.
Key Terms You Must Know
- Line = the dollar amount the insurer retains on each risk. Think of it as the insurer's "comfort level" for a single policy.
- Surplus = everything above the line that gets ceded to the reinsurer.
- Treaty limit = expressed as a multiple of lines. A "9-line surplus share" means the reinsurer accepts up to 9 times the insurer's line.
Ceded Percentage
(Value - Line) / Value
Max Reinsurer Accepts
Line x Number of Lines
Max Policy Insurer Can Write
Line + (Line x # Lines)
Worked Example: 9-Line Surplus Share (Line = $500,000)
The Setup: Midwest Insurance has a surplus share treaty. Their line is $500,000 and the treaty is a 9-line maximum.
Maximum the reinsurer accepts on any risk: 9 x $500,000 = $4,500,000
Maximum policy value the insurer can write: $500K + $4.5M = $5,000,000
| Policy | Insured Value | Insurer Keeps (Line) | Ceded to Reinsurer | Ceded % |
|---|---|---|---|---|
| Policy A — Small shop | $500,000 | $500,000 | $0 | 0% |
| Policy B — Warehouse | $2,000,000 | $500,000 | $1,500,000 | 75% |
| Policy C — Factory | $5,000,000 | $500,000 | $4,500,000 | 90% |
Now add a loss to Policy B: Fire causes a $400,000 loss. Policy B's ceded percentage is 75%.
Reinsurer pays
75% x $400,000 = $300,000
Insurer pays
25% x $400,000 = $100,000
Now add a loss to Policy A: Same $400,000 fire loss. Policy A's ceded percentage is 0% — the insurer pays the entire $400,000 itself because the policy fits within its line.
Advantages
- Keeps 100% of small risks — only cedes what exceeds the line
- Retains more profit on the smaller, bread-and-butter policies
- Increases large-line capacity — can write policies well beyond its own retention
Disadvantages
- Complex administration — every policy has a different cession percentage
- Detailed reporting — must send individual policy details to the reinsurer
- No catastrophe protection — a hurricane hitting 500 small policies within the line is not helped at all
2. Excess of Loss (Non-Proportional) Reinsurance
The Core Idea
The reinsurer only pays when losses exceed a specified threshold called the retention (or attachment point). Premium is NOT shared proportionally — the reinsurer charges a flat negotiated fee for the protection. Think of it like a very high deductible that the insurer buys for itself.
Key Notation: "$X xs $Y"
XOL treaties are written as "$X xs $Y" — read as "X excess of Y." Example: "$2M xs $500K" means the reinsurer covers up to $2 million of loss that exceeds the insurer's $500K retention. Maximum covered loss = $500K + $2M = $2.5M. Anything above $2.5M is uninsured unless there is another layer.
2A. Per Risk Excess of Loss
How it works: Applies to individual risks — one building, one policy. Each loss on a single risk is measured against the retention. If the loss is below the retention, the reinsurer pays nothing. Used primarily for property and large commercial risks.
Worked Example: $2M xs $500K Per Risk XOL
The Setup: Coastal Insurance has a per risk excess of loss treaty: $2,000,000 xs $500,000. This means the insurer pays the first $500K on any single risk; the reinsurer covers the next $2M above that.
What Happens: A fire destroys a warehouse. Total loss = $1,800,000.
The Result:
Insurer pays
First $500,000 (retention)
Reinsurer pays
$1,800,000 - $500,000 = $1,300,000
What if the loss were $3,000,000? Insurer pays $500K. Reinsurer pays $2M (the treaty limit). The remaining $500K is uninsured unless there is another layer above this one.
Another Scenario: Small Loss
The Setup: Same treaty — $2M xs $500K. A minor kitchen fire causes a $200,000 loss.
The Result: Insurer pays the entire $200,000. Reinsurer pays nothing because $200K is below the $500K retention. This is the key difference from pro rata — the reinsurer does not participate in small losses.
2B. Per Occurrence / Catastrophe Excess of Loss
How it works: Applies when a single event (hurricane, earthquake, tornado) causes losses across multiple policies. All losses from that one event are added together and measured against the retention. This is how insurers survive catastrophes.
Worked Example: $40M xs $10M Catastrophe XOL
The Setup: Sunshine Insurance writes homeowners policies across Florida. They have a catastrophe XOL treaty: $40,000,000 xs $10,000,000.
What Happens: A Category 4 hurricane causes damage across 200 policies. Total claims from this single event = $50,000,000.
The Result:
Insurer pays
First $10,000,000 (retention)
This is the insurer's "deductible" for the event
Reinsurer pays
$50M - $10M = $40,000,000 (at the treaty limit)
Without this, Sunshine Insurance might be bankrupt
Catastrophe XOL Is Often Layered
Instead of buying one massive treaty, insurers stack multiple layers. Each layer has a different reinsurer and a different price. Lower layers are cheaper per dollar (they trigger more often). Higher layers are expensive per dollar (rare but enormous).
Layer 3: $50M xs $50M
Covers losses from $50M to $100M — most expensive, least likely to trigger
Layer 2: $30M xs $20M
Covers losses from $20M to $50M — moderate price
Layer 1: $10M xs $10M
Covers losses from $10M to $20M — cheapest, most likely to trigger
Insurer Retention: First $10M
The insurer always absorbs this before any reinsurance kicks in
2C. Aggregate Excess of Loss (Stop Loss)
How it works: Instead of looking at individual risks or events, this covers the insurer's total losses over an entire year. The retention is typically expressed as a loss ratio (total losses divided by total earned premium). If the annual loss ratio exceeds the agreed threshold, the reinsurer pays the excess.
Worked Example: Stop Loss at 75% Loss Ratio
The Setup: Heartland Insurance earns $20,000,000 in annual premium. Their aggregate stop loss treaty says the reinsurer pays when the loss ratio exceeds 75%, up to a 95% cap.
What Happens: A terrible year with severe weather across the Midwest. Total claims = $18,000,000. Loss ratio = $18M / $20M = 90%.
The Result:
Insurer pays
75% x $20M = $15,000,000
Their retention: the first 75 cents of every premium dollar in losses
Reinsurer pays
(90% - 75%) x $20M = 15% x $20M = $3,000,000
Covers the gap between actual (90%) and threshold (75%)
What if the loss ratio hit 100% ($20M in losses)? The treaty caps at 95%, so the reinsurer pays (95% - 75%) x $20M = $4,000,000. The remaining 5% ($1,000,000) is on the insurer. Total insurer cost: $15M + $1M = $16M.
Why Is This Type Useful?
Aggregate stop loss protects against the accumulation of many smaller losses. A single hurricane is dramatic, but an insurer can also be crushed by a year where every line of business has slightly worse-than-expected losses. No single event triggers per risk or cat XOL, but the total adds up and devastates profitability. Stop loss is the safety net for that scenario.
3. Pro Rata vs. Excess of Loss: Side-by-Side
| Feature | Pro Rata (Proportional) | Excess of Loss (XOL) |
|---|---|---|
| Premium sharing | Yes — proportional split | No — flat negotiated fee |
| When reinsurer pays | On every loss, proportionally | Only when loss exceeds threshold |
| Ceding commission | Yes — reinsurer pays insurer 25-40% | No |
| Best for | Surplus relief, new/growing insurers, stabilizing results | Catastrophe protection, large-loss capacity |
| Complexity | Simple (quota share) to moderate (surplus share) | Moderate to complex (especially layered cat programs) |
| Subtypes | Quota share, surplus share | Per risk, per occurrence/cat, aggregate stop loss |
| Effect on balance sheet | Reduces both premium and loss on the books | Reduces only losses above the attachment point |
4. Layering a Complete Reinsurance Program
Real-world insurers do not pick just one type. They build a multi-layered program combining pro rata and excess of loss treaties to cover every level of loss — from everyday claims to once-in-a-century catastrophes. Each layer handles a different slice of the risk spectrum.
Typical Reinsurance Program Stack
Layer 4: Aggregate Stop Loss
If annual loss ratio exceeds 80%, reinsurer covers the excess
Safety net for "death by a thousand cuts" years
Layer 3: Catastrophe XOL — $50M xs $15M
Hurricane / earthquake → reinsurer covers aggregate event losses from $15M to $65M
Protects against multi-policy catastrophic events
Layer 2: Per Risk XOL — $10M xs $5M
Single large loss on one risk → reinsurer covers $5M to $15M
Handles individual big claims (factory fire, large liability verdict)
Layer 1: Quota Share — 40% of first $5M
Every policy → reinsurer takes 40% of premium and pays 40% of losses up to $5M
Provides surplus relief and steady ceding commission income
Base: Insurer Net Retention — $1M
After all reinsurance, the insurer's maximum exposure on any one risk is $1M
Worked Example: How the Stack Handles Three Different Scenarios
Scenario A: Routine Loss — $200,000 fire at one building
Only the quota share is involved. Insurer pays 60% = $120,000. Reinsurer pays 40% = $80,000. No XOL layers triggered because no individual or aggregate threshold is breached.
Scenario B: Large Single Loss — $8,000,000 factory explosion
Quota share handles 40% of the first $5M (reinsurer pays $2,000,000). The insurer's 60% net share of the first $5M = $3M. Then per risk XOL kicks in for the $3M above $5M — reinsurer pays $3,000,000. Insurer's total net cost is dramatically reduced.
Scenario C: Hurricane — $45,000,000 across 300 policies
Quota share reduces each individual policy's net exposure by 40%. Cat XOL kicks in above $15M in aggregate event losses — reinsurer covers up to $50M of the excess. If these losses also push the annual loss ratio past 80%, the stop loss layer catches the remainder. Multiple layers working together prevent insolvency.
Cheat Sheet
Print this page for quick referencePro Rata (Proportional)
- Quota Share — Fixed % on ALL policies. Simple. Gives away profit on good risks.
- Surplus Share — Variable % per policy (based on size vs. insurer's "line"). Keeps 100% on small risks.
- Both include ceding commission (25-40% of ceded premium) paid to insurer.
- Premium and losses shared in same proportion.
Excess of Loss (Non-Proportional)
- Per Risk XOL — One risk, loss exceeds retention. "$X xs $Y."
- Per Occurrence / Cat XOL — One event, many policies. Often layered.
- Aggregate / Stop Loss — Annual loss ratio exceeds threshold (e.g., 75%).
- Reinsurer charges flat premium. No ceding commission.
Surplus Share Formulas
- Ceded % = (Policy Value - Line) / Policy Value
- Max cession = Line x Number of Lines
- Max policy = Line + (Line x Number of Lines)
XOL Formulas
- Reinsurer pays = Loss - Retention (capped at treaty limit)
- Stop loss payout = (Actual LR - Threshold LR) x Earned Premium
- Notation: "$[limit] xs $[retention]"
Exam Trap Alerts
1. Quota Share Cedes EVERYTHING at the Same Percentage
The exam might describe a profitable policy and ask if the insurer can retain a larger share. No — quota share applies the same percentage to every policy in the treaty. The insurer cannot cherry-pick. That is the tradeoff for simplicity.
2. Surplus Share Percentage Is NOT Fixed
Do not confuse surplus share with quota share. In surplus share, a $500K policy with a $500K line = 0% ceded. A $2M policy with the same line = 75% ceded. The percentage depends entirely on the individual risk's insured value.
3. "xs" Means "Excess Of," NOT Multiplication
"$2M xs $500K" means $2 million in excess of $500K. The reinsurer covers losses from $500K to $2.5M. Do not misread "xs" as "times." The total coverage limit = retention + treaty limit.
4. XOL Has NO Ceding Commission
Ceding commissions only exist in pro rata treaties because the premium is shared proportionally. In XOL, the insurer pays a flat fee — there is no proportional premium flow, so no commission flows back.
5. Per Risk vs. Per Occurrence — Know the Trigger
Per risk looks at one policy's loss. Per occurrence adds up all losses from one event. A $300K loss on one building does not trigger a $500K per risk retention — but 200 such losses from one hurricane totaling $60M absolutely triggers a cat XOL treaty.
6. Aggregate Stop Loss Uses Loss RATIO, Not Dollar Amount
The threshold is a percentage of earned premium (like 75%), not a flat dollar figure. You must calculate losses / earned premium first, then compare to the threshold. An insurer with $10M premium and $8M losses has an 80% loss ratio — above the 75% threshold.
7. "Line" Means Retention, NOT Limit
In surplus share, the "line" is what the insurer keeps. A "9-line surplus share" means the reinsurer accepts up to 9x the line. Line of $500K means the reinsurer's max = $4.5M, and the max policy the insurer can write = $5M total.
Quick Reference Summary
Quota Share
Fixed % on all policies. Reinsurer shares premium + losses proportionally. Simple but gives away profit on every risk.
Surplus Share
Variable % per policy based on insurer's line. Keeps 100% on small risks, cedes heavily on large ones. More complex.
Ceding Commission
Pro rata only. 25-40% of ceded premium returned to insurer for acquisition costs. Does NOT exist in XOL.
Per Risk XOL
Reinsurer pays when ONE risk's loss exceeds retention. "$2M xs $500K" = covers $500K to $2.5M on a single risk.
Catastrophe XOL
One event, many policies. All losses aggregated and measured against retention. Often stacked in multiple layers.
Aggregate Stop Loss
Annual loss ratio exceeds threshold (e.g., 75%). Protects against accumulation of many smaller losses across an entire year.
Pro Rata vs. XOL
Pro rata shares every loss proportionally. XOL only pays above a threshold. Pro rata has ceding commissions; XOL does not.
Layered Programs
Stack quota share + per risk XOL + cat XOL + stop loss. Each layer handles a different slice of the risk spectrum.
Key Formulas
Surplus ceded % = (Value - Line) / Value. XOL payout = Loss - Retention (capped). Stop loss = (Actual LR - Threshold) x Premium.