6.3 Reinsurance Types, Treaties & Calculation Mechanics

Reinsurance Types, Treaties & Calculation Mechanics

Quick Answer: Reinsurance is structured under two foundational legal agreements: Treaty Reinsurance (an obligatory contract where the reinsurer automatically assumes all qualifying policies in an underwritten portfolio) and Facultative Reinsurance (a case-by-case transaction negotiated for an individual specific risk). Operationally, reinsurance contracts are divided into Pro Rata (Proportional) forms—such as Quota Share and Surplus Share, where premiums, losses, and unearned reserves are shared in identical mathematical proportions and the reinsurer pays a ceding commission—and Excess of Loss (Non-Proportional) forms—such as Per Risk, Per Occurrence Catastrophe, and Aggregate Stop-Loss, which indemnify the primary carrier only when covered losses pierce a predetermined dollar retention.

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Treaty vs. Facultative Reinsurance Agreements

Every reinsurance arrangement begins with a fundamental operational choice between portfolio-level automation and individual-risk underwriting:

                               REINSURANCE AGREEMENTS
                                          │
             ┌────────────────────────────┴────────────────────────────┐
             │                                                         │
     TREATY REINSURANCE                                       FACULTATIVE REINSURANCE
  (Automatic & Obligatory)                                  (Individual & Case-by-Case)
  - Covers entire portfolio                                 - Underwritten per single risk
  - Primary must cede all eligible                          - Primary has option to offer
  - Reinsurer must accept all eligible                      - Reinsurer has option to accept
  - Low administrative transaction cost                     - High per-transaction expense

1. Treaty Reinsurance

• Mechanics: An obligatory, contractual agreement under which the primary carrier agrees in advance to cede, and the reinsurer agrees in advance to assume, all policies falling within the defined underwriting scope of the treaty (e.g., all commercial general liability policies written in the Midwest with limits up to $5,000,000).
• Obligatory Nature: Neither party can selectively "cherry-pick." The primary carrier must cede every qualifying policy, and the reinsurer cannot decline individual accounts that meet the treaty criteria.
• Operational Advantage: Exceptional administrative efficiency, low per-policy transaction expenses, and instantaneous binding authority for primary underwriters.

2. Facultative Reinsurance

• Mechanics: A separate, customized transaction negotiated for an individual, specific policy or location. The primary insurer submits an individual risk slip; the reinsurer retains absolute discretion to accept, reject, or re-price the offer.
• Operational Applications:
  1. Exposures Exceeding Treaty Capacity: When a commercial property requires a $100,000,000 limit but the carrier's treaty program caps out at $60,000,000, the remaining $40,000,000 is placed facultatively.
  2. Treaty Exclusions: When an insured operates a hazardous business specifically excluded from treaties (e.g., fireworks manufacturing, underground coal mining, high-hazard chemical compounding).
  3. Unusual Risk Characteristics: Substandard loss history or unique exposures where the primary underwriter desires specialized reinsurer inspection and pricing guidance.
• Hybrid Form (Facultative Obligative / Fac-Oblig): A treaty where the primary insurer has the option to submit eligible risks, but the reinsurer is contractually obligated to accept them if they conform to agreed parameters.

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Pro Rata (Proportional) Reinsurance Structures

In pro rata reinsurance, the ceding insurer and reinsurer agree to share premiums and losses according to identical mathematical proportions:

• Ceding Commission: Because the primary carrier incurs all upfront policy production costs (agent commissions, state premium taxes, underwriting inspection fees), the reinsurer pays the primary insurer a ceding commission (typically 20% to 35% of ceded premium) to reimburse these acquisition expenses.

1. Quota Share Reinsurance

In a Quota Share treaty, the primary insurer retains a fixed percentage (e.g., 40%) of every qualifying policy and cedes the remaining fixed percentage (e.g., 60%) to the reinsurer. Every single policy in the book is split using the exact same ratio.

• Maximum Policy Limit: Quota share treaties carry a maximum dollar limit per policy (e.g., 60% Quota Share on policies up to $1,000,000).
• Mathematical Formulas: $$\text{Reinsurer's Share of Loss} = \text{Total Covered Loss} \times \text{Ceded Percentage}$$ $$\text{Net Reinsurance Premium} = (\text{Gross Premium} \times \text{Ceded \%}) - (\text{Gross Premium} \times \text{Ceded \%} \times \text{Ceding Commission \%})$$
• Strategic Value: Primary tool for generating statutory surplus relief and financing rapid premium expansion.

2. Surplus Share Reinsurance

A Surplus Share treaty is structured around the primary insurer's internal line guide and retention limit (a fixed dollar "line", such as $200,000).

• The "Line" Mechanics:
  • The primary insurer establishes a dollar retention limit representing one line (e.g., $200,000).
  • The treaty capacity is expressed as a multiple of this line (e.g., a "4-line surplus treaty" provides $200,000 × 4 = $800,000 of reinsurance capacity).
  • Total Underwriting Capacity: Retention ($200,000) + Reinsurance ($800,000) = $1,000,000 total policy limit.
• Allocation Principles:
  • Small Policies (≤ Line Retention): Policies with limits less than or equal to the line retention are 100% retained by the primary carrier. Zero premium or loss is ceded!
  • Large Policies (> Line Retention): For policies exceeding the line retention, the ceding percentage is calculated specifically for that policy: $$\text{Primary Insurer Retention Percentage} = \frac{\text{Line Retention}}{\text{Total Policy Limit}}$$ $$\text{Reinsurer Ceded Percentage} = \frac{\text{Total Policy Limit} - \text{Line Retention}}{\text{Total Policy Limit}} = \frac{\text{Ceded Lines}}{\text{Total Policy Limit}}$$
• Sharing of Premium & Losses: Once the ceding percentage is calculated for that specific policy, both premium and all covered losses on that policy are allocated using that exact proportion.

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Excess of Loss (Non-Proportional) Reinsurance Structures

In excess of loss reinsurance, there is no proportional sharing of premiums and losses:

• The reinsurer agrees to pay only the portion of any covered loss that exceeds the primary insurer's predetermined dollar retention (attachment point), up to a stated contractual limit.
• No Ceding Commission: The reinsurer pays zero ceding commission. Instead, the primary carrier pays a negotiated reinsurance premium (often calculated as a rate applied to the primary insurer's subject net written premium).

1. Per Risk (Per Policy) Excess of Loss

• Application: Applies to individual losses on a single insured risk or building.
• Structure: Expressed as Limit excess of Retention (e.g., "$1,000,000 excess of $250,000 per risk").
• Operation: If an industrial warehouse suffers an $800,000 fire, the primary carrier pays its $250,000 retention; the per-risk reinsurer pays the remaining $550,000.

2. Per Occurrence Catastrophe Excess of Loss

• Application: Protects against aggregate losses arising from a single catastrophic event (e.g., hurricane, tornado swarm, earthquake) across multiple insured risks.
• Key Treaty Provisions:
  • The Hours Clause: Catastrophic perils do not occur instantaneously. The treaty defines an "occurrence" as all claims arising from a single physical event within a continuous window—typically 72 hours for hurricanes, windstorms, and tornadoes, and 168 hours (7 days) for earthquakes and floods. Losses occurring outside the window constitute a separate occurrence requiring a second retention.
  • Co-Participation (Retention within the Layer): To prevent moral hazard and ensure the primary carrier actively mitigates claims during a disaster, treaties require the carrier to retain a percentage (typically 5% to 10%) of losses within the excess layer.
  • Reinstatement Premium Clause: When a catastrophe exhausts a treaty layer, the layer must be reinstated to protect against subsequent disasters in the same calendar year. When the treaty calls for reinstatement pro rata as to amount and time (some treaties use pro rata as to amount only), the ceding carrier pays a reinstatement premium calculated as: $$\text{Reinstatement Premium} = \text{Annual Reinsurance Premium} \times \frac{\text{Loss Paid}}{\text{Layer Limit}} \times \frac{\text{Days Remaining in Treaty Year}}{365}$$

3. Aggregate Excess of Loss (Stop-Loss Reinsurance)

• Application: Protects the insurer's entire company-wide portfolio or specific line of business over an entire calendar year.
• Trigger: Attaches when the insurer's cumulative annual loss ratio exceeds a specified percentage (e.g., attaches at an 80% loss ratio and covers losses up to a 105% loss ratio).
• Strategic Value: Protects the insurer against abnormal frequency of independent, moderate-sized losses across an entire fiscal year.

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Reinsurance Pricing Methodologies

Reinsurers establish treaty pricing through two primary actuarial techniques:

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Comprehensive Worked Calculation Models

Example 1: Quota Share Calculation Mechanics

Treaty Terms: 60% Ceded / 40% Retained Quota Share; 25% Ceding Commission. Policy Data: Policy Limit = $500,000; Gross Written Premium = $10,000. Loss Event: Covered fire loss of $80,000.

Step 1: Premium & Commission Allocation
  - Primary Retained Premium (40%):   $10,000 * 0.40 = $4,000
  - Ceded Reinsurance Premium (60%):  $10,000 * 0.60 = $6,000
  - Ceding Commission (25% of ceded): $6,000 * 0.25  = $1,500
  - Net Cash Remitted to Reinsurer:   $6,000 - $1,500 = $4,500

Step 2: Loss Allocation ($80,000 covered loss)
  - Primary Insurer Retained Loss:    $80,000 * 0.40 = $32,000
  - Reinsurer Paid Loss:              $80,000 * 0.60 = $48,000

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Example 2: Surplus Share Calculation Across Diverse Policy Sizes

Treaty Terms: Line Retention = $250,000 (1 line); 4-Line Surplus Treaty (Capacity = $1,000,000; Total Policy Limit Capacity = $1,250,000).

Key Mathematical Insight: Notice Policy A! Because its limit ($200,000) does not exceed the $250,000 line retention, it is 100% retained. The primary insurer keeps all $2,000 premium and pays all $50,000 loss. For Policy C, the retention percentage is $250,000 / $1,000,000 = 25%; the reinsurer assumes 75% of the premium and pays 75% of the $200,000 loss ($150,000).

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Example 3: Layered Catastrophe Excess of Loss Program with Co-Participation

Catastrophe Program Architecture:

• Primary Retention: $10,000,000 per occurrence.
• Layer 1: $20,000,000 excess of $10,000,000 (95% Reinsurer Participation / 5% Primary Co-Participation).
• Layer 2: $40,000,000 excess of $30,000,000 (100% Reinsurer Participation).
• Total Program Capacity: $70,000,000.

Catastrophe Event: A severe coastal hurricane strikes, generating $45,000,000 in gross covered property claims within the 72-hour window.

Mathematical Loss Apportionment:
1. Primary Retention ($0 to $10,000,000):
   - Primary Insurer Pays: $10,000,000
   - Remaining Loss: $45,000,000 - $10,000,000 = $35,000,000

2. Layer 1 ($20,000,000 excess of $10,000,000 — attaches at $10M, exhausts at $30M):
   - Full Layer 1 is exhausted ($20,000,000 of loss)
   - Reinsurer Pays (95%): $20,000,000 * 0.95 = $19,000,000
   - Primary Insurer Co-Participation (5%): $20,000,000 * 0.05 = $1,000,000
   - Remaining Loss: $35,000,000 - $20,000,000 = $15,000,000

3. Layer 2 ($40,000,000 excess of $30,000,000 — attaches at $30M):
   - Loss Entering Layer 2: $15,000,000
   - Reinsurer Pays (100%): $15,000,000
   - Primary Insurer Co-Participation: $0

TOTAL SUMMARY RECAP:
- Total Paid by Reinsurers:  $19,000,000 (Layer 1) + $15,000,000 (Layer 2) = $34,000,000
- Total Retained by Carrier: $10,000,000 (Retention) + $1,000,000 (Co-Part) = $11,000,000
- Reconciliation Check:      $34,000,000 + $11,000,000 = $45,000,000 [Exact Match]

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Common Exam Traps in Reinsurance Calculations