1.5 Proportional and Excess-of-Loss Reinsurance

Study Focus

Proportional reinsurance shares premiums and claims in the agreed proportions. Surplus reinsurance uses a retention and treaty lines to establish shares.

Structural Forms: Proportional vs. Non-Proportional Reinsurance

Reinsurance treaties are structured into two major mathematical forms: proportional (pro-rata) and non-proportional (excess of loss).

Form A: Proportional Reinsurance

In proportional reinsurance, the reinsurer shares in both the premiums and the losses in the exact same proportion as the sum insured is divided between the ceding company and the reinsurer. The reinsurer pays the ceding company an agreed ceding commission to reimburse the direct insurer for original acquisition costs (agent commissions, policy processing, and underwriting expenses).

1. Quota Share Treaty

Under a Quota Share Treaty, a fixed, predetermined percentage applies to every policy written in the covered portfolio, regardless of the size of the sum insured.

• Worked Numerical Example (RM):
  • Treaty Agreement: Ceding Company retains 30%; Reinsurer accepts 70%.
  • Policy Issued: Industrial plant with Sum Insured = RM 2,000,000; Gross Premium = RM 10,000.
  • Ceding Commission: 20% of ceded premium.
  • A covered fire causes a loss of RM 400,000.

2. Surplus Treaty (Lines Treaty)

Under a Surplus Treaty, the ceding company establishes a fixed monetary retention limit known as "one line" (for example, RM 100,000). The capacity of the treaty is defined as a multiple of this retention line (e.g., a "5-line surplus treaty" provides capacity of 5 x RM 100,000 = RM 500,000).

• Mechanics:

  • If the sum insured is less than or equal to one line, the cedant retains 100% of the risk; nothing is ceded.
  • If the sum insured exceeds one line, the excess amount (the "surplus") is ceded to the treaty up to the maximum number of lines.
  • Premium and claim liabilities are apportioned according to the final percentage of sum insured held by each party.

• Worked Numerical Example (RM):

  • Ceding Company Retention (1 Line) = RM 100,000.
  • Surplus Treaty Capacity = 4 Lines (RM 400,000). Total Treaty Capacity = RM 500,000.
  • Policy 1 (Small Risk): Sum Insured = RM 80,000. Retained 100% (RM 80,000) by cedant. Cession = RM 0.
  • Policy 2 (Large Risk): Commercial building Sum Insured = RM 500,000; Premium = RM 5,000; Loss = RM 150,000.

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Form B: Non-Proportional Reinsurance (Excess of Loss)

In non-proportional reinsurance, there is no proportional sharing of sum insured or primary policy premiums. Instead, the reinsurer agrees to pay only the amount of an individual loss (or accumulated losses from a single event) that exceeds a predetermined monetary threshold, known as the priority, retention deductible, or attachment point.

The ceding company pays a separate, actuarially priced reinsurance premium that is calculated independently (often via "Rate on Line" or "Burning Cost" methodologies).

Types of Non-Proportional Reinsurance

1. Working Excess of Loss (Per Risk XL): Covers individual losses on a single policy that exceed the priority limit. Designed to protect the cedant from unusually severe individual claims.
2. Catastrophe Excess of Loss (Per Event / Occurrence XL): Protects the insurer against an accumulation of multiple claims resulting from a single catastrophic peril (e.g., a regional flash flood damaging hundreds of properties in a single 72-hour period).
3. Stop Loss / Aggregate Excess of Loss: Protects the ceding company's overall annual loss ratio for an entire line of business (e.g., the reinsurer pays when the annual net loss ratio exceeds 75% up to a maximum cap of 105%).

• Worked Numerical Example: Per Risk Excess of Loss (RM):
  • Treaty Structure: Reinsurance coverage of RM 400,000 in excess of RM 100,000 (Priority = RM 100,000; Maximum Treaty Limit = RM 400,000; Total Insured Protection = RM 500,000).

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Comparison Table: Proportional vs. Non-Proportional Reinsurance