Reinsurance Structures: Proportional and Non-Proportional
A technical overview of reinsurance treaty types and how actuaries analyze their risk transfer properties.
Proportional Reinsurance
Proportional (or pro rata) reinsurance involves sharing premiums and losses between the ceding company and the reinsurer according to a fixed percentage. The fundamental principle is straightforward: the reinsurer participates in the same proportion of premiums, losses, and loss adjustment expenses. This alignment of interests between the ceding company and the reinsurer creates a natural incentive for both parties to manage the underlying risk effectively.
Two main structures fall under proportional reinsurance. In a quota share treaty, the reinsurer takes a specified percentage of every risk in a defined portfolio. For example, a 40% quota share means the reinsurer receives 40% of the premium and pays 40% of every loss. The ceding company retains the remaining 60%. Quota share treaties are simple to administer because the split applies uniformly across the portfolio, requiring no individual risk assessment by the reinsurer. They are commonly used by new or growing companies that need to expand their capacity quickly.
In a surplus share treaty, the reinsurer takes a percentage that varies by risk based on the ceding company's retention relative to the total sum insured. If the ceding company retains $500,000 on a risk with a $2,000,000 sum insured, the reinsurer covers the surplus of $1,500,000, or 75% of the risk. For a smaller risk with a $400,000 sum insured that falls entirely within the retention, the reinsurer has no participation. Surplus share treaties allow the ceding company to retain smaller risks entirely while ceding a portion of larger risks, making them more capital-efficient than quota share for companies with heterogeneous portfolios.
Quota Share Treaty Mechanics and Ceding Commissions
A critical element of proportional reinsurance economics is the ceding commission. The reinsurer pays the ceding company a commission to compensate for the acquisition expenses (agent commissions, underwriting costs, policy issuance) already incurred on the ceded business. Ceding commissions typically range from 20% to 40% of ceded premium, depending on the profitability of the underlying portfolio and market conditions.
Sliding scale commissions add a profit-sharing dimension to the arrangement. Under a sliding scale, the ceding commission increases when the portfolio performs well (low loss ratio) and decreases when performance deteriorates (high loss ratio). This mechanism aligns the financial interests of both parties more closely and provides the ceding company with additional incentive to maintain underwriting discipline. The commission formula typically specifies a provisional commission rate, a minimum commission, a maximum commission, and the loss ratio thresholds that trigger adjustments.
From a financial reporting perspective, quota share treaties provide several benefits to the ceding company. They reduce net written premium and net reserves, which lowers the required risk-based capital. The ceding commission can be recognized as income, partially offsetting the premium ceded. For growing companies, quota share treaties effectively allow the ceding company to finance its growth by transferring a portion of the underwriting risk and receiving a ceding commission that covers acquisition costs.
Non-Proportional Reinsurance
Non-proportional (or excess of loss) reinsurance provides coverage when losses exceed a specified retention, also called the attachment point. Unlike proportional treaties, the reinsurer does not share in every loss from the first dollar. Instead, the ceding company retains all losses up to the attachment point and the reinsurer pays losses (or a portion of losses) in the layer between the attachment point and the treaty limit.
Three main types of non-proportional reinsurance serve different purposes. Per-risk excess of loss covers individual large claims that exceed the retention on a single risk. For example, a per-risk treaty with a $500,000 retention and a $4,500,000 limit (often written as "$4.5M xs $500K") would pay the portion of any individual claim between $500,000 and $5,000,000. Per-occurrence (or per-event) excess of loss protects against the accumulation of losses from a single catastrophic event, such as a hurricane or earthquake, that generates claims across many policies. Aggregate stop-loss covers total losses exceeding a threshold over a defined period, typically expressed as a percentage of expected losses for the year.
Pricing Non-Proportional Treaties
Pricing non-proportional treaties requires analyzing loss distributions above the attachment point and estimating the expected loss in the reinsured layer. The experience rating approach uses the ceding company's historical large loss data, developed to ultimate and trended to the prospective period, to estimate expected losses in the layer. Loss development is particularly important because large losses often develop significantly over time as their full extent becomes known.
The exposure rating approach estimates expected losses based on the characteristics of the underlying portfolio rather than its historical loss experience. This approach uses increased limits factors (ILFs) that quantify the relationship between losses at different attachment points. The loss elimination ratio (LER) measures the percentage of total losses eliminated by a retention; the expected loss in a layer equals the total expected loss multiplied by (1 minus the LER at the attachment point minus (1 minus the LER at the attachment point plus the limit)).
For catastrophe excess of loss treaties, catastrophe models replace traditional actuarial methods. Models from vendors like AIR, RMS, and CoreLogic simulate thousands of potential catastrophic events and estimate the resulting losses to the ceding company's portfolio. The expected loss in the reinsured layer is computed from these simulated event losses. The catastrophe model output also provides exceedance probability curves that show the probability of losses exceeding various thresholds, which informs both pricing and capital allocation decisions.
Comparing Treaty Structures
The choice between proportional and non-proportional reinsurance depends on the ceding company's objectives. Proportional treaties provide broad capacity relief and stable underwriting results but require ceding a significant share of profitable business. Non-proportional treaties protect against specific adverse scenarios (large individual losses or catastrophic events) while allowing the ceding company to retain the profit on routine business. Most reinsurance programs combine both types to achieve a balanced risk transfer strategy.
Key factors in this decision include the volatility of the underlying portfolio, the company's capital position and risk tolerance, the cost of each structure in the current market, and regulatory capital requirements. Actuaries evaluate reinsurance program alternatives by modeling the distribution of net results under each structure, computing metrics such as the reduction in the coefficient of variation of net losses, the probability that net losses exceed a specified threshold, and the cost per unit of risk transferred.
Practical Considerations for Actuaries
When analyzing reinsurance structures, actuaries should consider the impact of reinstatement provisions in non-proportional treaties. Most excess of loss treaties provide one or two reinstatements, meaning the coverage is restored after a loss for an additional premium. The reinstatement premium is typically calculated as a pro rata portion of the original premium based on the loss amount relative to the layer size. Limited reinstatements create a cap on the total amount the reinsurer will pay during the treaty period, which the actuary must account for when estimating the net retained risk.
Credit risk is another important consideration. The ceding company relies on the reinsurer to pay its share of losses, and reinsurer insolvency can leave the ceding company fully exposed. Actuaries should consider the financial strength ratings of reinsurers when designing the program and may recommend diversifying across multiple reinsurers to mitigate concentration risk. Collateral arrangements, such as letters of credit or trust funds, provide additional security for reinsurance recoverables.