Aggregate Stop-Loss

Aggregate Stop-Loss for Self-Funded Health Plans

An employer that self-funds its health plan pays employees' claims from its own resources. Aggregate stop-loss limits that exposure for the group as a whole. The employer carries the year's claims up to a ceiling fixed in the contract, and a stop-loss carrier pays what lies beyond it. The term is used here in its United States employer health benefits sense. It works alongside specific stop-loss under a defined payment rule, and the same attachment percentage protects small and large groups very differently, a point that matters for pricing, for regulatory floors and for economic evaluation.

Why self-funded employers buy a ceiling on total claims

A self-funded employer gives up the fixed premium of a fully insured policy and takes on the variation in its own claims. In the United States the Employee Retirement Income Security Act (ERISA) contains a "deemer clause" under which an employee benefit plan shall not be deemed an insurance company or to be engaged in the business of insurance for the purposes of state insurance law. The National Association of Insurance Commissioners (NAIC) white paper on stop-loss insurance and self-funding summarises the result, which is that self-funded employers and their plans are exempt from state insurance regulation, while the stop-loss policies they buy remain subject to it.

The Department of Labor's Technical Release 2014-01 notes that a stop-loss contract does not usually guarantee benefits to plan participants and more often only insures the employer against losses, so the cover changes who finally bears a high-claims year, not what members are owed. The NAIC white paper describes a typical policy as having two parts, a specific attachment point that protects against claim severity, and an aggregate attachment point that protects against claim frequency. Aggregate cover answers the risk that many ordinary claims, none of them large enough to reach the specific layer, add up to more than the employer planned for.

The payment rule and how it sits on top of specific cover

The aggregate layer works on the employer's accumulated claims for the contract year. The NAIC white paper is explicit that claims paid by the specific coverage do not count towards the aggregate attachment point, which prevents the same dollar being reimbursed twice. Written formally, the rule is as follows.

$$S = \sum_{i=1}^{n} X_i, \qquad L = \min\{\max(S - A,\ 0),\ M\}$$

where $S$ is the employer's eligible claims for the contract year net of specific stop-loss recoveries, $n$ is the number of covered members, $X_i$ is member $i$'s eligible claims net of specific recoveries, $A$ is the aggregate attachment point, $M$ is the policy's maximum aggregate payment if it has one, and $L$ is the payment by the stop-loss carrier. The employer's retained claims are $S - L$; with no maximum this equals $\min(S, A)$, so retained claims can never exceed the attachment point.

Which claims count also depends on the contract basis. The NAIC white paper notes that, unless a policy contains a provision or endorsement extending coverage, it reimburses only claims incurred and paid in the same policy year; run-out cover extends this to claims incurred in the year but paid later, and run-in cover to claims incurred before the year began.

The attachment point is usually set by reference to the claims the group is expected to incur. A common way to write it is as follows.

$$A = a \times E[S]$$

where $A$ is the aggregate attachment point, $a$ is the attachment factor (for example 1.25 for an attachment point set at 125% of expected claims) and $E[S]$ is expected annual eligible claims net of specific recoveries. Claims paid by the specific cover do not count towards the aggregate attachment point, so $E[S]$ is defined here on the same net basis, whereas the regulatory floors described below use the NAIC Model Act's own definition of expected claims, which is gross of stop-loss; the Act's drafting note allows carriers to use different contractual definitions. A lower factor transfers more risk and costs more.

Pooling and group size, and why one percentage means different things

The protection an aggregate attachment point gives depends on how much the group's total claims vary, and that depends on the size of the risk pool. Arrow observed in 1963 that pooling independent medical risks reduces the insurer's risk to relatively small proportions, while noting that real pools are finite and risks may be correlated, for example through epidemics. The variance of a sum of independent variables gives this a precise form. If members' net claims are independent with the same mean and standard deviation, the following holds.

$$E[S] = n\mu, \qquad SD(S) = \sigma\sqrt{n}, \qquad CV(S) = \frac{\sigma}{\mu\sqrt{n}}$$

where $\mu$ is the expected net claims per member, $\sigma$ is the standard deviation of net claims per member, $n$ is the number of members, $SD(S)$ is the standard deviation of total claims and $CV(S)$ is the coefficient of variation of total claims. Total claims grow in proportion to $n$ but their spread grows only with $\sqrt{n}$, so the relative spread falls as the group grows, in line with the law of large numbers.

An attachment point set at 125% of expected claims therefore lies within ordinary year-to-year variation for a small group and well into the upper tail for a large one. Expected claims are also harder to estimate for small groups, and the NAIC white paper notes that the experience of a smaller group, for example one of 51 to 100 employees, is not fully credible.

Worked example with one attachment rule and two group sizes

The figures in this example are illustrative and do not describe any real market or policy. Two employers buy aggregate stop-loss with the attachment point at 125% of expected claims. In both groups, each member's eligible claims net of specific recoveries have mean $7,500 and standard deviation $15,000, and members' claims are treated as independent. Employer 1 covers 200 members and Employer 2 covers 20.

1. Expected claims and spread. For Employer 1, expected claims are 200 × 7,500 = 1,500,000 dollars and the standard deviation is 15,000 × 14.142 = 212,132 dollars, since the square root of 200 is 14.142. For Employer 2, expected claims are 20 × 7,500 = 150,000 dollars and the standard deviation is 15,000 × 4.4721 = 67,082 dollars. The coefficients of variation are 0.141 and 0.447.

2. Attachment points. Employer 1's attachment point is 1.25 × 1,500,000 = 1,875,000 dollars and Employer 2's is 1.25 × 150,000 = 187,500 dollars.

3. Chance of reaching the attachment point. A normal approximation to total claims gives the following.

$$z = \frac{A - E[S]}{SD(S)}, \qquad P(S > A) \approx 1 - \Phi(z)$$

where $z$ is the distance from expected claims to the attachment point in standard deviations and $\Phi$ is the standard normal cumulative distribution function. Employer 1's attachment point lies 375,000 dollars above expected claims, and 375,000 / 212,132 = 1.768 standard deviations, so the probability is about 0.0386, roughly one year in 26. Employer 2's lies 37,500 dollars above, and 37,500 / 67,082 = 0.559 standard deviations, so the probability is about 0.288, a little more than one year in four.

4. Expected payment by the carrier. Under the same approximation the expected excess over the attachment point is as follows.

$$E[(S - A)_+] \approx SD(S)\,\big[\phi(z) - z\,(1 - \Phi(z))\big]$$

where $(S - A)_+$ is the excess of total claims over the attachment point, or zero when claims fall below it, and $\phi$ is the standard normal density. For Employer 1 the bracket is 0.08362 − 1.7678 × 0.03855 = 0.01547, and 212,132 × 0.01547 = 3,282 dollars, about 0.22% of expected claims. For Employer 2 the bracket is 0.34123 − 0.559 × 0.28808 = 0.18019, and 67,082 × 0.18019 = 12,088 dollars, about 8.1% of expected claims.

5. One realised year for Employer 1. If net claims after specific recoveries come to $1,980,000, the aggregate carrier pays 1,980,000 − 1,875,000 = 105,000 dollars and the employer retains $1,875,000 of claims plus its premiums.

6. Interpretation. The smaller employer is more than seven times as likely to reach the attachment point and its expected recovery is a much larger share of its claims, so the same rule transfers far more of its risk. For the larger employer the expected payment is small, so loading would be a large share of any premium. Because claims are skewed and can share common shocks, the normal approximation understates the upper tail, especially for 20 members, so the figures show the direction of the effect rather than a price.

Pricing the layer and the value of risk transfer

The carrier's expected cost is the expected excess $E[(S - A)_+]$, known in actuarial work as the stop-loss premium in its net form. The premium actually charged adds a loading. Arrow listed administrative costs, the cost of capital tied up by irregular payments and any risk aversion of the insurer as reasons for loading. The employer's question is whether lower variance in its retained claims is worth that loading.

Expected utility theory gives a clear benchmark. Arrow proved that if an insurer offers any policy at a premium that depends only on the policy's actuarial value, a risk-averse buyer chooses full coverage above a deductible. Applied to the employer, with its net claims for the year treated as the loss, the same logic points to cover of the aggregate stop-loss form, in which the employer keeps every claim up to a threshold and transfers everything above it. Arrow's second proposition shows that a pure threshold contract is not optimal when the insurer is risk-averse and has no other costs.

An employer able to absorb large swings in claims is close to risk-neutral over this risk, so the loading may outweigh the gain, whereas a small employer facing the wide distribution in the example may value the cover highly. The cover also changes incentives at the margin, because once the attachment point is reached, further claims cost the employer nothing within that contract year, apart from effects on renewal premiums and any maximum aggregate payment, which weakens its incentive to manage spending above the threshold, a form of moral hazard at the level of the plan sponsor.

Regulatory floors on the attachment point

Because a low attachment point makes a self-funded plan behave much like an insured one, the NAIC model law, and states that adopt it, set minimum attachment points. The NAIC Stop Loss Insurance Model Act, adopted in 1995 and amended in 1999, defines expected claims as the claims projected to be incurred by the group through its health plan in the absence of a stop-loss policy or other insurance. It says an insurer shall not issue a policy with an annual specific attachment point below $20,000, an annual aggregate attachment point for groups of 50 or fewer below the greater of $4,000 times the number of group members, 120% of expected claims or $20,000, or an annual aggregate attachment point for groups of 51 or more below 110% of expected claims. Each state decides whether and how to adopt the model.

Technical Release 2014-01 states the Department of Labor's view that a state law prohibiting stop-loss contracts with attachment points below specified levels would not be preempted by ERISA, and warns that very low attachment points give nearly all the risk protection of a conventional health insurance policy without the consumer protections required for such policies. The NAIC white paper sets out the adverse selection concern behind this, namely that self-funded plans are expected to attract lower-risk groups, and stop-loss that is not adequately regulated could compete with the community-rated small group market while being rated on health status and claims experience.

Aggregate versus specific stop-loss and reinsurance

Mechanisms that limit the cost of high claims differ in who buys the cover and which part of the claims distribution it addresses. Keeping them apart matters when a model has to say who pays.

Stop-loss is sometimes called reinsurance, but the NAIC white paper points to the difference in buyer. Reinsurance covers a licensed insurer for its obligations under insurance policies, while stop-loss covers a self-funded employer for its obligations under a health benefit plan.

Using aggregate stop-loss in budget impact and economic evaluation

A self-funded employer's exposure to a new treatment or programme depends on where its costs fall relative to the stop-loss layers. In a budget impact analysis from the employer's perspective, a single very costly treatment mainly falls on the specific layer, while a widely used treatment that adds modest costs for many members moves the group towards its aggregate attachment point. Modelling gross claims alone overstates the employer's exposure in a bad year.

From a health system or societal perspective, a payment from the carrier to the employer is a transfer that saves no resources; the resource costs are the loading for administration and capital and any change in care that follows from altered incentives. An evaluation should therefore report gross claims, stop-loss recoveries, premiums and retained costs separately, and state which perspective counts which items.

Where analyses of aggregate stop-loss go wrong

The most common error is double counting, which means adding specific stop-loss recoveries and aggregate recoveries calculated on gross claims, when the aggregate accumulation should exclude amounts already reimbursed by the specific cover. A second is to treat the attachment point as a firm cap on the employer's cost while ignoring premiums, any maximum aggregate payment, excluded services and claims that fall outside the contract basis.

A third concerns timing. The NAIC white paper points out that a self-funded employer pays claims as they arise, so an employer that reaches its aggregate attachment point late in the year has already paid the whole retention from its own cash flow. Finally, an analysis should test high-utilisation years and correlated shocks rather than rely on a normal approximation of the kind used in the worked example.

Sources

• Arrow KJ. Uncertainty and the welfare economics of medical care. American Economic Review. 1963;53(5):941-973. Section IV and Appendix (Propositions 1 and 2).
• Kaas R, Goovaerts M, Dhaene J, Denuit M. Modern Actuarial Risk Theory: Using R. 2nd ed. Berlin: Springer; 2008.
• National Association of Insurance Commissioners. Stop Loss Insurance Model Act (Model 92). Adopted 1995, amended 1999. https://content.naic.org/sites/default/files/model-law-092.pdf
• National Association of Insurance Commissioners. Stop Loss Insurance, Self-Funding and the ACA. White paper. 2015. https://content.naic.org/sites/default/files/inline-files/SLI_SF.pdf
• United States Code. Title 29, section 1144(b)(2)(B) (ERISA section 514(b)(2)(B)). Text as accessed 1 October 2026. https://www.law.cornell.edu/uscode/text/29/1144
• US Department of Labor, Employee Benefits Security Administration. Guidance on State Regulation of Stop-Loss Insurance. Technical Release 2014-01. 6 November 2014. https://www.dol.gov/agencies/ebsa/employers-and-advisers/guidance/technical-releases/14-01