Signature
A = a * E_S
| Inputs | Definition | Unit |
|---|---|---|
a | Attachment factor, the attachment point as a multiple of expected claims, entered as 1.25 for 125% | ratio |
E_S | Expected annual eligible claims of the group net of specific stop-loss recoveries | dollars |
A | Aggregate attachment point for the contract year | dollars |
|---|
Function
Aggregate stop-loss payment and expected payment function
Maps a self-funded employer's eligible claims for the contract year, net of specific stop-loss recoveries, to the payment due from the aggregate stop-loss carrier and the claims the employer retains, given the aggregate attachment point and any maximum aggregate payment. Applied to the distribution of the year's claims instead of one realised year, the same rule gives the carrier's expected payment, the net stop-loss premium before any loading. The records follow the notation of the Aggregate Stop-Loss article, where S is net claims for the year, A is the aggregate attachment point and L is the carrier's payment.
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Implementations
Excel
Aggregate attachment point from a factor in one cell
Excel multiplies the attachment factor in a cell named AttachFactor by expected net claims in a cell named ExpClaims.
=AttachFactor*ExpClaims
Assumptions
Expected claims on the net basis of the aggregate contract
E_S is measured net of specific recoveries, like the claims that count towards the attachment point. The NAIC Stop Loss Insurance Model Act defines expected claims for its regulatory floors as the claims projected in the absence of stop-loss or other insurance, which is a gross figure, and its drafting note allows carriers to use different contractual definitions. A factor taken from one basis cannot be applied to expected claims on the other.
Credible estimate of the group's expected claims
The formula takes E_S as known. For a smaller group, for example one of 51 to 100 employees, the group's own experience is not fully credible, so expected claims and therefore the attachment point carry more estimation error.
Worked examples
Attachment point at 125% of expected claims for a 200-member group
Employer 1 in the article has expected net claims of $1,500,000. An attachment factor of 1.25 gives an attachment point of 1.25 × 1,500,000 = 1,875,000 dollars.
a = 1.25; E_S = 1500000; A = 1875000
Attachment point at 125% of expected claims for a 20-member group
Employer 2 in the article has expected net claims of $150,000. The same factor gives an attachment point of 1.25 × 150,000 = 187,500 dollars.
a = 1.25; E_S = 150000; A = 187500
Common errors
Entering only the margin as the attachment factor
Entering 0.25 for an attachment point at 125% of expected claims gives an attachment point of $375,000 for Employer 1 instead of $1,875,000, far below expected claims of $1,500,000, so the modelled carrier would pay in almost every year.
Mixing gross and net expected claims in the attachment point
Applying a factor to expected claims gross of specific stop-loss, as in the NAIC model act's definition, while claims accumulate net of specific recoveries places the attachment point higher relative to the claims that count than the factor suggests. A model comparing a contract with the regulatory floor has to state which basis each figure uses.
Sources
NAIC model act definitions of expected claims and attachment point
National Association of Insurance Commissioners. Stop Loss Insurance Model Act (Model 92). Adopted 1995, amended 1999. Section 2 definitions of attachment point and expected claims, the drafting note allowing different contractual definitions, and section 3(A)(1), which states minimum aggregate attachment points as percentages of expected claims (120% for groups of 50 or fewer, subject to dollar minimums, and 110% for groups of 51 or more).
Canonical Identity
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