Signature
G = (P + beta) / (1 - gamma)
| Inputs | Definition | Unit |
|---|---|---|
P | Net or risk premium, the expected claims cost per covered person for the year | currency per person per year |
beta | Fixed amount per covered person for expenses that do not vary with the premium | currency per person per year |
gamma | Share of the gross premium set aside for variable expenses, the security margin and any profit, entered as a decimal (0.10 for 10%) | proportion, at least 0 and below 1 |
G | Gross annual premium or contribution per covered person, covering expected claims and all loadings | currency per person per year |
|---|
Function
Actuarial claims costing, premium loading and claims reserving function
Maps utilisation rates, unit costs and the size of a covered group to the expected claims cost of a health insurance scheme, turns that expected cost into a gross premium or contribution with loadings, measures how predictable the group's average cost is, and estimates the claims incurred but not yet paid at a reporting date. These are the calculations of the Actuarial Analysis article. The plan generosity measure is covered separately on the Actuarial Value page.
Try this function
Implementations
Excel
Gross premium from loadings in one cell
Excel returns the gross premium from named cells holding the net premium, the fixed loading per person and the proportional loading as a decimal.
=(NetPremium+FixedLoad)/(1-PropLoad)
Assumptions
Proportional loading defined on the gross premium
The proportional loading is a share of the gross premium, as in the ILO compendium's variable cost supplement, and is below 1. If a loading is quoted as a markup on the net premium, the formula is G = P(1 + markup) + beta instead.
One-year premium without discounting
The formula is the one-period form of the ILO present-value premium equation. It suits annual premiums and contributions set year by year; level premiums over many years need the present values of claims and premiums.
Net premium for the same rating group and year
The net premium is the expected claims cost for the group and year to which the gross premium applies, for example from the expected claims cost formula on this page.
Worked examples
Gross premium addition for the physiotherapy benefit
In the article's example the net premium is £12 per member, with no fixed loading and a proportional loading of 10%. The gross premium addition is £13.33 per member per year, raising about £2.67 million from 200,000 members.
P = 12; beta = 0; gamma = 0.10; G = 13.33
Gross premium for the physiotherapy benefit with induced use of a half
If induced use of a half lifts the net premium to £14.40, the same 10% proportional loading gives a gross premium of £16.00 per member per year.
P = 14.40; beta = 0; gamma = 0.10; G = 16
Actuarially fair premium with no loadings
With both loadings set to zero the gross premium equals the net premium of £12, the actuarially fair premium, a limiting case that checks the implementation.
P = 12; beta = 0; gamma = 0; G = 12
Common errors
Applying the proportional loading as a markup on the net premium
Multiplying the net premium by 1.10 gives £13.20 rather than £13.33. A 10% share of £13.20 is £1.32, leaving £11.88 for claims, so the scheme is short by £0.12 per member, about £24,000 a year across 200,000 members.
Treating the gross premium as the expected cost of care
The gross premium includes expenses and the security margin. Using £13.33 as the cost of the physiotherapy benefit in an economic model overstates the expected claims of £12 per member by the loading.
Sources
ILO net premium, fixed and variable cost supplements and gross premium
Cichon M, Newbrander W, Yamabana H, Weber A, Normand C, Dror D, Preker A. Modelling in Health Care Finance: A Compendium of Quantitative Techniques for Health Care Financing. Geneva: International Labour Office; 1999. Issue Brief 3, section 3.4, printed p. 272: the net premium covers the cost of benefits, and a fixed cost supplement and a variable cost supplement proportionate to the gross premium are added to give the gross premium.
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