Pure premium: the cost of risk before anyone is paid to sell it
The pure premium is the expected cost of claims per unit of exposure, and it is the only part of a rate that is about risk. Everything else in the price — commission, taxes, claim handling, the underwriter's salary, the shareholder's return — is the cost of running the business that carries the risk.
It is calculated as frequency × severity, where frequency is claims per exposure unit and severity is the average cost per claim. Multiplying them gives expected losses per exposure unit, which is a well-defined quantity: 0.08 claims per car-year at $4,200 a claim is $336 of expected loss per car-year, whatever anyone charges for it. That is the number an actuary defends in a filing and the number a reinsurer prices against.
The exposure base has to be right for any of this to mean anything. Auto is written per car-year, workers compensation per $100 of payroll, general liability per $1,000 of receipts or per square foot, property per $100 of insured value. Frequency and severity must both be measured against the same base, over the same period, and trended to the middle of the period the rate will be in force. A frequency measured over three historical years and a severity trended to next year do not multiply to anything useful.
The pure premium concept underpins the rest of this section of the site. It is the expected loss in the experience modifier calculator, the class rate that own-experience is blended against in the credibility weighting calculator, and the quantity that develops to ultimate in the IBNR reserve calculator.
Why the loading is a division and not an addition
The instinct is to add expenses to the pure premium. That fails for the expenses expressed as a percentage of premium, because premium is what you are solving for. Commission at 15% of premium and premium tax at 3% of premium are circular: adding them to the loss cost gives a premium, which changes the commission, which changes the premium.
The algebra resolves it in one line. Write R for the gross rate. Then R = pure premium + LAE + fixed expense + V·R + Q·R. Collect the R terms: R(1 − V − Q) = pure premium + LAE + fixed expense. So
R = (pure premium with LAE + fixed expense) ÷ (1 − V − Q).
The denominator has a name. 1 − V − Q is the permissible loss ratio, the fraction of every premium dollar available to pay losses and fixed costs after variable expense and profit are provided for. It is the single most quoted number in ratemaking, because it is what an actual loss ratio is compared against to decide whether a rate change is indicated.
Two bases are in play and they are easy to confuse. LAE is a percentage of losses, because claim-handling cost scales with claims, not with premium. Variable expense and profit are percentages of premium. Enter a 12% LAE where a 12% of-premium figure belongs and the rate is wrong by an amount that looks plausible, which is the worst kind of error.
One consequence worth noticing: when the fixed expense per exposure is zero, the expected loss and LAE ratio at the resulting rate equals the permissible loss ratio exactly, because R = ppLAE ÷ PLR gives ppLAE ÷ R = PLR. When the fixed expense is positive, the expected loss ratio comes out below the permissible loss ratio, since the fixed expense is recovered inside the rate alongside the losses. That relationship is exact and it is the fastest way to check a rate indication by hand.
Worked example: a rate at 0.08 frequency and $4,200 severity
A line of business expects 0.08 claims per exposure unit per year, an average claim of $4,200, LAE at 12% of losses, $45 of fixed expense per exposure, variable expense at 22% of premium and a 5% profit and contingency load.
- Pure premium. 0.08 × $4,200 = $336.00.
- Add LAE. $336.00 × 1.12 = $376.32. The LAE component alone is $40.32.
- Permissible loss ratio. 1 − 0.22 − 0.05 = 0.73, or 73%.
- Gross rate. ($376.32 + $45.00) ÷ 0.73 = $421.32 ÷ 0.73 = $577.15.
- Check the build-up. Variable expense is $577.15 × 22% = $126.97; profit is $577.15 × 5% = $28.86. Add them to the pure premium, the LAE and the fixed expense: 336.00 + 40.32 + 45.00 + 126.97 + 28.86 = $577.15. The components reconcile exactly, which is the arithmetic proof that the division did what the addition could not.
- Expected loss ratio. $376.32 ÷ $577.15 = 65.20%, below the 73% permissible loss ratio by exactly the amount the $45 fixed expense consumes.
Read the shares. Of every dollar charged, 58.2 cents pays claims, 7.0 cents pays for handling them, 7.8 cents covers fixed policy costs, 22 cents is commission and tax, and 5 cents is profit. The pure premium is $336 and the customer pays $577.15, so the loading is $241.15, or 71.8% on top of the risk cost. That is not unusual for a line with meaningful acquisition cost, and it is why reducing distribution cost moves a rate more than most underwriting refinements do.
How to read the result
The permissible loss ratio is the benchmark you carry forward. Once the rate is in force, compare the actual loss and LAE ratio against it: an actual ratio above the permissible one means the rate is inadequate, and the indicated rate change is roughly (actual ÷ permissible) − 1. The insurance loss ratio calculator does that comparison directly.
Look next at the share of the rate that is not loss cost. If expense and profit are a large fraction of the rate, the rate is dominated by distribution rather than by risk, which is normal for small personal-lines policies with a fixed cost spread over a small premium and abnormal for large commercial accounts. A high fixed expense per exposure on a low-premium product is the classic reason a rate looks expensive relative to the claims it pays.
Then stress the two loss inputs. Frequency and severity are estimates with real uncertainty, and they multiply, so a 10% error in each compounds to 21% in the pure premium. Where your own data is thin, the honest answer is not a more precise point estimate but a credibility weighting against a broader class rate.
Finally, treat the profit load as a policy decision rather than an actuarial output. A load that ignores investment income overstates the required rate for a long-tailed line, where premium is held and invested for years before claims are paid. Casualty rates commonly carry a lower underwriting profit provision than property rates for exactly that reason.
Gross rate at different expense and profit levels
| Variable expense + profit | Permissible loss ratio | Gross rate | Expected loss & LAE ratio |
|---|---|---|---|
| 25% | 75.0% | $561.76 | 66.99% |
| 27% | 73.0% | $577.15 | 65.20% |
| 30% | 70.0% | $601.89 | 62.52% |
| 35% | 65.0% | $648.18 | 58.06% |
| 40% | 60.0% | $702.20 | 53.59% |
| 45% | 55.0% | $766.04 | 49.13% |
Each rate is ($376.32 + $45.00) ÷ PLR and each loss ratio is $376.32 ÷ rate, generated by the calculator's own expressions. The expected loss ratio sits below the permissible loss ratio in every row by the amount the $45 fixed expense absorbs.
What a filed rate has that this calculator does not
A rate filing that reaches a regulator carries considerably more than this build-up. It shows loss development to ultimate, loss and premium trend selections with supporting data, an on-level adjustment restating historical premium at current rate levels, a credibility weighting against a broader body of experience, a catastrophe provision for perils whose historical average is meaningless, a reinsurance cost provision, and an investment income offset in the profit provision. Actuarial Standard of Practice No. 53 sets out what a cost estimate for prospective risk transfer must consider. Use this calculator to understand and check the structure of a rate; use a filed indication to set one.
Where a hand-built rate goes wrong
- Mixing the expense bases. LAE is a percentage of losses; commission, tax and profit are percentages of premium. Entering one on the other's base produces a wrong rate that looks entirely reasonable.
- Adding percentage-of-premium expenses instead of dividing. Adding 27% to the loaded loss cost gives $421.32 × 1.27 = $535.08 where the correct rate is $577.15 — a 7.3% shortfall, and one that only shows up in the loss ratio a year later.
- Untrended severity. Severity must be trended to the average date of loss under the new rate, which for an annual policy is roughly a year past the effective date. Historical severity understates it by however much claim costs are inflating.
- Undeveloped losses. Recent accident years are not fully reported. Using them raw understates both frequency and severity, and the effect is largest on long-tailed lines.
- Treating the average as the answer on a catastrophe-exposed line. Where the loss distribution has a long tail, the historical mean of a short period is not the expected value. Catastrophe exposure needs a modelled provision, not an average.
- Ignoring investment income. On a long-tailed line, premium collected today pays claims years from now and earns a return in between. A profit provision set without that credit overstates the rate.
Pure premium versus loss ratio ratemaking
There are two standard methods and this calculator implements the first. The pure premium method builds a rate from scratch: losses per exposure, loaded up. It needs a reliable exposure count and it produces a rate rather than a rate change, which makes it the right tool for a new product, a new class, or any situation where there is no existing rate to adjust.
The loss ratio method works the other way. It compares the experienced loss and LAE ratio against the permissible loss ratio and produces an indicated rate change: indicated change = (experienced ratio ÷ permissible ratio) − 1. It needs no exposure count, only premium and losses, which is why it dominates in practice for established lines. The permissible loss ratio calculated here is the denominator that method depends on, so the two are not alternatives so much as two ends of the same equation.
Both methods break down when the underlying experience is too thin to believe. That is not a reason to abandon the calculation but a reason to weight it: blend your own indication with a broader class or countrywide rate using limited-fluctuation or Bühlmann credibility, which is exactly the problem the credibility calculator on this site solves. And in either method the losses feeding the calculation must be developed to ultimate first — a rate built on undeveloped recent years is systematically too low, which is the failure mode that produces an underwriting cycle rather than a single bad year.