The price

Four lines produce a premium, and each of them can be re-derived: the prize, the estimate of the peril, the expected loss they multiply to, and the load the insurer adds on top of it.

Open the partner account Read a promotion first

Slip stub

Prize: 1,000,000.00
Peril estimate: 0.351%, from 2 of 570 league-seasons
Expected loss: 3,510.00
Load: 40.0% of the expected loss = 1,404.00
Premium: 4,914.00, or 0.0393 per qualifying account

the perilOne stated act that must happen for the prize to be owed - and the estimate of how often it has

the retentionThe largest prize the promoter funds from the promoted product’s own margin, before any cover responds

the coverA schedule of twelve fields that indemnifies the promoter, and is never a reader’s protection

Desk The Cover Slip, cycle 62 · Page the arithmetic of a premium · Formula premium = prize x peril estimate x (1 + load) · Sample 1,000,000.00 x 0.351% x 1.40 = 4,914.00 · Not quoted no real insurer’s rates or terms

Direct answer A premium is the expected loss plus a load. The expected loss is the prize multiplied by the estimate of the peril; the load pays for uncertainty, expenses and the insurer’s margin. On the sample terms 1,000,000.00 at 0.351% gives 3,510.00, and a 40.0% load turns that into 4,914.00.

The four lines, and the two that are judgements

The prize is the only line that is not an estimate

The sum insured is read straight off the promotion. Everything else on the schedule is a judgement about the peril, which is why two insurers can quote the same promotion quite differently without either of them being wrong.

The peril estimate is an argument about frequency

The sample uses a reference set of 570 completed league-seasons in which the stated act happened twice, giving 0.351%. The estimate is not a property of the act; it is a property of the reference set. Narrow the set to the last twenty seasons and the number changes, and with it the premium.

A promoter publishing the same offer for a second year does not get the same price twice for the same reason. The reference set grows, and one season in which the act happened is a large share of a short set.

The load is what uncertainty, expenses and margin cost

On the sample terms the load is 40.0% of the expected loss, so 1,404.00 on top of 3,510.00. The insurer’s expected margin is that 1,404.00, which is 28.6% of the premium it collects - a share that looks large until the variance is taken into account, because the insurer is paid 4,914.00 for a promise it may have to settle at 1,000,000.00.

Divided by the audience, the premium is small

Spread across the 125,000 accounts that qualify, 4,914.00 is 0.0393 each - under four pence per qualifying account. That is the figure a promoter actually compares, and it is the reason a headline prize can be published at all: the cost of moving the risk is a rounding error on the customer base.

The premium, with the check on every lineperil estimate = 2 / 570 = 0.00351 -> 0.351% expected loss = 1,000,000.00 x 0.00351 = 3,510.00 load = 3,510.00 x 0.40 = 1,404.00 premium = 3,510.00 + 1,404.00 = 4,914.00 insurer margin share = 1,404.00 / 4,914.00 = 28.6% cost per account = 4,914.00 / 125,000 = 0.0393 the same formula on the golf day: expected occurrences = 1,400 shots / 12,500 = 0.112 expected loss = 0.112 x 25,000.00 = 2,800.00 premium at a 35% load= 2,800.00 x 1.35 = 3,780.00 insurer margin = 3,780.00 - 2,800.00 = 980.00 = 25.9% of premium cost per shot = 3,780.00 / 1,400 = 2.70

A lower load is not a better deal for the reader. The premium is a cost inside a marketing budget. It changes what the promoter pays to publish the promise; it changes nothing about what the winner is owed.

0.351% perilpremium 4,914.00expected loss 3,510.000.0393 per account

The insurer’s book

What 40 promotions at once do to the same arithmetic

Keep or transfer

The line that decides whether a premium is paid at all