The Cover Slip / The book
Forty promotions at once
The insurer’s book
A premium looks comfortable until the same insurer writes many promotions. Then the arithmetic that makes one risk cheap makes a book fragile, and the two instruments that fix it are the ones a promoter never sees.
Slip stub
- Promotions a year
- 40 across the whole book
- Sum insured
- 48,000,000
- Expected loss
- 322,000
- Premium income
- 450,800, being 1.40 times the expected loss
- Expected profit
- 128,800, or 1 in 106.4 of the sum insured
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 insurer’s own book · Scale 40 promotions, 48,000,000 of sum insured · Two instruments a per-event limit the insurer keeps, and reinsurance above it · Sample one invented book, no real insurer
Direct answer An insurer’s book converts many small expected losses into one large promise. Forty promotions carrying 48,000,000.00 of sum insured produce 322,000 of expected loss and 450,800.00 of premium, so a single 1,000,000.00 settlement consumes 6.8 years of expected profit - which is why the insurer buys reinsurance above its own attach point.
Where the fragility is
01The ratio that shows the shape of the business
Forty-eight million of promises against 450,800.00 of premium is 1 in 106.4. The ratio is not a warning by itself, because the expected loss is 322,000 rather than 48,000,000: the promises are contingent and the premium is certain. It is a warning about one thing only, which is that a single occurrence is many times any single premium.
02One event, against a year of profit
Expected profit for the year is 450,800.00 minus 322,000, which is 128,800.00. A single 1,000,000.00 settlement turns that into a loss of 871,200.00 - 6.8 years of expected profit from one peril in one promotion. That is the number the insurer manages, and it is the reason the load exists.
03Reinsurance moves the top of the tail
Above an attach point of 500,000.00 per event, the sample insurer cedes 12.0% of its premium - 54,096 - and stops carrying the whole of a large single loss. Reinsurance does not reduce the expected loss; it changes who pays it when it arrives all at once.
A promoter never sees this instrument. It sits between two insurers, and the promise to the winner is unaffected by which of them ends up paying.
04Capital is held against the unexpected, not the expected
The sample insurer holds 2,000,000.00 of capital, which is 4.4 times its premium income and 4.4 times its 450,800.00. Capital of that order is not there to settle the expected 322,000 of losses; it is there for the year the expected losses arrive together, which is the only scenario in which a book of this shape is in difficulty.
The book in one columnsum insured across 40 promotions 48,000,000
expected loss 322,000
premium income = 1.40 x 322,000 = 450,800
expected profit = 450,800 - 322,000 = 128,800
promises per 1.00 of premium = 106.4 -> 1 in 106.4
one 1,000,000.00 settlement:
result = 128,800 - 1,000,000 = -871,200
years of profit = 871,200 / 128,800 = 6.8
reinsurance:
attach point 500,000 per event
ceded = 12.0% x 450,800 = 54,096
net premium retained = 450,800 - 54,096 = 396,704
capital held / premium income = 2,000,000 / 450,800 = 4.4
The insurer’s book is not the reader’s business, and that is the point. Two of the twelve fields on a schedule exist only to describe it - the aggregate limit and the renewal basis. A reader gains nothing by reading them, and loses nothing by not.
1 in 106.4attach 500,000ceded 12.0%6.8 years of profit
The claimWhat happens when the peril the book was priced on actually happens