Burning cost is the oldest method for pricing an excess of loss layer, and the most used, because it fits in one division. You take the losses a layer would have paid had it existed over past years, set them against the premium base of those same years, and the ratio gives the gross cost of the layer as a percentage of the base. Over five years, if the layer would have paid 9 million euros against 300 million of premium, the gross burning cost comes out at 3%.
The word burning carries its own warning: what you measure is what burned, not what can burn. The method says nothing about the event that did not occur during the observation period, which is why it suits working layers, that see losses every year, and does not suit cat layers, whose history is empty while their exposure is not. Applying a burning cost to a layer never touched gives zero, and zero is not a price.
A gross burning cost is always wrong in the same direction, and three corrections put it right. The first is indexation, or bringing losses to current level. A 1.8 million loss occurring in 2019 is not worth 1.8 million today: it must be restated at today's repair cost before being compared to an attachment set today. Without that correction, old losses that would pierce the layer today stay below the attachment, and the cost is understated by as much.
The second is loss development. Recent years are not finished: their losses are partly reserved, and those reserves rise more often than they fall, the more so the longer the tail of the class. A burning cost computed on open years therefore measures an incomplete burden. Development factors are applied to project each year to its ultimate cost, and the last observed year deserves particular suspicion, its factor being the largest and the least certain.
The third is bringing the base to current level, and it is the one most often forgotten. The denominator, the premium of past years, corresponds to a portfolio that is no longer today's: it has grown, its rates have moved, its mix has changed. Setting restated losses against unrestated premium produces a ratio that means nothing. Premiums are therefore adjusted to represent the portfolio of the year ahead, and the rate change measure used for that is one of the most argued numbers of a renewal.
Once those three corrections are made you get an adjusted burning cost, which remains an expected cost and not a price. The price follows from a loading covering the cost of the capital the reinsurer ties up, its expenses, brokerage, and a margin for the volatility of the layer. That loading is heavier the higher and rarer the layer, which makes sense: a layer hit one year in ten requires the reinsurer to tie up its capacity through nine years that earn one premium.
What remains is the limit no correction lifts. Five years of observation contain at best five realizations of chance, and a working layer hit twice a year offers only about ten. A single exceptional loss in the period makes the burning cost jump; its absence makes it collapse. That is why it is always read alongside an exposure analysis, and why two actuaries working on the same history can legitimately produce two different prices depending on the period they retain.
For the January 1, 2027 renewal of a layer of "4 million euros excess of 1 million" per risk, a cedant supplies five years. Losses that would have hit the layer, as reported: 2022 none, 2023 one of 2.2 million, 2024 one of 1.4 million, 2025 two of 1.6 and 3.1 million, 2026 one of 1.2 million. Premium base: 44, 47, 52, 58 and 63 million euros. The broker quotes a gross burning cost and proposes a rate. What must be corrected before that rate can be discussed?
The gross figure comes first, since it is the common starting point. The part of each loss touching the layer is its amount less the 1 million attachment: 1.2 in 2023, 0.4 in 2024, 0.6 and 2.1 in 2025, 0.2 in 2026, that is 4.5 million in total. The cumulative base of the five years is 264 million. The gross burning cost therefore comes out at 1.70%. Three corrections are due before that number means anything. Indexation first: the 1.2 million loss of 2026 exceeds the attachment by only 200,000 euros, and the 1.4 million of 2024 by only 400,000, so that a few points of repair cost inflation move those amounts substantially, and losses not listed, sitting just under 1 million, may enter the layer once restated. The full history below the attachment must therefore be requested back, failing which the correction cannot be made at all. Development next: 2025 and 2026 are open years, their two most recent losses are reserve estimates, and the 1.2 million of 2026 is very close to the attachment, therefore the most sensitive to an upward revision. Bringing the base to current level last: premium grew 43% between 2022 and 2026, and it is not known whether that growth came from volume or from rate. If from volume, the older base must be lifted, which lowers the burning cost; if from rate, the correction runs the other way. Without that distinction the proposed rate cannot be argued, for want of a denominator describing the 2027 portfolio.
- 01Burning cost sets the losses a layer would have paid against the premium base of the same years.
- 02It measures what burned, not what can burn: it suits working layers and not cat layers, whose history is empty while their exposure is not.
- 03Three corrections put it right, and all run the same way: index the losses, project open years to ultimate, bring the base to the level of the portfolio ahead.
- 04The gross figure is always understated: without indexation, losses that would pierce the layer today stay below the attachment.
- 05An adjusted burning cost is still an expected cost; the price follows from a loading that weighs more the higher and rarer the layer.
- 06Five years contain five realizations of chance: one exceptional loss makes the measure jump, and its absence makes it collapse.