loss elimination ratio

An insurer is deciding whether to add a 500 deductible to its motor policies and wants a single number that answers: 'what fraction of the losses we used to pay will this deductible save us?' The loss elimination ratio is exactly that number — the proportion of total expected losses that a deductible (or other modification) eliminates from the insurer's bill.

Concretely, the loss elimination ratio for a deductible d is the expected amount eliminated by the deductible divided by the expected loss with no deductible. The amount eliminated per loss is min(X, d) — you keep all of a small loss below d, and exactly d of any larger loss — so the LER equals E[min(X, d)] divided by E[X]. If average losses are 2,000 and a 500 deductible eliminates an average of 360 per loss, the LER is 360/2,000 = 0.18, meaning the deductible removes 18% of expected losses. The insurer can then cut the loss portion of the premium by roughly that 18%.

The loss elimination ratio is the standard bridge between a policy modification and its effect on price: it translates 'we are adding this deductible' into 'expected losses fall by this percent'. It shows up in deductible pricing, in designing layers, and in explaining rate changes. An important caution: the LER measures the reduction in expected losses, not the reduction in the premium one-for-one — expenses, profit loading, and the fact that fixed costs do not shrink with the deductible mean the premium does not fall by the full LER. And because it is an expectation, the LER says nothing about how a deductible reshapes the variability of what remains, which can matter for capital.