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State every original outcome
| Loss units | Probability |
|---|---|
| 0 | 99% |
| 100 | 0.9% |
| 1,000 | 0.1% |
Find the lower 95% threshold
F(0)=99%, already above the 95% confidence level. The lower loss quantile is therefore zero. That result does not remove the 1% probability of positive losses or identify their severity.
Fill the worst 5% mass
Take all 0.1% at loss 1,000 and all 0.9% at loss 100, then fill the remaining 4% with zero loss. The selected weighted loss is 0.001×1,000+0.009×100=1.9. Divide by 0.05 to obtain ES=38 loss units.
Keep the full-model mean separate
The full-model expected loss is also a weighted sum, but its denominator is one and equals 1.9 units. ES 38 and mean loss 1.9 summarise different probability masses. The maximum listed loss is 1,000; it is not a guaranteed real-world bound.