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Convert percentages before subtracting
A 90% confidence input is c=0.9, so 1−c=0.1 or 10%. A 97.5% input gives a selected 2.5% tail. Subtracting 90 from 1 mixes percentage numbers and decimal probability units.
Keep threshold exceedance separate
In a discrete model, probability strictly above the selected lower quantile need not equal 1−c. At 90% confidence in the original model, strictly above VaR 10 is only 5%; at or above 10 is 30%. Neither is the selected 10% mass by itself.
Read three probability questions
| Measure | Amount |
|---|---|
| Selected ES tail | 10% |
| Strictly above VaR 10 | 5% |
| At or above VaR 10 | 30% |
Retain model uncertainty
The confidence parameter describes a quantile of the supplied model. It does not certify that historical inputs remain valid or that losses beyond the model’s observed maximum are impossible.