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Hold the scenario model fixed
The comparison uses the original −10/0/10/50 loss model with 30/40/25/5 percent probabilities. Changing confidence changes the selected summary, not the probabilities or the outcomes themselves.
Read both quantities
| Confidence | Selected tail | Lower loss quantile | Expected shortfall |
|---|---|---|---|
| 90% | 10% | 10 | 30 |
| 95% | 5% | 10 | 50 |
| 97.5% | 2.5% | 50 | 50 |
Explain a discrete jump
The lower quantile remains 10 at the exact 95% cumulative boundary and becomes 50 just above it. Expected shortfall already equals 50 at that boundary because the selected tail contains only the loss-50 outcome. A threshold jump and a tail-average change need not have the same size.
Do not claim a new loss forecast
A smaller selected tail is not a lower probability that the entire model is wrong. Confidence is a measure parameter, and its interpretation depends on the estimated or assumed distribution. Document the chosen level and the intended horizon with each result.