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Read both original quantities
In the −10/0/10/50 model, the largest listed loss is 50. The lower 90% quantile is 10. These numbers differ because the maximum asks about the end of the supplied support, while the quantile asks where cumulative probability reaches a level.
Retain severity above the threshold
At 90%, the 50-unit outcome still has 5% probability even though VaR is 10. Expected shortfall combines that outcome with part of the boundary mass and equals 30. A VaR label alone does not report every listed tail loss.
Keep model support distinct from reality
| Quantity | Question |
|---|---|
| VaR | Where does the cumulative model reach confidence? |
| Model maximum | What is the largest listed outcome? |
| Real-world worst case | What events could occur beyond supplied assumptions? |
Avoid an impossible-loss claim
The maximum of an observed or assumed record is not proof of the largest possible future loss. Missing scenarios, nonlinear exposures or model changes can create outcomes outside that record.