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Begin with the declared example
Default losses −10/0/10/50 use one loss unit and common horizon, with probabilities 30/40/25/5 percent. Confidence is 90%. These inputs are hypothetical and are not market-data estimates.
Interpret the labeled quantities
| Output | Result | Question answered |
|---|---|---|
| Lower VaR | 10 loss units | First cumulative crossing at 90% |
| Expected shortfall | 30 loss units | Average of worst 10% mass |
| Strictly above VaR | 5% | Probability of L > 10 |
| At or above VaR | 30% | Probability of L ≥ 10 |
| Mean loss | 2 loss units | Average over the entire model |
Open the allocation table
At loss 50 all 5% probability is included. At loss 10 only 5% of its available 25% is included. The included masses sum to 10%. The chart’s tail bars are inclusion portions of the same model, not an additional independent probability distribution.
Make a controlled comparison
Changing confidence holds the model fixed; changing an outcome changes its severity; changing probabilities changes the distribution. Retain separate records so a result change can be connected to the input that caused it.