- Lower loss quantile (VaR)
- 10 loss units
- Expected shortfall
- 30 loss units
- Selected worst-tail probability
- 10 %
- Loss probability strictly above VaR
- 5 %
- Loss probability at or above VaR
- 30 %
- Mean of the whole loss model
- 2 loss units
Positive inputs are losses; negative inputs are gains. VaR uses the lower cumulative loss quantile. Expected shortfall averages exactly the worst selected tail mass, including a fraction of a boundary loss when necessary. All inputs share one horizon and loss unit; no horizon scaling, forecasting or regulatory-capital calculation is performed.
Each bar uses the declared loss model. Tail bars show the portion of probability included in the expected-shortfall average, not a second independent distribution. This is an illustrative example.
- Whole-model probability
- Included tail probability
View the chart values
| Series | Loss units | Probability (%) |
|---|---|---|
| Whole-model probability | -10 | 30 |
| Whole-model probability | 0 | 40 |
| Whole-model probability | 10 | 25 |
| Whole-model probability | 50 | 5 |
| Included tail probability | -10 | 0 |
| Included tail probability | 0 | 0 |
| Included tail probability | 10 | 5 |
| Included tail probability | 50 | 5 |
View loss and tail allocation
| Loss units | Model probability (%) | Cumulative probability (%) | Included tail probability (%) |
|---|---|---|---|
| -10 | 30 | 30 | 0 |
| 0 | 40 | 70 | 0 |
| 10 | 25 | 95 | 5 |
| 50 | 5 | 100 | 5 |
On this page
Enter one compatible loss record
Use 2–100 comma-separated probabilities and losses in matching order. Probabilities are percentages and must total 100%. Positive loss values mean losses; negative values mean gains. Every loss uses one common unit and horizon. Confidence is supported from 50% through 99.99%.
Read the declared convention
VaR is the lower loss quantile: the smallest loss whose cumulative probability reaches the confidence level. Identical loss amounts are grouped by adding their probabilities. This is not an interpolated sample percentile.
Inspect the selected mass
Expected shortfall averages exactly the worst 1−confidence probability mass. The allocation can include only part of a boundary outcome. The table reports original probabilities, cumulative probabilities and included-tail probabilities so the denominator can be checked.
Use the original default record
Losses −10/0/10/50 and probabilities 30/40/25/5 percent at 90% confidence give VaR 10, ES 30 and full-model mean loss 2. Strictly above VaR has 5% probability, while at or above it has 30%. The selected ES tail is 10%.
Keep the calculation separate from estimation
The tool summarises entered assumptions. It does not infer exposure repricing, choose sample weights, scale horizons, forecast outcomes or implement regulatory capital. A single positive-probability loss produces a constant model and does not require a distribution chart.