On this page
State which losses the record represents
A set of past realised portfolio returns is not automatically the historical repricing loss distribution of today’s holdings. In a historical-simulation model, identify the current exposure record and how observed factor changes are applied. Keep nonlinear repricing and any approximation explicit.
Choose an empirical quantile convention
For an equal-weight record of n losses sorted ascending, this page’s lower-quantile convention selects rank ceil(nc), counting from one. The public discrete tool can inspect an already supplied loss record; it does not reconstruct current holdings or run a historical repricing engine.
Inspect an original equal-weight record
For twenty equally weighted hypothetical losses 1 through 20, 95% confidence gives rank ceil(20×0.95)=19 and VaR 19. The worst 5% mass is the final observation, giving expected shortfall 20. These invented values are not market data.
| Confidence | Lower-quantile rank | VaR | Expected shortfall |
|---|---|---|---|
| 90% | 18 | 18 | 19.5 |
| 95% | 19 | 19 | 20 |
Review data before calling it evidence
Record dates, missing-data handling, weights, horizon, pricing basis and sample convention. An observed record can omit severe events or reflect a different regime. Neither a correct rank nor a large sample guarantees future tail coverage.