Estimate average loss within the selected empirical tail.
It makes the prices, cash flows, rates, time periods, weights, and model conventions explicit so you can inspect an entered scenario without hidden live-market assumptions.
Calculation structure
Follow the stated model and units
Expected shortfall = exposure × negative average return among the worst ceil[(1−confidence)×n] observations.
Visual explanation
See how the inputs become the result
Capital and cash flowstime and rate→entered modelScenario resultChanging one assumption changes the model—not the marketExpected shortfall = exposure × negative average return among the worst ceil[(1−confidence)×n] observations.
Read the estimate correctly
Use the result within its boundaries
At 75% confidence, returns −10%, −5%, 0%, 5%, and exposure 1,000 use the worst one observation and produce expected shortfall 100.
Historical expected shortfall is sample-dependent and does not predict or cap future losses. A gain-only selected tail is floored at zero loss.
Quick guide
How to use this calculator
Enter observations in chronological or paired order exactly as the row help specifies.
Keep all return periods, currencies, weights, and value units consistent.
Review the sample, population, quantile, or compounding convention before interpreting the result.
Calculation method
Calculation method
Expected shortfall = exposure × negative average return among the worst ceil[(1−confidence)×n] observations.
Entered fixed decimals are parsed exactly. Statistical square roots and geometric averages are marked approximate and reject undefined or non-finite cases.
Worked example
Worked example
At 75% confidence, returns −10%, −5%, 0%, 5%, and exposure 1,000 use the worst one observation and produce expected shortfall 100.
Expected shortfall = exposure × negative average return among the worst ceil[(1−confidence)×n] observations.
Supported inputs
Precision and limits
Visible input limits
Lists accept 1–2,000 rows. Each fixed decimal accepts at most 30 digits and 12 decimal places and is capped at an absolute value of 1e12. Formula-specific positive, weight, and probability domains are enforced.
International scope
No currency, exchange, benchmark, security, observation frequency, market-data source, or regulatory risk convention is selected automatically.
Decision boundary
Historical and scenario statistics do not predict returns, measure every risk, cap losses, or recommend an investment.
Calculator-specific assumptions
Historical expected shortfall is sample-dependent and does not predict or cap future losses. A gain-only selected tail is floored at zero loss.
