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.