Expected Shortfall Calculator
An Expected Shortfall calculator averages the weighted worst tail of the entered P&L sample at the selected confidence. It shows historical Value at Risk beside that tail mean, while making clear that neither statistic predicts the next loss or captures events absent from the sample.
Enter one consistent P&L sample
Use signed amounts from one currency, observation frequency and clean-or-dirty P&L convention. The calculator weights exactly N × tail probability observations.
Every amount must use this same currency.
The calculator averages the worst one-minus-confidence mass.
Enter 20 to 5,000 values separated by new lines, commas, spaces or semicolons.
Historical weighted tail mean
Entered Market Risk Diagnostics 1.0.0.
| Ordered rank | Signed P&L | Tail weight | Weighted P&L |
|---|
How Expected Shortfall is calculated
Tail total = Worst k complete observations + fractional next observation
Expected Shortfall loss = max(0, −Tail total ÷ Tail mass)
Version 1.0.0 sorts the signed P&L sample from smallest to largest, then uses exactly N times the lower-tail probability as empirical mass. Complete observations receive weight one. If the tail mass is fractional, only that fraction of the next ordered observation is included.
The signed weighted mean and its positive loss magnitude are both shown. The page also applies the shared NIST percentile estimator to display historical VaR as a threshold comparator. Expected Shortfall answers how large the entered tail observations are on average; VaR answers where its threshold sits.
Worked example from the audited fixture
The audited fixture contains the same 20 signed USD observations and selects 95% confidence, producing a 5% tail.
- Tail mass is 20 × 0.05 = exactly one observation. The worst entered P&L is −USD 480, so its weight is one and the signed tail mean is −USD 480.
- Expected Shortfall is therefore USD 480 as a loss magnitude. The separately interpolated historical VaR comparator is USD 471.50.
Reproduce it: select “Load audited example” above to use the immutable Batch 34 values.
How to interpret the result
- Expected Shortfall includes loss severity beyond the selected VaR threshold, so it can reveal information that the threshold alone omits.
- A larger loss magnitude than VaR is expected when the entered lower tail contains losses, but neither number is a maximum-loss estimate.
- Small or unrepresentative samples make the tail depend heavily on a few observations. Review the visible weights instead of treating the result as stable.
Assumptions and limits
- The model uses an empirical sample and makes no normal-distribution assumption.
- The chosen weighted empirical estimator is disclosed because Expected Shortfall implementations can differ at sample boundaries.
- The tool does not model changing positions, liquidity horizons, portfolio revaluation, stress calibration or currency conversion.
- Clean and dirty P&L, frequencies and currencies must not be mixed.
- No capital requirement, future-loss probability, compliance conclusion, grade, signal or recommendation is produced.
Value at Risk vs Expected Shortfall vs VaR backtesting
These tools share a signed-P&L vocabulary but should not be substituted for one another. VaR locates a threshold, Expected Shortfall summarizes tail severity, and backtesting checks whether previously produced limits had the entered exception frequency.
| Measure | Evidence unit | Question answered | Main boundary |
|---|---|---|---|
| Historical VaR | One signed P&L sample | Lower-tail threshold | Not a maximum-loss guarantee. |
| Expected Shortfall | Same signed P&L sample | Weighted lower-tail mean | Not a future expected-loss forecast. |
| VaR backtesting | Chronological paired P&L and VaR limits | Exception coverage | Unconditional frequency only. |
Frequently asked questions
- It averages the weighted worst one-minus-confidence mass of the entered signed P&L sample.
- No. VaR locates a lower-tail threshold; Expected Shortfall summarizes the average entered P&L within the selected tail.
- Complete worst observations receive weight one and only the required fraction of the next ordered observation enters the tail mean.
- The signed value preserves the original P&L direction, while the separate positive loss magnitude is easier to compare with VaR.
- No. It applies a disclosed weighted empirical estimator directly to the entered sample.
- At high confidence, only a few worst observations may carry the tail, so one value can materially change the result.
- No. Expected is the statistical measure name; this page does not forecast a future loss or probability.
- No. The calculator omits portfolio revaluation, liquidity horizons, stress calibration and supervisory rules and makes no compliance conclusion.
Sources and methodology
- Bank of England — Market risk and Expected Shortfall — Primary explanation that ES considers both size and likelihood beyond a confidence threshold.
- Basel Committee — Fundamental review of the trading book — Primary rationale for moving from VaR toward Expected Shortfall to capture tail risk.
Compare threshold, tail and drawdown measures
Verify the records behind your entered P&L
Before interpreting a loss-tail statistic, confirm that the account statement or platform history uses the currency, observation horizon, open-position treatment and trading-cost convention you selected. Do not mix gross and net outcomes or values converted at different rates.
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Review available statements, history exports and instrument specifications for the account used.
Check XM termsFXOpen
Verify statement currency, costs and position-history conventions before entering values.
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