Historical Value at Risk Calculator
A historical Value at Risk calculator locates the entered P&L sample’s lower-tail percentile and expresses a negative threshold as a positive loss magnitude. It describes one historical sample under a disclosed percentile rule; it is not a maximum-loss limit or a forecast.
Enter one consistent P&L sample
Use signed amounts from one currency, observation frequency and clean-or-dirty P&L convention. Losses are negative, gains positive and zeros remain in the sample.
Every amount must use this same currency.
The lower-tail probability is one minus this entered confidence.
Enter 20 to 5,000 values separated by new lines, commas, spaces or semicolons. Example: -480, -310, 25, 80.
Historical lower-tail threshold
Entered Market Risk Diagnostics 1.0.0.
| Ordered rank | Signed P&L | Position vs percentile |
|---|
How historical Value at Risk is calculated
Percentile rank = q × (N + 1)
Historical VaR loss = max(0, −Lower-tail P&L percentile)
Version 1.0.0 sorts a copy of the entered signed P&L values from the largest loss to the largest gain. It then applies the NIST q(N + 1) order-statistic convention, interpolating between adjacent observations when the rank is fractional and clipping only at the sample endpoints.
The percentile remains visible as a signed P&L amount. When it is negative, the calculator reports its absolute value as the positive historical VaR loss magnitude. If the entered lower tail contains no loss, the loss magnitude is zero rather than a negative risk amount.
Worked example from the audited fixture
The audited fixture contains 20 signed USD observations from −480 through +250 and selects 95% confidence, so the lower-tail probability is 5%.
- The NIST rank is 0.05 × (20 + 1) = 1.05. Interpolating 5% from the worst observation (−480) toward the second-worst (−310) gives −471.50.
- Historical VaR is therefore USD 471.50 as a positive loss magnitude. One entered observation lies strictly below the interpolated percentile.
Reproduce it: select “Load audited example” above to use the immutable Batch 34 values.
How to interpret the result
- USD 471.50 means the selected historical sample’s disclosed 5th-percentile P&L is −USD 471.50 under this exact estimator.
- It does not mean losses are capped at USD 471.50. Historical VaR deliberately says little about the size of observations beyond the threshold.
- Changing the sample window, observation frequency, position set, cost treatment or percentile convention can change the result.
Assumptions and limits
- The model does not retrieve prices, positions, broker statements or exchange rates.
- Every input must use one currency and one clean-or-dirty P&L convention; the tool cannot detect mixed units.
- No parametric-normal, Monte Carlo, volatility scaling, holding-period conversion or annualization is performed.
- The sample may omit stress events, changing exposure, gaps, liquidity effects and future market conditions.
- The output is not a capital requirement, maximum loss, safe-risk level, signal or recommendation.
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 locates a selected lower-tail percentile in the entered signed P&L sample and expresses a negative threshold as a positive loss magnitude.
- Enter 20 to 5,000 signed P&L observations in one currency and convention, then select confidence greater than 50% and below 100%.
- Version 1.0.0 sorts the values and uses the disclosed NIST q times N plus one rank with interpolation and endpoint clipping.
- The lower-tail P&L percentile is shown signed; when it is negative, its absolute value is displayed separately as the loss magnitude.
- No. Losses can exceed the percentile threshold, and events absent from the entered sample are not represented.
- No. Version 1.0.0 is an empirical historical calculation and performs no normal, Monte Carlo or volatility-scaled estimation.
- No. Use one observation frequency, currency, position basis and clean-or-dirty cost convention throughout the entered sample.
- The output describes the entered sample only and creates no safe level, capital rule, forecast, signal or recommendation.
Sources and methodology
- Reserve Bank of Australia — Value at Risk — Primary discussion of historical-simulation VaR using historical portfolio value changes.
- NIST — Percentiles — Primary order-statistic and q(N + 1) percentile convention used by version 1.0.0.
Continue the historical loss-tail review
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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