Historical VaR and Expected Shortfall Calculator
Inspect an empirical loss percentile and the average worst-tail loss from an entered return sample.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Convert returns to signed loss fractions, sort ascending for nearest-rank VaR, and integrate the worst empirical tail with fractional boundary weights for expected shortfall.
Loss=−return; VaR=sorted loss[ceil(confidence×n)]; ES=average worst (1−confidence) fraction
Worked example
At 90% confidence for the ten example returns, VaR is 4% and expected shortfall is 8%; on 10000 these are 400 and 800.
Assumptions and input details
2–500 equally weighted observations. Nearest-rank VaR and fractional empirical-tail ES are specified to remove sample-quantile ambiguity. Signed losses remain negative for gains. Horizon equals the observation period; no square-root scaling, distribution fit, regulatory capital or worst possible future loss is claimed. Tiny tails can consist of one observed worst return. No live market data or national tax rules are inferred. Enter consistent amounts in one currency unless explicitly stated otherwise.
References: BIS: market-risk terminology
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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