Expected Shortfall Calculator

• Loss conversion: Loss_i = −(Position × Return_i)
• Value at Risk: VaR_α = Quantile_α(Loss)
• Expected Shortfall: ES_α = Average(Loss_i | Loss_i ≥ VaR_α)
• Horizon scaling: Return_H ≈ Return × √H (practical approximation)

1. Enter your position value and a confidence level such as 0.95.
2. Select returns or prices. Choose units if using returns.
3. Paste data as comma, space, or newline separated values.
4. Set the time horizon in days for scaled results.
5. Click Calculate. Results appear above the form.
6. Use Download CSV or Download PDF for documentation.

Why Expected Shortfall Improves Tail Risk Measurement

Expected shortfall focuses on the average severity of losses beyond a chosen quantile. Unlike a single threshold, it summarizes how bad outcomes can get when markets move into stressed regimes. This matters when two portfolios share the same VaR but one has heavier tails. In risk governance, ES helps compare strategies with similar day‑to‑day volatility but different downside asymmetry.

Interpreting Confidence, Horizon, and Position Effects

Confidence controls how deep the tail slice becomes. A 0.99 setting typically produces fewer tail scenarios than 0.95, but those scenarios can be larger. The position value converts returns into currency P&L, making results directly usable for limits. Horizon converts a one‑day view into an approximate multi‑day view by scaling returns with √days, supporting quick sensitivity checks.

Data Quality Checks That Change the Result

Historical ES depends on the input distribution. Small samples can understate tail thickness, while stale data can ignore recent volatility clustering. Include enough observations to capture both quiet and turbulent periods. For prices, converting to log returns avoids distortions from level changes. If your series includes outliers, verify they reflect real moves rather than bad prints.

Using Tail Scenario Tables for Control and Review

Tail tables reveal which observations drive the estimate. Risk teams can tag scenarios to events such as earnings surprises, rate shocks, or liquidity gaps. This supports model validation, because the narrative behind extreme losses should be explainable. When tail rows look inconsistent with known history, revisit data cleaning and the chosen horizon.

Operational Reporting with Exports and Thresholds

Export files help create audit trails for risk committees. CSV supports spreadsheets and monitoring dashboards, while the PDF snapshot supports reporting packs. Use consistent confidence settings across desks for comparability, then set escalation triggers based on ES changes rather than single‑day VaR jumps. Over time, tracking ES alongside realized losses improves limit calibration and governance discipline.

1) What does expected shortfall represent?

It is the average loss given that losses have exceeded the VaR threshold at your confidence level. It summarizes tail severity rather than only the cutoff point.

2) Why can two portfolios share VaR but differ in ES?

VaR is a quantile, so it ignores how large losses are beyond the quantile. ES averages those tail losses, so heavier tails produce higher ES even with similar VaR.

3) Should I enter returns or prices?

Use returns if you already have a return series. Use prices if you only have levels; the calculator converts them into log returns before computing P&L and tail metrics.

4) How is the time horizon handled here?

The calculator scales returns by the square root of days as a practical approximation. For products with strong autocorrelation or path dependency, use a dedicated horizon model.

5) What sample size is recommended?

Larger samples produce more stable tail estimates. As a rule, use enough observations so the tail contains multiple scenarios at your confidence level, not just one or two points.

6) What do the CSV and PDF exports include?

They include the key metrics, inputs summary, and tail scenario rows (losses at or above VaR). This supports documentation, reviews, and sharing results with stakeholders.