Portfolio Value at Risk (Parametric VaR) & Expected Shortfall Calculator

Quantify worst-case portfolio loss threshold at 95% and 99% confidence.

Parametric Value at Risk (VaR)
USD 14,746.13
Horizon Volatility (σ_T) 3.59 %
Conditional VaR (Expected Shortfall) USD 18,432.67
1-Day VaR Equivalent USD 4,663.14
Inputs
Amounts are treated in the selected currency; no foreign-exchange conversion is applied.
USD
Total marked-to-market portfolio value.
%
Annualized portfolio standard deviation (%).
days
Risk horizon in trading days (e.g., 1-day or 10-day Basel VaR).
z
Confidence Z-score (1.645 for 95%, 2.326 for 99%).
Results & Graph
Parametric Value at Risk (VaR)
USD 14,746.13
Horizon Volatility (σ_T)
3.59 %
Conditional VaR (Expected Shortfall)
USD 18,432.67
1-Day VaR Equivalent
USD 4,663.14

Parametric Value at Risk (VaR)

Graph 1 • Portfolio Value Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 USD 11.9k USD 23.9k USD 50%: 7,373.07 USD 7.4k 50% 75%: 11,059.6 USD 11.1k 75% 100%: 14,746.13 USD 14.7k 100% 125%: 18,432.67 USD 18.4k 125% 150%: 22,119.2 USD 22.1k 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Parametric Value at Risk (VaR) USD 14,746.13 Horizon Volatility (σ_T) 3.59 % Conditional VaR (Expected Shortfall) USD 18,432.67 1-Day VaR Equivalent USD 4,663.14
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Parametric Value at Risk (VaR)USD 14,746.13Horizon Volatility (σ_T)3.59 %Conditional VaR (Expected Shortfall)USD 18,432.671-Day VaR EquivalentUSD 4,663.14
Summary: Over a 10-day trading horizon at z=1.645, portfolio VaR is USD 14,746.13 (5.9% of portfolio).
Summary: Over a 10-day trading horizon at z=1.645, portfolio VaR is USD 14,746.13 (5.9% of portfolio).
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Formula & Mathematical Methodology: Value at Risk (VaR) Mathematical Formula

VaR95 = Portfolio × z0.95 × (σannual / √252) × √HoldingDays
VaR_95 = Portfolio × z_0.95 × (σ_annual / √252) × √HoldingDays
  • portfolioValue: Portfolio Value (USD)
  • annualVolatilityPct: Annual Volatility Pct (%)
  • holdingPeriodDays: Holding Period Days (days)
  • zScoreConfidence: Z Score Confidence (z)

Rounding: Intermediate calculations retain full IEEE-754 floating-point precision; displayed currency and ratios round to 2 decimal places.

Worked Example: Benchmark Scenario: Value at Risk (VaR)

Quantify worst-case portfolio loss threshold at 95% and 99% confidence.

  1. Enter the portfolio, option, lease, or corporate balance-sheet inputs.
  2. Evaluate the core equation: VaR_95 = Portfolio × z_0.95 × (σ_annual / √252) × √HoldingDays.
  3. Inspect the primary valuation output, risk metrics, and 3 visual SVG graphs.
Result: Computes Value at Risk (VaR) using VaR_95 = Portfolio × z_0.95 × (σ_annual / √252) × √HoldingDays.

Frequently Asked Questions

How does the Portfolio Value at Risk (Parametric VaR) & Expected Shortfall Calculator calculate results?

It evaluates VaR_95 = Portfolio × z_0.95 × (σ_annual / √252) × √HoldingDays directly in your browser and updates the three domain SVG visualizations immediately as you adjust any input.

Can I compare multiple investment or financing scenarios side by side?

Yes. Click "Compare (0/3)" in the results toolbar to pin up to three scenarios side by side.

Are my financial numbers kept private?

Yes. All calculations run 100% locally in your browser with zero server uploads.

Finance & Investing · Quantitative Investing & Derivatives

Portfolio Value at Risk (Parametric VaR) & Expected Shortfall Calculator: inputs, method, and how to read the result

Quantify worst-case portfolio loss threshold at 95% and 99% confidence.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Display Currency: Amounts are treated in the selected currency; no foreign-exchange conversion is applied.
  • Portfolio Value: Total marked-to-market portfolio value.
  • Annual Volatility Pct: Annualized portfolio standard deviation (%).
  • Holding Period Days: Risk horizon in trading days (e.g., 1-day or 10-day Basel VaR).

What the calculation includes

With the default values shown, Parametric Value at Risk (VaR) is USD 14,746.13. The calculation follows Value at Risk (VaR) Mathematical Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Portfolio Value from 250,000 USD to 275,000 USD changes Parametric Value at Risk (VaR) from USD 14,746.13 to USD 16,220.75. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard quantitative finance, GAAP/IFRS operating ratios, and continuous/periodic compounding conventions.
  • For educational and analytical modeling only; consult a licensed CPA, CFA, or fiduciary advisor before executing tax or derivative transactions.

Scope: Global Financial & Corporate Valuation Standard Check the assumptions and limitations against your situation before relying on the estimate.

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