Quantitative Risk & Treasury Lab

Value at Risk (VaR) Lab

Calculate Value at Risk (VaR), Expected Shortfall (CVaR), parametric tail risk, and capital reserve requirements at 95% and 99% confidence in a free lab.

VaR Model Risk Breakdown VaR Theory FAQ

Portfolio Risk Presets

Load benchmark treasury risk profiles.

Step 1: Define Portfolio Capital & Volatility Parameters

Portfolio Value & Risk Inputs

Portfolio Assets & Expected Return

$
Total capital or asset base subjected to market/credit risk.
%
Mean annual drift rate ($mu$).

Volatility & Time Horizon

%
Annual standard deviation of asset price returns ($sigma$).
10d (Basel), 30d, 252d (1yr).
Value at Risk (VaR)
$136,750.45
2.74% of Portfolio (99% Conf, 10d)
Expected Shortfall (CVaR)
$156,712.18
3.13% Expected Loss Beyond VaR
Prudential Capital Reserve
$180,219.01
3.60% Liquidity Capital Buffer
Horizon Volatility ($σ\sqrt{t}$)
1.20%
Annual Vol: 6.0% (252-day scaled)

Quantitative Risk & Capital Adequacy Audit

Risk & Capital Metric Calculated Value Prudential Definition & Standard

Corporate Risk & Treasury

Mastering Value at Risk (VaR)

Value at Risk (VaR) answers the fundamental executive question: "What is the maximum dollar loss our business could suffer over a given period under normal market conditions at a 99% probability?"

  • Time Scaling ($sqrt{t}$): Volatility grows with the square root of holding duration, allowing short-term daily volatility to translate into multi-week regulatory liquidity horizons.
  • Expected Shortfall (CVaR): Because VaR does not capture the severity of extreme tail exceedances ("black swans"), CVaR computes the expected loss conditional on exceeding VaR.
  • Capital Adequacy Buffer: Corporate treasuries maintain liquidity buffers calibrated to CVaR to ensure ongoing payroll, debt service, and operating continuity.

Stress test operating cash flow in the Resilience Stress-Test Lab.

Quantitative Risk Formulas

Essential risk formulas

Scaled Volatility = σ × √(Days ÷ 252)

Parametric VaR = Portfolio Value × ( Z_α × Scaled Vol - Mean Return )

Expected Shortfall (CVaR) = Portfolio Value × ( [ϕ(Z_α) ÷ (1 - α)] × Scaled Vol - Mean Return )

Prudential Capital Reserve = CVaR × 1.15

Evaluate annual loss exposure in the Risk Matrix & ALE Lab.

FAQ

Value at Risk and portfolio risk questions

What is Value at Risk (VaR)?

Value at Risk (VaR) is a quantitative risk metric that estimates the maximum loss expected on a portfolio or business treasury over a specific time horizon at a given statistical confidence level (such as 95% or 99%).

What is Conditional Value at Risk (CVaR) or Expected Shortfall?

Conditional Value at Risk (CVaR), also called Expected Shortfall (ES), measures the average expected loss in the extreme tail cases where losses exceed the VaR threshold. It is a coherent risk measure that captures severe tail risk.

How does time horizon scale in VaR?

Under the assumption of independent returns, portfolio volatility scales with the square root of time (sqrt(t)). A 10-day volatility is approximately sqrt(10) times the 1-day volatility.

What is a Prudential Capital Reserve Buffer?

A Prudential Capital Reserve Buffer is the recommended liquidity cushion set aside by risk committees to absorb CVaR tail disruptions without threatening organizational solvency.

Can I export the VaR audit to CSV?

Yes. You can export complete portfolio parameters, VaR loss thresholds, CVaR tail metrics, and capital reserves as a UTF-8 CSV spreadsheet with formula injection defense.

Is this tool certified financial risk management software?

No. This tool provides educational simulations for quantitative risk analysis without certified regulatory compliance or banking warranties.

Continue Exploring Risk & Resilience Tools

Explore our Risk & Resilience Hub, model risk events in the Risk Matrix Lab, calculate bankruptcy risk in the Financial Ratio & Altman Z Lab, or stress test business continuity in the Resilience Stress-Test Lab.