Value at Risk (VaR) calculator

Value at Risk estimates the loss a position should not exceed over a given horizon at a chosen confidence level. Expected Shortfall is the average loss in the cases where that threshold is breached.

Value at Risk

83,415.53

8.34% of the position

Expected Shortfall: 95,566.21
Volatility over horizon: 3.59%

1. Mathematische Formel & Bewertungsgleichung

σ_horizon = σ_annual × √(days ÷ 252)

VaR = Position × z_α × σ_horizon

Expected Shortfall = Position × σ_horizon × φ(z_α) ÷ (1 − α)

2. Anwendung & Eingabeparameter

Enter the position size, its annualised volatility, the confidence level and the holding horizon in trading days.

Volatility is scaled to the horizon with the square-root-of-time rule, then multiplied by the normal quantile for the confidence level.

3. Modellannahmen & Anwendungsbeschränkungen

Assumes normally distributed returns with zero mean. Real returns have fatter tails, so parametric VaR tends to understate extreme losses.
Single position only; for a portfolio you would need the full covariance matrix.

4. Häufige Fragen & Risikohinweise (FAQ)

Why show Expected Shortfall as well as VaR?

VaR says nothing about how large losses are once the threshold is crossed. Expected Shortfall does, which is why Basel market-risk rules moved to a 97.5% Expected Shortfall measure.

Why 252 days?

252 is the usual number of trading days in a year. Using calendar days would understate daily volatility.

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