Value at Risk Calculator
Putting a Dollar Figure on "How Bad Could It Get?"
Value at Risk answers a specific question: over a given time horizon, how much could this portfolio plausibly lose, with a stated level of confidence? It doesn't predict the worst possible outcome — it estimates a loss threshold that shouldn't be exceeded except in the tail of outcomes beyond the chosen confidence level.
The Formula
This is the parametric (variance-covariance) method. Z is the z-score for the chosen confidence level, σ is the portfolio's standard deviation per period (as a decimal), and T is the time horizon in periods. The square root of time scales single-period volatility up to the chosen horizon, assuming returns are independent day to day.
Z-Scores Used
| Confidence Level | Z-Score |
|---|---|
| 90% | 1.2816 |
| 95% | 1.6450 |
| 99% | 2.3263 |
$100,000 Portfolio, 2% Daily Volatility
| Confidence | VaR (1 day) |
|---|---|
| 90% | $2,563.20 |
| 95% | $3,290.00 |
| 99% | $4,652.60 |
Extending the same portfolio to a 10-day horizon at 95% confidence raises VaR to $10,403.89 — risk scales with the square root of time, not linearly.
Where This Is Used
- Risk limits — trading desks and funds often cap positions based on a maximum acceptable VaR.
- Regulatory capital — banks use VaR-based models as part of regulatory capital requirement calculations.
- Portfolio monitoring — tracking VaR over time flags when a portfolio's risk profile is drifting higher.
How to Use This Calculator
- Enter the Portfolio Value.
- Enter the Portfolio Standard Deviation per period, as a percentage.
- Enter the Time Horizon in days.
- Select the Confidence Level — 90%, 95%, or 99%.
- Select Calculate to see the estimated Value at Risk.
Related Calculations
Need the standard deviation input first? Calculate it with the Risk Calculator, or check a multi-asset portfolio's combined volatility with the Portfolio Standard Deviation Calculator.