Value at Risk (VaR) Calculator
Calculate portfolio VaR with the parametric method.
Enter value, daily volatility, confidence level, and holding period to find your maximum expected loss.
Value at Risk (VaR)
Value at Risk (VaR)
Value at Risk is the maximum loss a portfolio is expected to suffer over a given time period, at a specified confidence level, under normal market conditions.
Parametric VaR Formula:
VaR = Portfolio Value × z × σ_daily × √t
| Variable | Meaning |
|---|---|
| z | Z-score from the confidence level |
| σ_daily | Daily standard deviation of portfolio returns (%) |
| t | Holding period in trading days |
Z-scores by confidence level:
| Confidence | Z-score | Interpretation |
|---|---|---|
| 90% | 1.282 | 1 in 10 days expected to exceed this loss |
| 95% | 1.645 | 1 in 20 days expected to exceed this loss |
| 99% | 2.326 | 1 in 100 days expected to exceed this loss |
Example:
- Portfolio: $1,000,000
- Daily volatility: 1.5%
- Confidence: 95%, Holding period: 1 day
- VaR = $1,000,000 × 1.645 × 0.015 × √1 = $24,675
- Interpretation: On 95% of days, losses will not exceed $24,675
Scaling VaR across time:
VaR scales with the square root of time (for normally distributed returns).
10-day VaR = 1-day VaR × √10
Limitations of parametric VaR:
- Assumes normal distribution of returns — real markets have fat tails (larger losses happen more often than the model predicts)
- Underestimates risk during market stress events (2008 crisis, COVID crash)
- Does not tell you what losses look like beyond the confidence threshold
- Historical VaR and Monte Carlo VaR are alternatives that handle fat tails better
Regulatory use: Banks use 99% confidence, 10-day VaR under Basel III capital requirements. This calculator uses the parametric (variance-covariance) method.