How this calculator works
The model scales expected daily return by the number of observations and daily volatility by its square root. A positive z-score defines the one-sided lower return quantile. VaR is expressed as a loss, so it can be negative if even the chosen adverse quantile implies a gain. It is not a maximum loss: losses can exceed VaR, especially with fat tails, correlated days or changing volatility.
Formula
VaR = portfolio value x [z x daily volatility x sqrt(days) - expected daily return x days]. One-sided z values: 90% = 1.28155157; 95% = 1.64485363; 99% = 2.32634787.
Worked example
At 95% confidence, $100,000 with 1% daily volatility and zero expected return has one-day VaR of $1,644.85. A four-day horizon doubles it to $3,289.71 under independent returns.
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Frequently asked questions
Is VaR the largest possible loss?
No. It is a selected quantile. The model allows worse losses beyond that quantile.
Are days trading days?
Enter the count of return observations, normally trading days. Unit conversion does not infer market holidays.
Why assume normal returns?
It gives a simple parametric estimate. Historical simulation or heavier-tailed models may be more appropriate for some portfolios.