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Value at Risk Calculator

Estimate a single-position VaR amount using a normal parametric model or a historical return sample.

VaR inputs

Method

Position value

Confidence

Horizon (days)

Daily sigma σ

Expected return μ

parametric VaR = (z × σ × sqrt(t) - μ) × V

VaR result

Value at Risk—

VaR percent—

z value—

Scaled sigma—

Confidence—

VaR is not the maximum possible loss.

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Quick answer

Parametric VaR uses VaR = (z × sigma × sqrt(t) - mu) × position value. At 95% confidence, z = 1.645. For a $1,000,000 position with daily sigma 2% and one-day horizon, VaR is 1.645 × 0.02 × 1,000,000 = $32,900.

How it works

What VaR means

Value at Risk estimates a loss threshold at a chosen confidence level and horizon. A one-day 95% VaR is a model estimate of the loss level exceeded in the worst 5% tail under the model or sample. VaR is not the maximum possible loss.

Parametric formula

This tool uses the single-tail z table from the clean-room spec:

90% = 1.282, 95% = 1.645, 97.5% = 1.960, 99% = 2.326

The formula is:

sigma_t = sigma × sqrt(horizon days)

VaR = (z × sigma_t - mu) × position value

With mu = 0, a $1,000,000 position, sigma = 0.02, one day and 95% confidence gives $32,900. At 99%, the same inputs give $46,520.

Historical simulation formula

Historical VaR converts each return into position P&L, sorts the P&L values ascending, and takes the loss-tail percentile. This implementation uses linear interpolation: rank = p × (n - 1), then blends between the lower and upper ranked observations.

For returns [-5%, -4%, ..., 4%], a $100,000 position and 90% confidence, the 10th percentile rank is 0.10 × 9 = 0.9. Interpolating between -$5,000 and -$4,000 gives -$4,100, so VaR is $4,100.

Important limitations

VaR is not a maximum loss. Losses beyond the VaR threshold can be much larger.
Normal VaR can understate fat tails. The parametric method assumes a normal return shape and can miss crisis tails.
Do not add separate VaRs for a portfolio. VaR is not subadditive in general, and portfolio VaR needs correlations or a full joint sample.
Historical VaR is sample-bound. It only replays the returns you entered and cannot show regimes absent from the sample.

Frequently asked questions

What does a 95% VaR mean?

It is a model loss threshold for the worst 5% tail over the chosen horizon. It does not say losses cannot exceed that number.

Why is VaR shown as a positive number?

The result is reported as loss amount. Historical mode takes a loss-tail P&L percentile and flips the sign so the displayed VaR is positive.

What z values does the calculator use?

It uses the clean-room single-tail table: 90% = 1.282, 95% = 1.645, 97.5% = 1.960 and 99% = 2.326.

How does the historical percentile work?

The tool sorts P&L values ascending and uses linear interpolation with rank = p × (n - 1), where p = 1 - confidence.

Can I add VaR numbers across assets?

No. This tool is single-asset. Portfolio VaR needs the joint distribution or covariance structure; simply adding separate VaRs can be misleading.