Value at Risk (VaR)

By Jarosław Wasiński • Published: Mar 17, 2026 • Updated: Oct 11, 2026

Value at Risk (VaR) is a loss quantile estimated for a chosen horizon and confidence level under a stated model. It is not the worst possible loss or the average of losses beyond the threshold. A one-day 95% VaR of $1,000 means the model assigns about 5% probability to a larger daily loss, not that such losses are impossible.

Example. Illustrative model: a one-day 95% VaR of $1,000 describes a loss threshold exceeded with approximately 5% model probability. A $3,000 loss is still possible. The figure does not say how large losses beyond $1,000 will be.

Specify the model

State the horizon, confidence level, portfolio, data window and estimation method. Changes in volatility, dependence and liquidity can make historical estimates misleading. Backtest exceedances without treating their expected frequency as a guarantee for any short sequence.

Beyond the threshold

Expected shortfall describes an average in the loss tail under its stated convention; stress tests examine specified scenarios. These answer different questions from VaR. None removes uncertainty about events outside the model.

Confidence and repeated observations

A 95% model quantile does not imply exactly five exceedances in every block of 100 days. Sampling variation, dependence and model error matter. A continuous normal-loss model would use a different quantile for 99%; changing confidence is a change of question, not a guarantee of complete tail coverage.

FAQ

Is VaR the largest possible loss?

No. It is a modelled quantile. Losses beyond the threshold remain possible and can be much larger.

Can a 95% daily VaR be multiplied by ten to get ten-day VaR?

Not generally. Horizon scaling needs explicit assumptions about returns, dependence and the model; even square-root scaling is conditional.

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