Value at risk

Value at risk (VaR) is the maximum loss a portfolio is expected to suffer over a set time horizon at a given confidence level, expressed as one euro figure.

What it is

See it move

Loading infographic...

A €5,000,000 portfolio has daily returns with a 1.2% standard deviation. At 95% confidence, the z-score is 1.645. One-day value at risk multiplies the three together: 1.645 × 1.2% × €5,000,000 = €98,700 — the most the portfolio should lose on 95% of days.

The formula

LaTeX

VaR = z \times \sigma \times V

Variables

$V a R$: Value at risk (€)
$z$: Z-score for the chosen confidence level (ratio)
$σ$: Standard deviation of portfolio returns over the horizon (%)
$V$: Portfolio value (€)

The parametric (variance-covariance) estimate of the maximum loss over the chosen horizon, at the confidence level corresponding to z.