Value at Risk Z-Score Calculator

Parametric Value at Risk answers one question: assuming normally distributed returns, what loss should not be exceeded at a chosen confidence level? The confidence level fixes a z-score, the z-score times the portfolio's volatility fixes the loss threshold.

This calculator maps confidence to z-score and draws the tail being accepted: 95 percent confidence corresponds to 1.65 standard deviations, 99 percent to 2.33. Applied to a portfolio's daily volatility, the result is the one-day VaR, the loss expected to be exceeded on roughly one day in twenty at 95 percent, one in a hundred at 99.

The assumption is the caveat: real return distributions have fatter tails than the normal curve, so parametric VaR systematically understates extreme risk. That is why practitioners pair it with expected shortfall, the average loss in exactly the cases VaR stops counting.

Background reading: Value at Risk in the Knowledge Hub · All tools