Value at Risk (VaR)
The maximum loss not expected to be exceeded over a given time horizon at a chosen confidence level, e.g. 95% or 99%.
Parametric VaR = Portfolio Value × Z-score × Daily Volatility
Value at Risk (VaR) estimates the worst probable loss on a portfolio over a specific time period at a given confidence level. A 1-day 95% VaR of $1,000 means there is a 5% chance of losing more than $1,000 in a single day.
VaR is widely used in institutional risk management but has important limitations: it says nothing about the size of losses beyond the threshold (tail risk), and it tends to understate risk in market crises when correlations spike.
- Parametric VaR assumes normally distributed returns — dangerously wrong in fat-tailed markets.
- Historical VaR replays actual past returns — better, but blind to new regimes.