Value at Risk (VaR)
The maximum expected loss at a given confidence level — but doesn't tell you how bad the tail is.
VaR estimates the worst-case loss over a time horizon at a specified confidence level. For example, a 95% 1-day VaR of $100,000 means there's a 5% chance of losing more than $100,000 tomorrow. Critical limitation: VaR tells you the threshold, but not how severe losses beyond that threshold could be. A portfolio with $100k VaR could lose $101k or $1 million in the worst 5% of outcomes — VaR doesn't distinguish. This is why CVaR (Expected Shortfall) is often used alongside VaR — it measures the average loss in the tail. VaR is widely used for regulatory capital (Basel III), risk limits, and reporting, but should never be the only risk metric. Use it with stress tests, max drawdown, and scenario analysis.
Formula