Value at risk (VaR)

Value at risk estimates the maximum loss a portfolio would be expected not to exceed over a given time horizon, at a stated confidence level. A one-day 95% VaR of $1 million means that, under the model's assumptions, losses should exceed $1 million on no more than 5% of days.

VaR can be estimated several ways: the historical method resamples actual past returns, the variance-covariance method assumes returns are normally distributed and uses standard deviation, and Monte Carlo simulation generates many simulated paths. Unlike expected shortfall, which averages the losses in the worst-case tail beyond the VaR threshold, VaR only marks the boundary of that tail and says nothing about how bad losses get beyond it.

VaR is widely used in bank risk management and regulatory capital requirements because it compresses a full distribution of possible outcomes into one number, and it is often reported alongside maximum drawdown and volatility. Its best-known pitfall is exactly that boundary problem: two portfolios can have identical VaR while one has a far worse worst-case outcome hiding just past the threshold, which is why regulators and risk managers increasingly pair VaR with expected shortfall rather than relying on it alone.