Value-at-Risk
One number summarizing tail loss, computed parametrically, historically, or by simulation.
Value-at-risk compresses a portfolio’s loss distribution into one number: the loss threshold not exceeded with a stated confidence, typically 99 percent over one or ten trading days. Three families compute it. Parametric, or variance-covariance, VaR assumes jointly normal returns and scales the standard deviation by a normal quantile. Historical simulation revalues today’s book against actual past returns, keeping fat tails and option nonlinearity without distributional assumptions. Monte Carlo simulates thousands of hypothetical paths and reprices the book on each, handling path-dependent derivatives. VaR became the regulatory standard because it is simple, aggregable, and auditable, but its blind spots are famous, and the next node explains them.