Value at Risk

From Open Risk Manual

Definition

Value at Risk (VaR) is a Risk Measure that aims to capture the downside value risk of a Market Portfolio (a collection of financial instruments that can be marked-to-market).

Formula

VaR is a quantile Risk Measure and requires the specification of:

  • An aggregate (Portfolio) PnL (Profit and Loss) random variable that is constructed as the sum of potential individual market losses L=\sum L_{i}
  • A Confidence Level \alpha


Given the confidence level \alpha\in(0,1), the VaR of calculated portfolio loss L at the confidence level \alpha is the smallest number K such that the Probability that the lossL exceeds K is at least \alpha.

\operatorname{VaR}_\alpha(L)=-\inf\big\{l\in\mathbb{R}:F_L(l)>\alpha\big\}

See also