Value at Risk

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 loss$L$ exceeds $K$ is at least $\alpha$.

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

See also

• Economic Capital
• Expected Shortfall
• Value at Risk
• Credit Value at Risk