Value at Risk

Definition

Value at Risk (VaR) is a Risk Measure that aims to capture the downside value risk of a Market Portfolio.

Formula

VaR is a quantile Risk Measure and requires the specification of

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

Given a 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 $\alpha$.

See also

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