# 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
- A Confidence Level

Given the confidence level , the VaR of calculated portfolio loss at the confidence level is the smallest number such that the Probability that the loss exceeds is at least .