Difference between revisions of "Value at Risk"
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Given the confidence level <math>\alpha\in(0,1)</math>, the VaR of calculated portfolio loss <math>L</math> at the confidence level <math>\alpha</math> is the smallest number <math>K</math> such that the [[Probability]] that the loss<math>L</math> exceeds <math>K</math> is at least <math>\alpha</math>. | Given the confidence level <math>\alpha\in(0,1)</math>, the VaR of calculated portfolio loss <math>L</math> at the confidence level <math>\alpha</math> is the smallest number <math>K</math> such that the [[Probability]] that the loss<math>L</math> exceeds <math>K</math> is at least <math>\alpha</math>. | ||
− | :<math>\operatorname{VaR}_\alpha(L)=-\inf\big\{l\in\mathbb{R}:F_L(l)>\alpha\big\} | + | :<math>\operatorname{VaR}_\alpha(L)=-\inf\big\{l\in\mathbb{R}:F_L(l)>\alpha\big\} </math> |
== See also == | == See also == |
Latest revision as of 11:34, 18 March 2024
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 .