Difference between revisions of "Value at Risk"
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== Definition == | == Definition == | ||
− | '''Value at Risk''' (VaR) is a [[Risk Measure]] that aims to capture the downside [[Economic Value | value]] risk of a Market Portfolio. | + | '''Value at Risk''' (VaR) is a [[Risk Measure]] that aims to capture the downside [[Economic Value | value]] risk of a Market [[Portfolio]] (a collection of financial instruments that can be marked-to-market). |
== Formula == | == Formula == | ||
− | VaR is a quantile [[Risk Measure]] and requires the specification of | + | 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 <math>L=\sum L_{i}</math> | + | * An aggregate (Portfolio) PnL (Profit and Loss) random variable that is constructed as the sum of potential individual market losses <math>L=\sum L_{i}</math> |
* A [[Confidence Level]] <math>\alpha</math> | * A [[Confidence Level]] <math>\alpha</math> | ||
− | Given | + | 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\} = F^{-1}_Y(1-\alpha).</math> | ||
== See also == | == See also == |
Revision as of 11:32, 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 .