Credit Value at Risk

Definition

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

Formula

CVaR is a quantile Risk Measure and requires the specification of

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

Given a confidence level $\alpha \in (0,1)$, the CVaR 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 $\alpha$.

Usage

Credit Value at Risk is used in conjunction with a Credit Portfolio Model, a computational approach for the generation of future scenarios including different risk realizations.

Issues and Challenges

• CVaR has been developed largely as a mirror of the Value at Risk measure for portfolios of marketable securities, yet the more illiquid nature of credit portfolios forces substantial further assumptions and associated Model Risk
• CVaR inherits the weaknesses of VaR frameworks

See also

• Economic Capital
• Monte Carlo Simulation of Credit Portfolios
• Expected Shortfall

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