# Credit Value at Risk

From Open Risk Manual

## 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
- A Confidence Level

Given a confidence level , the CVaR of calculated portfolio loss at the confidence level is the smallest number such that the probability that the loss exceeds is at least .

## 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