CVaRR

CVaRR stands for Conditional Value at Risk. It is a risk management measure used to quantify the expected loss on an investment or portfolio, given that the loss exceeds a certain threshold, typically the Value at Risk (VaR). While VaR estimates the maximum potential loss at a given confidence level over a specific time horizon, CVaRR provides a more comprehensive view of tail risk. It answers the question: "If things go badly, how bad will they be on average?"

To calculate CVaRR, one first determines the VaR. For example, if the 95% VaR is $1 million, it means there is a 5% chance of losing more than $1 million. CVaRR then considers the average of all possible losses that fall into that worst 5% tail. Therefore, CVaRR is always greater than or equal to VaR. This makes CVaRR a more conservative measure of risk, as it accounts for the severity of extreme losses, not just their probability.

Financial institutions commonly use CVaR for stress testing and risk budgeting. It is particularly useful for portfolios with skewed return distributions where large, infrequent losses can have a significant impact. Unlike VaR, which can sometimes be misleading by ignoring the magnitude of losses beyond the threshold, CVaR provides a more robust understanding of potential downside risk. Its coherent properties, such as subadditivity, also make it a preferred choice in many regulatory frameworks.