What is Conditional Value at Risk (CVaR)?
Conditional Value at Risk (CVaR), also known as Expected Shortfall, is a risk assessment metric that provides the average of losses that exceed the Value at Risk (VaR) threshold, offering a deeper insight into tail risks. While VaR identifies the maximum loss within a confidence interval, CVaR measures the expected loss when this threshold is breached, giving a more comprehensive view of potential extreme losses in a portfolio.
CVaR Calculation: CVaR is calculated by taking the average of the losses that exceed the VaR level at a given confidence interval. The formula for CVaR is:
CVaR = E[Loss | Loss > VaR] Here, E[Loss] represents the expected loss, and the condition Loss > VaR denotes that the losses are greater than the VaR threshold.
CVaR provides a clearer understanding of the severity of worst-case losses and is useful for managing tail risks that VaR might underestimate.
CVaR Calculation: CVaR is calculated by taking the average of the losses that exceed the VaR level at a given confidence interval. The formula for CVaR is:
CVaR = E[Loss | Loss > VaR] Here, E[Loss] represents the expected loss, and the condition Loss > VaR denotes that the losses are greater than the VaR threshold.
Understanding Conditional Value at Risk
CVaR enhances risk management by focusing on the tail end of the loss distribution:- Tail Risk Measurement: CVaR captures the risk of extreme losses beyond the VaR estimate, offering a clearer understanding of tail risk, especially in highly volatile markets or during financial crises.
- Improved Risk Assessment: By considering the average of the worst losses, CVaR provides a more conservative estimate of risk than VaR, which only looks at the threshold value.
- Example: If the 1-day VaR for a portfolio is $100,000 at a 95% confidence level, and the average of the losses beyond this $100,000 threshold is $150,000, the 1-day CVaR would be $150,000.
Example Calculation
Suppose you are managing a portfolio with a 1-day VaR of $50,000 at a 99% confidence level. If the average loss on days when losses exceed $50,000 is $80,000, the 1-day CVaR is $80,000. This means that on the worst 1% of trading days, the average loss is expected to be $80,000.CVaR provides a clearer understanding of the severity of worst-case losses and is useful for managing tail risks that VaR might underestimate.