Conditional value-at-risk (CVaR) is the extended risk measure of value-at-risk that quantifies the average loss over a specified time period of unlikely scenarios beyond the confidence level. For example, a one-day 99% CVaR of $12 million means that the expected loss of the worst 1% scenarios over a one-day period is $12 million. CVaR is also known as expected shortfall.

Practitioners in both risk management and portfolio management are increasingly using CVaR. For example:

• CVaR is replacing VaR for calculating market risk capital in the Fundamental Review of the Trading Book (FRTB) by Basel Committee on Banking Supervision (BCBS).
• CVaR is being adopted for portfolio optimization.

Depending on the asset classes and types of risk exposure, risk managers employ various mathematical techniques to calculate CVaR, including:

• Monte Carlo simulation
• Copula-based portfolio simulation
• Pricing and valuation of financial derivatives
• Econometrics models (e.g., interest rate models and GARCH models)

For more information, see Statistics and Machine Learning Toolbox™, Financial Toolbox™, Financial Instruments Toolbox™, and Risk Management Toolbox™.