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Expected Shortfall (ES) - Conditional Value at Risk

Conditional Value at Risk (CVaR) and Expected Shortfall

Risk ModelingAll Asset Classes

Key Insights

ES measures the average loss beyond VaR, providing complete tail risk information
Formula: ES = E[L | L > VaR] - expected loss given loss exceeds VaR threshold
Always ≥ VaR for the same confidence level and provides more information about extreme losses
Coherent risk measure with better mathematical properties than VaR for optimization
Two main calculation approaches: empirical (historical data) and parametric (analytical formula)
Increasingly used in regulatory frameworks (Basel III) for capital adequacy requirements
More complex to calculate and interpret than VaR but provides superior risk information
Sensitive to model assumptions and data quality, especially in distribution tails
Best used alongside VaR for comprehensive risk assessment and stress testing
Particularly valuable for tail risk management and extreme scenario planning

Understanding Expected Shortfall

Expected Shortfall (ES) addresses a significant limitation of Value at Risk (VaR): while VaR tells us the threshold of potential loss at a given confidence level, it doesn't reveal how bad losses could be beyond that threshold. ES fixes this problem by measuring the average loss beyond VaR.

Expected Shortfall is the average loss beyond VaR, measuring the expected loss in the tail of a distribution beyond a certain quantile level (e.g., 95%), providing insight into potential losses exceeding the Value at Risk.

For example, if a portfolio's 1-day VaR is $1 million at 95% confidence, ES tells us the expected loss amount in the remaining 5% of worst-case scenarios, making it a more comprehensive tail risk measure.