Expected Shortfall (ES), also called Conditional Value at Risk (CVaR), is a risk measure that quantifies the average of losses in the tail of a distribution beyond the VaR threshold at a given confidence level. While VaR identifies a loss cutoff, ES describes the size of losses when extreme events occur, providing a fuller picture of tail risk.
ES is used to assess downside risk in portfolios. It can be estimated from historical data, assumed parametric distributions, or simulations. At level alpha, ES represents the conditional expectation of losses given that losses exceed VaR at that level, effectively the mean of the worst alpha percent of outcomes. Because it takes into account the magnitude of extreme losses, ES is often used in risk budgeting, capital planning, and stress-testing exercises. It is also used in portfolio optimization to impose tail-risk constraints and compare strategies on their tail performance.
ES is a coherent risk measure, satisfying properties such as subadditivity and translation invariance, and it changes smoothly as the loss distribution shifts. Common practice reports ES at common confidence levels such as 95% or 99%, reflecting assumptions about potential adverse market moves.
Example: If a portfolio's 95% ES is $8 million, this reflects the average loss among the worst 5% of market outcomes (beyond the 95% VaR threshold).
Value at Risk (VaR) · Tail risk · Conditional Value at Risk (CVaR) · Risk management · Stress testing · Capital adequacy