What is Conditional Value at Risk (CVaR)?
– Definition: Conditional Value at Risk (CVaR), also called expected shortfall (ES), is the average loss that occurs in the worst tail of a loss distribution beyond a chosen Value at Risk (VaR) cutoff. In plain terms: if VaR tells you a loss threshold that will not be exceeded with, say, 95% probability, CVaR tells you the average loss if that 5% worst-case event happens.
Why use CVaR instead of VaR?
– VaR (Value at Risk) is a quantile: it gives a loss level L such that losses exceed L only (1 − α) of the time for confidence level α. VaR does not describe how large losses are once that threshold is breached.
– CVaR captures tail severity. For portfolios with fat tails or nonlinear payoff structures (options, derivatives, small-cap stocks, engineered products), CVaR gives a clearer picture of extreme losses.
– CVaR is coherent (it satisfies