CVaR (Conditional Value at Risk), also called Expected Shortfall, is the average loss in the worst-case scenarios beyond the VaR threshold — it answers 'how bad is the damage when things go really wrong?'
While VaR tells you the loss threshold at a given confidence level, CVaR tells you the average loss in the scenarios that breach that threshold. If 1-day 95% VaR is ₹50,000, CVaR is the average loss on those 5% of worst days — which might be ₹1,00,000. CVaR is considered a more complete risk measure than VaR because it captures tail risk (the severity of extreme losses, not just their probability). It is a 'coherent' risk measure and is increasingly preferred in regulatory frameworks globally.
VaR says: 'On bad days, you'll lose more than ₹50,000.' CVaR says: 'On those bad days, your average loss will actually be ₹95,000.' CVaR is the answer to 'when the worst happens, how bad is it on average?' This is more useful for tail-risk management. During a Black Swan event (2008 financial crisis, COVID crash), VaR was breached every day — CVaR captured the actual magnitude of devastation.
Calculate VaR at the desired confidence level.
CVaR = Average of all losses that exceed the VaR threshold.
For 95% confidence: CVaR = average loss of the worst 5% of scenarios.
CVaR ≥ VaR always (it's the average of the tail, including the VaR boundary).
Preferred by sophisticated risk managers and regulators for capturing tail risk.
CVaR(α) = E[Loss | Loss > VaR(α)]