Expected Shortfall (ES) / CVaR

VaR has a flaw: It tells you the threshold, but not the severity of the crash.

• VaR: "You won't lose more than ₹10 Lakhs (95% of time)."
• Question: "Okay, but in that bad 5% case, do I lose ₹11 Lakhs or ₹50 Lakhs?"
• VaR Answer: "I don't know."

Enter Expected Shortfall (ES), also known as Conditional VaR (CVaR).

What is Expected Shortfall?

ES is the average of all losses that exceed the VaR threshold.

It answers: "If things do go wrong (i.e., we cross the VaR line), how bad will it be on average?"

Why is ES Better?

1. Sub-Additivity (Coherence): VaR fails a mathematical property called sub-additivity. Sometimes, VaR(A+B) > VaR(A) + VaR(B), which implies diversification increases risk (which is nonsense). ES never violates this.
2. Captures Tail Risk: ES specifically looks at the tail (the crashes) and averages them. It is far more sensitive to "Black Swan" events.

Implementation in Basel IV

Because VaR failed to capture the severity of losses during the 2008 crisis, global regulators (Basel Committee) are moving from VaR to Expected Shortfall for market risk capital calculations.

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