Expected shortfall (CVaR)

A risk measure equal to the average loss across the worst-tail outcomes — say the worst 5% — so unlike a single percentile it captures how bad the bad cases actually get.

Expected shortfall, also called conditional value at risk or CVaR, is the average loss you take in the worst slice of outcomes — say the worst 5% of cases. Where value at risk only marks the threshold you should not exceed with 95% confidence, expected shortfall goes further and averages everything beyond that line, so it answers not just how often a bad day happens but how bad it is on average when it does. That makes it a tail-risk measure rather than a single cut-off.

In practice it matters most for strategies with fat, one-sided tails — naked puts, short strangles, ratio spreads — where value at risk can look reassuring while the losses hiding past it are catastrophic. Two positions can share the same 5% VaR yet have very different expected shortfalls if one blows out far more violently in the extreme. Reading the average of the tail, not just its edge, is what stops a run of small winners from being erased by a single uncapped loss.

The common mistake is leaning on VaR alone and ignoring the shape of the tail behind it. A percentile tells you where the bad zone starts; expected shortfall tells you how deep it goes. For defined-risk trades the two nearly converge because the loss is capped, but for undefined-risk positions the gap between them is the whole point — and the number you should size against.

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