Expected shortfall (CVaR)

Una misura di rischio pari alla perdita media sugli esiti della coda peggiore — diciamo il peggior 5% — così, a differenza di un singolo percentile, coglie quanto siano davvero gravi i casi negativi.

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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