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Rare extreme events and value at risk

Question

What is meant by a black swan, and what does it imply for value at risk and conventional statistical risk measures?

Short answer

A rare, extreme, unforeseen event. A black swan has a huge impact and seems explainable only after the fact. VaR and similar tools usually rely on historical data and often normal distributions, so they underestimate fat tails and say nothing about losses beyond the cut-off; supplement them with stress tests, scenario analysis and tail measures such as expected shortfall.

Adapted from Crack, Heard on the Street, Q5.3.24, p.52; question and answer rewritten by SelfMadeQuant.com.

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