Why it matters
A calm sample and a small standard deviation do not establish the maximum possible loss. If a model underestimates rare large outcomes, its ordinary range cannot be treated as a safety guarantee.
A common error
Do not declare every large fall to confirm a particular distribution law. That conclusion requires sufficiently broad data, a defined threshold and comparison with alternatives. One extreme observation is not enough to estimate the shape of a tail precisely.
A practical next step is an [conditional stress test](/guides/fat-tails-stress/): set joint adverse changes and test losses and the need for money. Such a scenario does not state its probability and does not promise exhaustive risk coverage.
Primary materials
[1] Gabaix, Power Laws in Economics and Finance; review of empirical regularities and mechanisms. [Power Laws in Economics and Finance](https://www.nber.org/papers/w14299)