Tail Events and Black Swans

Risk management approaches that ignore low-probability tail events are often inadequate. In domains with long-tailed distributions, rare and highly extreme events that can dominate the overall expected impact from risks.

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Review Questions

Why is it difficult to plan responses to tail events in advance?


Tail events are so rare that we do lack evidence to predict when they will happen or what precise form they will take. We can prepare capabilities to develop an appropriate response, but not the full details of the response.

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Consider the following two types of harmful events: shark attacks on humans, and wildfires destroying forests. For each phenomenon, identify whether it is likely to be long-tailed or thin-tailed and explain why. Describe what this will mean for the following characteristics:

  1. The share of the total received by the top few events
  2. Whether the total impact is determined by the few highest-impact events or by all the events collectively
  3. The scalability of a single event
  4. How predictable the impact of a single event is


Shark attacks on humans are likely to be thin-tailed. A shark cannot usually attack a lot of people simultaneously. The most deadly shark attacks in which the most people were killed or injured will have a relatively small share of the total number of people ever killed or injured in all shark attacks. The total number is determined by all attacks, rather than largely by the top few most deadly ones. A single shark attack cannot scale to become very large in terms of number of people affected. We can probably accurately estimate the order of magnitude of the number of people affected in a shark attack.

Forest fires are likely to be long-tailed, because a forest is a highly interconnected system where fire can spread easily from one tree to others nearby. This means there is potential for a forest fire to scale up dramatically. The total area of forest destroyed in forest fires may be largely determined by the top fraction of most destructive fires, more than by all fires. These top few may be responsible for a highly disproportionate amount of total destruction in forest fires. If we try to predict the severity of the next forest fire, our best guess could be incorrect by orders of magnitude.

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