Fat Tails


Years of returns can get wiped out in a month in the markets. While investors mostly focus on the average, the tails end up dictating their actual returns. (Introduction)

Sampling and Measurement

Typically, a uniform sample is taken. The problem with this is it under-represents the tails. This leads to models that work on average but blow up on occasion. One way to overcome this problem is through stratified sampling. (Sampling)

Expected shortfall (ES) is a risk measure that can be used to estimate the loss during tail-events. (Measuring)


All assets have fat tails. It is a feature, not a bug. (Historical)

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