Kurtosis
How do we tell whether extreme price moves happen more often than a bell curve would predict?
In plain words
Kurtosis describes how much of a distribution sits in its tails, or extremes, compared with a normal (bell-shaped) curve. High kurtosis means extreme values appear more often and the middle is thinner than a bell curve suggests.
Why it matters
Risk models built on a bell curve understate the frequency of rare, large moves. With fat tails, a position sized for a typical day can be hit by a move many times larger, so stop distances, margin buffers and scenario tests all need wider margins.
In a real week: ETH, week of 15 October 2018
In the week of 15 October 2018, ETH opened at 196.84 and closed at 207.49, up 5.41%, yet its range was 22.82%: the high of 239.0 came at 06:00 UTC Monday, the low of 194.6 at 00:00 UTC Monday. One hour on Monday, 05:00 UTC, carried an 11.6% move, while the best day gained 8.92% and the worst day lost only 3.13%. Realised volatility reached 119.1% a year, and the close sat in the lower third of the week range. A single early-session tail event dominated an otherwise modest week.
A common mistake
Equating kurtosis with volatility. Volatility measures the typical size of swings; kurtosis measures how often the extremes depart from the pattern the rest of the data sets.