Normal distribution
What does the bell curve assume about market returns, and where do real markets depart from that assumption?
In plain words
A normal distribution is the bell-shaped pattern of outcomes where most results sit near the average and extreme results become rapidly less likely the further out you go. Financial returns are often modelled as roughly normal, but they tend to have 'fat tails', meaning large moves occur more often than the bell curve allows.
Why it matters
Risk limits, position sizing and stress tests are frequently built on normal-distribution maths. If the real distribution has fat tails, a model that calls a fall 'once in a decade' can deliver one in a few years, and a position sized on average swings can be badly exposed to a single unusual hour.
In a real week: ETH, week of 18 November 2019
In the week of 18 November 2019 (Mon) to 24 November 2019 (Sun), ETH fell 23.86%, from an open of 183.82 to a close of 139.96, with a range of 33.38%. Its realised volatility was 80.9% annualised, yet the largest single hour move was only -4.61% on 22 November at 10:00 UTC (Fri). The weekly return sat in the 7th percentile against 92 weeks of history, and the worst single day was -7.86% on 21 November.
A common mistake
Assuming returns are normal simply because a standard deviation can be calculated from them. The number exists either way; the question is whether the extremes are heavier than the bell curve allows.