Return distribution
What does a single weekly return hide about the spread of outcomes a market actually produced?
In plain words
A return distribution is the full spread of returns a market produced over a period, rather than one headline number. It shows how returns were spread across days and hours, how extreme the best and worst moves were, and how unusual the total was against past weeks.
Why it matters
A weekly total can look smooth while the path was not. Two weeks with the same total can differ greatly in daily swings, one-hour shocks and where the close sat inside the range, which affects what position sizes, stops and holding periods can realistically survive.
In a real week: ETH, week of 1 April 2019
In the week of 1 April 2019, ETH rose 23.19% from 141.41 to 174.21, but its range was 27.4%: the low of 139.57 came on Monday and the high of 177.81 on Wednesday. Daily returns ranged from 15.63% on 2 April to -2.02% on 3 April, with a largest one-hour move of -5.5% late Wednesday. The week ranked in the 97th percentile of 59 weeks of history.
A common mistake
Reading the single weekly return as the typical outcome. It is one point drawn from a wide spread, and it says nothing about the path, the extremes or how unusual the week was.