Expected shortfall
Once losses pass a threshold, how large were those losses on average, rather than where the threshold sat?
In plain words
Expected shortfall is the average size of losses in the tail of a distribution, measured only over the cases that fall beyond a chosen threshold, such as the worst one day in twenty.
Why it matters
A threshold tells a risk manager where bad outcomes begin; expected shortfall tells them how deep those outcomes actually go once they begin. A model can pass a threshold check and still leave a portfolio exposed to losses far larger than the threshold implied.
In a real week: ETH, week of 6 August 2018
In the week of 6 August 2018, ETH fell 22.23%, with a range of 35.75% and a worst day of -8.65% on 10 August. Expected shortfall asks, beyond a threshold of bad days, how large were those losses on average? The data supplies the losses themselves, opening at 408.77 and closing at 317.89, but records no threshold. The largest one-hour move of 6.22% on Saturday 11 August at 17:00 UTC is stated as a size only, with no direction given.
A common mistake
Treating the threshold itself as the loss estimate. The threshold marks where the tail starts; expected shortfall is the average depth inside that tail, which is usually larger.