Testing the untestable

backtest for Expected Shortfall (ES) has been the object of a long quest for many years. For a coherent alternative to Value at Risk, there remained , similar to the established VaR backtest

Image: Hans Reniers

The quest of a backtest for Expected Shortfall (ES) started soon after its appearance, in 2002.

Backtesting ES a puzzle for many years (2002 - 2019).

Is the ES backtestable?
In the absence of a rigorous definition of what is a backtest, the question was ill posed.

You could write any test with some relation with the tail properties of a distribution and name it a “ES backtest”. Which is what happened. We count at least 30 different self-styled backtests proposed between 2002 and 2019.