I would like to do a qualitative question about the Expected shortfall in the Basel 3 document.
First of all let me introduce few definitions.
Suppose to have a portfolio $P$ depending on a family of risk factors. Let $T$ be a time horizon (for the Basel document $T = 10 $ days).
Now I introduce a family of liquidity horizons usefull to classificate the risk factors:
$$ \begin{matrix} j & & LH_j \\ \hline & & \\ 1 & & 10 \ days \\ 2 & & 20 \ days \\ 3 & & 40 \ days\\ 4 & & 60 \ days\\ 5 & & 120 \ days \end{matrix} $$
Thanks to this definition we can introduce the families $Q(P,j)$ of the risk factors whose liquidity horizons are at least as long as $LH_j$.
Finally we define the following terms: \begin{align} ES_T(P) = & \mbox{ES for the horizon T wrt all the risk factors} \\ ES_T(P,j) = & \mbox{ES for the horizon T where all the risk factors NOT belonging} \\ & \mbox{to Q(P,j) are freezed} \end{align}
Now that we have done with definitions I can make my question:
The Basel document gives this definition of Expected shortfall that I can not understand from an economical point of view: $$ ES = \sqrt{\left(ES_T(P)\right)^2 + \sum_{j\geqslant 2} \left( ES_T(P,j) \sqrt{\frac{LH_j - LH_{j-1}}{T}} \right)^2} $$
The first term is just the right term...but it seems a good idea to introduce other terms in order to take in account of ES wrt a subset of risk factors.
Now: I really do not understand the presence of the terms $\frac{LH_j - LH_{j-1}}{T}$, in particular it seems like they have to do the job of a weighted terms but in general they are equal to the following values $(1, 2, 2, 6)$ so that I can' t understand what is the meaning or the purpose of such terms.
Thank you in advice for your help. Ciao!