A small investment firm has two trading desks and the 5% Expected Shortfall

(ES) for the two desks has been computed to be $2 million and $0.9 million respectively. An analyst at the firm has been told to compute a firm-wide 5% ES value and so reports the sum of the two values, i.e. $2.9 million, as the firm-wide ES since he has learned that ES is a coherent risk measure. In a few sentences (absolutely no need to write a whole page), critique this approach.