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VaR Portfolio and individual VaR


New Member
In the porfolio VaR formula we have sigma(P)
But the cross term in the sigma(P) formula has wi wjrhosigma(i)sigma(j) without a 2 which is missing I think.
Also it is know that VaR is not coherent and hence not subadditive then how come we can add component wise Var to get total VaR which looks like a subadditive property.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Re cross term, if it counts twice; e.g., sigma(1)sigma(2) and sigma(2)sigma(1) that is the same as (2)sigma(1)sigma(2)....the (2) collapses two different summation

VaR (i.e., individual VaR) is not subadditive (neither is incremental VaR) but component VaR, by definition, is subadditive.