I have been reading up on VaR and get very confused by the subadditivity concept.
On wikipedia, it says "VaR is not subadditive: VaR of a combined portfolio can be larger than the sum of the VaRs of its components."
However, as I am reading through John Hull's Options, Futures and other Derivatives, it has the following example talking about the benefit of diversification with VaR:
The 10-day 99% VaR for the portfolio of Microsoft shares is $1,473,621.
The 10-day 99% VaR for the portfolio of AT&T shares is $368,405.
The 10-day 99% VaR for the portfolio of both Microsoft and AT&T shares is $1,622,657.
The amount (1,473,621+368,405) - 1,622,657 = $219,369
So my confusion is that, in this case, isn't the portfolio VaR less than the sum of individual VaR? It looks like it is subadditive here. So where does the conflict come from? Thanks in advance.