VaR

I frequently hear Value at risk i.e. VaR is not a coherent risk measure
because, sum of VaR for two individual assets may be LOWER than VaR of
portfolio consists of that two aseets i.e. VaR may not be sub-additive.
However when I calculate VaR for general assets like Equity, commodity etc,
I see that VaR is actually sub-addtive i.e. portfolio VaR is always less
than sum of individuals, which is reported as "diversification benefit". Can
anyone give me a particular example why VaR is not sub-additive?

Thanks