[R-SIG-Finance] [R-sig-finance] VaR

[Christian Langkamp]

Hello
I remember a simple example given for this subadditivity feature in the GARP
Magazine some time ago. I will try to reproduce it, but ask for apologies if
I mixed up two different terms.
You have a portfolio of two credit default swaps (digital options, ... main
point is something extremely unsmooth and really tail oriented)
A and B both Payout -1 with respective probabilities 0.5 % and no
correlation.
You compare then the 1 % VaR of the portfolio of A, B, and A+B. 
VaR(A, 1%) = 0 = VaR(B, 1%) whereas VaR (A+B, 1%) = 1 (in 1% of cases either
A or B defaults) which shouldn't be the case because Diversification should
reduce the risk.

Whilst this can occur in a banking context, in a corporate where all payouts
are linear (forwards) or continuous (normal options) this situation
practically cannot occur and thus this aspect is highly irrelevant. On a CDS
portfolio this is an entirely different game I think, but the extent of the
problem I am not familiar with. 

The amount of assumptions to construct a portfolio where this Subadditivity
feature produces 'wrong results' I think shows that whatever problems VaR
holds, this is not its major one, and hence should not be worried about too
much.

Please feel free to correct the above, or supply a link to the original if
ready at hand
Christian Langkamp
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