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

Christian Langkamp christian.langkamp at basf.com
Wed Mar 4 12:30:52 CET 2009

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
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

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