VaR
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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