# CMBX and implied default rate

Anyone know the exact calculations to find the implied default probablity for a CMBX tranche? I know for regular CDS the calculation is P(default) = Spread / Loss Rate but that calculation doesnt work out when looking at CMBX. Any help would be appreciated. Thanks.

Not sure, but since it’s an index of CDS, isn’t essentially an average of individual implied probabilities?

It also trades based on spread rather than price (which always confuses me when comparing with ABX). Like ahahah notes, it is an index and that investing in a CMBX tranche essentially means you invest in the 25 CDS’ underlying the index. Unfortunately, I’m pretty sure that neither of your calculations are right and I don’t know what the right one will be. I would figure at least that it is weighted, but there could be some correlation between the underlying products which means you can’t just take the average. I’m not sure though. However, I would check out this product: http://markit.com/information/products/category/indices/cmbx/calculator.html which might help you out.

there’s also the “think of the biggest number you can imagine” method and it’s probably pretty close to the actual implication… The way the market is today, I wouldn’t be surprised if we saw an implied default rate >100%… (kidding)

thanks for the responses…i have been reading a CMBX primer from Citi and in one section they say the quick “first pass” calculation is the spread/Loss Rate. they go on to say that there is a better way to calculate it that includes several nuances such as treatment of interest shortfalls. they reference another paper for the calculations but of course i cant find the paper. you are right ahahah, the market is pretty crazy, the CMBX4 AAA piece closed last night at 277 and a week ago it was 215. a research update i saw did some calculcations and at a spread of 235 there would be a tranche loss of 19.5% which is on top of the 30% CE. There is no way (i hope) that would happen even with the most severe recession.