Question

An investment bank has created a CDO by pooling 100 bonds which will either pay off $0 (in case of default) or pay off $1. The CDO has three risk classes rated AAA, BBB, and CCC with face values of $70, $20, and $10, respectively. The current prices of the tranches are respectively, $66, $12, and $1. Consider the strategy of buying one unit (out of 100 units) of the BBB class and shorting one unit of the AAA tranche. How many bonds will have to default for this portfolio to make money?

Answer 1

1 unit of BBB (Going long) will have money out stream = $12/20= $.60

1 unit of AAA (Going Short) will have money inflow = $66/70 = $ .9429

Financial specialist can profit just when AAA tranches will default. So we should accept Total 30 (For defaults up to BBB) + x (Defaults in AAA) bonds are required for break even at that point

Break Even if there should be an occurrence of defaults .9429* x/70 - .60 = 0 x = 44.55 = 45

So if aggregate of 30+45=75 bonds or more will default then speculator will profit

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Hope that helps.

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