My question relates to this exam question from your sample exam for level II in March 2010: 47. Consider a CDO portfolio that consists of 100 loans, each having the notional value of $10 million. A mezzanine tranche of this structure has a notional value of $50 million with an attachment of 5% and width of 2%. The spread is 150 basis points. Assume the recovery rate is 45%. Which of the following percentages comes closest to the loss of this tranche if 11defaults happen? A. 33% B. 43% C. 53% D. 63% The answer is said to be C. Is this really correct? The entire portfolio has a value of 10 x $100M = $1B. The loss arising from 11 defaults is $110M x 0.55 = $60.5M. (45% = recovery rate, so 55% is lost). $50M is absorbed by the equity tranche (5% of $1B = $50M). $60.5M - $50M = $10.5M is left for the mezzanine tranche to absorb. 10.5 / 50 = 0.21 = 21%. Not 53%. I am not quite sure how the notional value of the mezzanine tranche comes into this equation…
The impact on this tranche is requested. => Divide the tranche loss by the tranche width, which is 20M. 10.5/20 = 0.525
Thanks! But how is the tranche width related to the notional of the tranche then?
The tranche width or thickness is the difference between the attachment and the detachment point. Since both are expressed in terms of percentage of the total pool notional, the thickness must do that, as well. If 5% correspond to 50M, 2% correspond to 20M.
This would be logical. However, in Q47 it says the width of the mezzanine tranche is 2% and the notional $50M…