We review the mathematics of evaluating the credit risk of tranches of structured transactions with simple loss-priority structure for two common tranching approaches: PD-based tranching where the probability of default of a tranche is the quantity of interest; and EL- based tranching where the expected loss on a tranche is the quantity of interest. While comparing the attributes of these two tranching approaches, we examine their relative (level of credit enhancement) conservatism. While the mathematics is simple some implications of the results are interesting. We discuss the impact of the collateral LGD assumption on attachment points; show that, all else equal, lowering attachment point or the detachment point necessarily increases the tranche EL; and provide upper-bounds on senior-most tranche LGD under reasonable distributional assumptions. One implication of the low LGDs associated with the senior tranches is that under some EL definitions, it may be impossible to create a tranche with a given EL under the EL-based approach, even though they are always possible under the PD-based approach.

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