Differences in Tranching Methods: Some Results and Implications*
We review the mathematics of evaluating the credit risk of tranches of structured transactions with simple loss-priority structure using 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.1 These approaches are used to either evaluate the credit quality of an exogenously defined tranche or to determine the theoretically appropriate attachment and detachment points for a tranche to meet an exogenously defined target PD or EL. We compare the attributes of different tranching approaches.
We also examine the relative conservatism of different approaches to tranching. We define tranching framework X as more “conservative” than tranching framework Y in a specific setting if, in that setting, tranche credit enhancement (CE) levels are higher when using framework X than when using framework Y. For our discussions, we assume that the “target” or idealized levels of EL and PD are exogenously defined.
We collect a series of sometimes disparate observations that follow simply from the mathematics of calculating PD and EL for a given tranche. Though these observations follow logically, a number of results may appear counter-intuitive. To illustrate, we use stylized collateral ...