In a typical asset-backed note issue, a pool of collateral is purchased by a special purpose company through the issuance of notes. In some cases there will be a mismatch between the interest rate of the underlying collateral and the notes which it is necessary for the SPC to hedge. However, for many collateral types the principal amount outstanding will be uncertain but the SPC requires a hedge for any level of amortization. In other words, the hedging counterparty will be required to assume interest rate risk and amortization uncertainty. One simple hedge would be an amortizing cap but this could be expensive. The following article shows one method, primarily using an interest rate swap, by which an SPC can efficiently hedge such interest rate mismatches and amortization uncertainty for a limited type of collateral.
The following diagram sets out a typical multi-tranched asset-backed structure together with a hedge. It is assumed there is no revolving period, no controlled amortization and that the underlying collateral has low prepayment volatility.
Initially, this appears to be a standard application of an interest rate swap. However, the amortizations of the underlying collateral and each tranche are dependent on variables which may change during the life of the transaction.
The first step in pricing the swap is the estimation of amortization limits using a model that reproduces the cash flows and their interrelationship together with their dependence on the many input variables. To do this efficiently, it is necessary to decide on the smallest subset of input variables for a scenario analysis and the maximum "stress" that would be applied to any scenario. Accordingly, "base case" and "worst case" amortization profiles can be derived for the different tranches. The following graphs represent amortization profiles that can emerge with some two tranche senior-subordinated structures under normal and stressed scenarios.
For the senior tranche, the stressed and base cases are largely similar except that the stressed amortizations are larger, slightly reducing the average life of the notes. For the subordinated tranche, the level of stress used for the analysis is sufficient to trigger a cessation in the amortization of the subordinated notes after a certain time (this trigger is part of the underlying note structure assumed in the example). Following the accelerated senior tranche amortizations, only when the senior note balance has been reduced to zero are the subordinated notes amortized. This produces the "amortization plateau" for roughly 60% of the life of the subordinated notes.
There are many ways to hedge the structure although none is a perfect hedge. One simple route is a swap with amortizations that correspond to the base case together with a hedge for the difference per period between the base and stressed cases (the different tranches would be separately hedged) using interest rate options which would be put in place at the start of the transaction. If the amortization in any period differs from the amount assumed in the swap, a cap or floor hedges the difference in that period depending on the sign of the difference between the base and stressed case principal. If the stressed case is sufficiently severe, the options may over-hedge as the chances of realizing such a deviation from the base case are unlikely.
It is difficult to know what probability to assign any particular amortization profile. The amount of stress applied to the input variables can be analyzed in a more quantitative fashion by looking at historical data for the collateral pool, if such data exists. For example, the mean and standard deviation of the default rate can be estimated and used to define different levels of stress, each being at a specific multiple of the standard deviation of the default rate above the mean value.
The example above is based on a real case where there was a significant body of data on the underlying collateral type, which permitted the calculation of confidence limits and which achieved a reasonably efficient hedge for the SPC, at a cost which was not excessive. The SPC was able to hedge the interest rate risk between the fixed-rate collateral pool and the floating-rate note issue and the risk of uncertain amortization also was passed to the swap counterparty.
This week's Learning Curve was written by Peter Fink, senior v.p. with Sumitomo Bank Capital Markets, Inc.in New York.
