Tranche Pricing in Subordinated Loan Securitization

Abstract

Because of both inconsistencies in the regulatory definition of capital adequacy for credit risk and the quest for more efficient refinancing sources through asset-backed securitization (ABS), collateralized loan obligations (CLOs) have become a prominent fixture in structured finance. However, the inherent risks in leveraged investments in times of stress have only recently received much attention by regulators and investors alike. This article presents a single-factor, loss-based asset pricing model for the valuation of constituent tranches within a CLO-style security design. The model specifically examines how tranche subordination transposes securitized credit risk into investment risk of CLO tranches as asset-backed debt securities. We simulate the tranche-specific default term structure based on the aggregate loss-given-default of an equally-weighted, perfectly diversified credit portfolio of identical exposures with an i.i.d. sequence of pairwise correlated defaults under both robust statistical analysis and extreme value theory (EVT). In this way, we are able to decompose the securitized default-generating asset process into a collection of state-contingent debt claims with divergent mean-variance profiles. We find a dichotomous effect of asset subordination, which engenders distinctly different default term structures of CLO tranches, whose leveraged exposure escapes notional size-based risk measurement. The most junior tranche (“first loss position”) carries large amounts of expected loss, whereas all the more senior tranches are mainly exposed to loss volatility (unexpected loss). This finding might explain why issuers retain the most junior tranche as credit enhancement to attenuate asymmetric information between issuers and investors. Offloading unexpected risk also constitutes implicit risk transfer and makes more senior investment very risk-sensitive to only marginal increases of default correlation. Hence, regulatory oversight should be vigilant of the risk impact of loss subordination on senior tranches. Anecdotal evidence of market practitioners indicates that the majority of improvident investment occurs in these low-yielding risk slices of CLO transactions.