An Empirical Study of the Returns on Defaulted Debt and the Discount Rate for Loss-Given-Default

Abstract

Prudential management of credit risk and supervisory requirements call for the accurate measurement of loss conditional upon default (LGD). In the case of banks, in order to achieve Advanced Internal Ratings Based (AIRB) compliance under the Basel II minimum regulatory capital framework, loss arising fro m counterparty default must be estimated. However, the discount rate to be applied to post-default cash flows is a largely unsettled issue, amongst both practitioners and bank supervisors. In this study we survey various methodologies extant in the literature for determining an appropriate discount rate. We propose an approach in which the discount rate is conditional upon the level or undiversifiable risk inherent in the recovery cash flows associated with defaulted facilities. We present a stylized theoretical framework for understanding such an approach. This is followed by an empirical exercise that utilizes a comprehensive and commercially available database of workout recoveries (Moody’s Ultimate Recovery Database - MURD), in which we analyze the returns on marketable bonds and loans, having market prices at default and at the resolution of the default event. We propose alternative empirical measures of the recovery risk inherent in post-default cash-flows: the annualized simple return on defaulted debt (RDD) and discount rates implied from a structural model of credit risk incorporating systematic recovery risk, a generalization of the asymptotic single risk factor (ASRF) framework (Gordy, 2003). We find our empirically derived estimates to be significantly higher than what has been found in the previous literature, as well as what is used in industry, mean RDD of 29.2%; this compares to benchmarks such as the 15% reported by Araten et al (2003), the 200bps over the risk-free rate suggested by Machlachlan (2004), or rates in the range of 10-15% derived from model-based estimations (one or two factor structural credit models in conjunction with an assumption on the systematic risk factor). Principal findings are that returns on defaulted debt, which can be interpreted as an appropriate discount rate for workout recoveries, vary significantly according to various factors. There is some evidence that discount rate metrics are elevated for loans having better collateral quality rank or better protected tranches within the capital structure; and for obligors rated higher at origination, more financially levered or having higher Cumulative Abnormal Returns (CARs) on equity just prior to default. However, the discount rate is increasing in market implied loss severity at default. We also find evidence that LGD discount rates vary procyclically, as they increase with industry default rates, but there tends to be some asynchronousity in this relationship; further, they are inversely related to short-term interest rates. However, for other demographics the results are inconclusive, such as the industry group of the obligor. Finally, we conduct an analysis of the impact of the discounting method upon the distribution of estimated LGD and regulatory capital. We find that a regression model based discounting, for a sub-sample of the MURD database, results in a capital charge 73 bps greater than discounting at a constant punitive rate of 25%, and 113 bps larger than discounting at the contractual coupon rate (where the capital charge ranges in 7-8%). This conservativeness of the risk-sensitive RDD model, as well as the evidence that the risk in recovery cash flows contain a significant non-diversifiable component, supports the appropriateness of this framework for regulatory capital calculations.