Elsevier

Journal of Banking & Finance

Volume 40, March 2014, Pages 116-129
Journal of Banking & Finance

Ultimate recovery mixtures

https://doi.org/10.1016/j.jbankfin.2013.11.021Get rights and content

Abstract

We propose a relatively simple, accurate and flexible approach to forecasting the distribution of defaulted debt recovery outcomes. Our approach is based on mixtures of Gaussian distributions, explicitly conditioned on borrower characteristics, debt instrument characteristics and credit conditions at the time of default. Using Moody’s Ultimate Recovery Database, we show that our mixture specification yields more accurate forecasts of ultimate recoveries on portfolios of defaulted loans and bonds on an out-of-sample basis than popular regression-based estimates. Further, the economically interpretable outputs of our model provide a richer characterization of how conditioning variables affect recovery outcomes than competing approaches. The latter benefit is of particular importance in understanding shifts in the relative likelihood of extreme recovery outcomes that tend to be realized more frequently than observations near the distributional mean.

Introduction

The economic value of debt in the event of default is a key determinant of the default risk premium required by a lender and the regulatory capital charged to limit exposure to losses. The pricing of default risk insurance (CDS contracts) and the emergence of distressed debt as an investment class add further incentive to better understand the distribution of payoffs in the event of default.2 Adding to market-driven incentives, Basel II and III provide regulatory incentives to the development of recovery models in financial institutions adopting an advanced internal ratings based (IRB) approach to computing capital requirements.

Recognizing the importance of capturing the behavior of recoveries in the event of default to quantitative models of credit risk, recent years have seen a wave of research from academics and industry professionals seeking to document the key empirical features of observed recovery outcomes. While payoffs to debt holders in the event of default depend on the interplay of many factors, often idiosyncratic, notable empirical regularities from prior research are evident.

  • 1.

    Recovery distributions tend to be bimodal, with recoveries either very high or low, implying as Schuermann (2004)3 observes, that the concept of average recovery is potentially very misleading.

  • 2.

    Collateralization and degree of subordination are the key determinants of recovery on defaulted debt. The (proportional) value of claims subordinate to the debt at a given seniority, known as the Debt Cushion, also seems to matter. The analysis of Keisman and Van de Castle (1999) suggests that all else equal, the larger the Debt Cushion, the higher the expected recovery outcome.

  • 3.

    Recoveries tend to be lower in recessions and other periods when the rate of aggregate defaults is high. Altman et al. (2005) demonstrate an association between default rates and the mean rate of recovery whereby up to 63% of the variation in average annual recovery can be explained by the coincident annual default rate. Further, Frye (2000) shows that a 10% realized default rate results in a 25% reduction in recoveries relative to its normal year average.

  • 4.

    Industry matters. Acharya et al. (2007) suggest that macroeconomic conditions do not appear to be significant determinants of individual bond recoveries after accounting for industry effects. More recently, Jankowitsch et al. (2012) find that the type of default, seniority of the bond and industry are as important determinants of recovery as balance sheet ratios motivated by structural credit risk models, macrovariables and transaction cost variables.

  • 5.

    Variability of recoveries is high, even intra-creditor-class variability, after categorization into sub-groups. For example, Schuermann (2004) notes that senior secured bond investments have a flat distribution – indicating that recoveries are relatively evenly distributed from 30% to 80%.

Clearly, the empirical features of historical recoveries suggest the need for caution in applying popular (parametric) tools of inference – such as OLS regressions and calibrated Beta distributions. While OLS regression models provide simple, intuitive summaries of data relationships, they make strong assumptions about the conditional distribution of recovery outcomes and focus attention on variation in the mean. Alternatively, Beta distributions calibrated to historical data are used in many commercial models of portfolio risk to characterize the distribution of loss outcomes.4 While Beta distributions offer a simple, parsimonious way of capturing a very broad range of distributional shapes over the unit interval, Servigny and Renault (2004) observe that they cannot accommodate bi-modality, or probability masses near zero and unity – important features of empirical recovery distributions.

While stylized models and a growing body of empirical evidence reveal much about the important influences on debt recovery outcomes, they also serve to highlight the challenges inherent in building a quantitative model to account for: characteristics specific to the defaulted instrument, borrower characteristics, macroeconomic conditions at the time of default, and the idiosyncrasies of recovery distributions’ shape. Building on insights from empirical research and the findings of recent studies documenting the relative merits of non-parametric and regression based approaches, we present in this paper a novel approach to modeling recoveries on defaulted debt using mixtures of Gaussian distributions.

More specifically, our paper makes three contributions to the literature. First, we present an approach to modeling recovery distributions that retains the flexibility of non-parametric methods while providing transparency with respect to the economic sources of variation in recovery outcomes. Second, we estimate and evaluate the out-of-sample performance of our model using Moody’s Ultimate Recovery Database spanning a 25 year sample period ending in 2011. As noted by Bastos, 2010, Qi and Zhao, 2011, very few studies to date have evaluated the predictive performance of alternative modeling methodologies. While they present tests of non-parametric approaches relative to regression-based alternatives, neither of the studies consider semi-parametric models. Third, our model provides further clarity on the role and importance of economic influences on recovery outcomes.

The remainder of our study proceeds as follows. We provide in Section 2 an overview of recent approaches to recovery modeling and an overview of the approach proposed in this paper. In Section 3 we describe the ultimate recoveries data used in this study and we detail the econometric approach in Section 4. We report model estimates and comparative performance metrics in Section 5 and summarize our findings in Section 6.

Section snippets

Recovery modeling approaches

Recent studies have investigated the forecasting performance of non-parametric estimation approaches relative to a variety of parametric regression specifications. Using loss data on defaulted Portuguese bank loans, Bastos (2010) finds that non-parametric regression trees tend to outperform parametric regression-based forecasts over shorter (annual) horizons. Similarly, using a larger US sample of defaulted loans and bonds, Qi and Zhao (2011) find that forecasts based on regression trees and

Data description

We use discounted ultimate recoveries from Moody’s Ultimate Recovery Database provided by Moody’s of New York. Moody’s database provides several measures of the value received by creditors at the resolution of default – usually upon emergence from Chapter 11 proceedings. Moody’s estimate of the discounted value of ultimate recovery is our choice of the measure of the economic value accruing to a creditor at the time of default. Moody’s calculates discounted ultimate recoveries by discounting

Econometric framework: some elaboration

As noted, we commence by assuming a Gaussian form for the approximating densities f(.) in Eq. (2), modeling the data y using a probability pj weighted mixture of m Gaussian likelihoods:ϕ(y|α,σ,p)=1(2π)N2i=1Nj=1mpjσjexp-12σj2(yi-αj)2where αj is the mean of mixture component j and σj its standard deviation.9 The sample

Results

Given that a primary objective of our empirical analysis is to estimate and evaluate the predictive performance of our proposed conditional mixture model, we note from the outset our split of the overall sample into 2307 estimation observations comprising the sample up to and including 2001, and 2413 test observations covering the period beginning 2002 to the end of 2011. As such, our results are based on true out of sample data. Unless stated otherwise, our discussion of the model focuses on

Conclusion

We present in this paper a new approach to modeling the distribution of recoveries on defaulted loans and bonds using mixtures of distributions. We take a Bayesian perspective and model (transformed) ultimate recoveries using a mixture of Gaussian distributions wherein the mixing probabilities are explicitly conditioned on borrower characteristics, debt features and the economic conditions prevailing at the time of default.

Our empirical findings suggest that our formulation delivers predictive

Acknowledgements

We thank David Keisman (Moody’s Investor Services) for providing us with access to Moody’s Ultimate Recovery Database. We thank participants at Macquarie University’s 2012 Financial Risk Day, the 2012 Methods in International Finance Conference (Sydney), and the 2013 International Risk Management Conference (Copenhagen) for helpful comments and suggestions. We are especially grateful to Philip Gray, Chris Heaton, Xinxin Shang, Pedro Sottile, and an anonymous referee for many constructive

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