Understanding and Predicting Ultimate Loss-Given-Default for Defaulted Bonds and Loans

Michael Jacobs, Jr.1

Office of the Comptroller of the Currency

Ahmet K. KaragozogluHofstra University

Draft: June 2006

J.E.L. Classification Codes: G33, G34, C25, C15, C52.

Keywords: Recoveries, Default, Loss Given Default, Financial Distress, Bankruptcy, Restructuring, Credit Risk, Entropic Methods, Bootstrap Methods, Forecasting

1 Corresponding author: Senior Financial Economist, Credit Risk Modelling, Risk Analysis Division, Office of the Comptroller of the Currency, 250 E Street SW, 2nd Floor, Washington, DC 20024, 202-874-4728, michael.jacobs@occ.treas.gov. The views herein are those of the authors and do not necessarily represent the views of the Office of the Comptroller of the Currency.

Abstract

In this study we empirically investigate the determinants of and build a predictive econometric model for loss-given-default (LGD) using a sample of S&P and Moody’s rated defaulted firms. We extend prior work by incorporating contractual, firm specific, industry, macroeconomic debt/ equity market determinants of LGD (Acharya et al, 2003) in a Kullback-Leibler relative entropy framework (Friedman et al, 2003). We are also able to model to duration of time in default in an internally consistent manner, generating a predicted bivariate distribution of time to resolution and ultimate LGD. We confirm many of the stylized facts and findings of the literature in regard to the determinants of LGD and find in addition the independent significance of a macroeconomic factor, equity returns and the price of traded debt at default in explaining the LGD. The model is validated rigorously through resampling experiment in a rolling out-of-time and out-of-sample framework.

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1. Introduction and Summary

Loss given default (LGD) 2, the loss severity on defaulted obligations, is a critical component of risk management, pricing and portfolio models of credit. This is among the three primary determinants of credit risk, the other two being the probability of default (PD) and exposure of default (EAD). However, LGD has not been extensively studied as, and is considered a much more daunting modeling challenge in comparison to, PD. Starting with the seminal work by Altman (1968), and after many years of actuarial tabulation by rating agencies, predictive modeling of default rates is currently in a mature stage. The focus on PD is understandable, as traditionally credit models have focused on systematic components of credit risk which attract risk premia, and unlike PD, determinants of LGD have been ascribed to idiosyncratic borrower specific factors. However, now there is an ongoing debate about whether the risk premium on defaulted debt should reflect systematic risk, in particular whether the intuition that LGDs should rise in worse states of the world is correct and how this could be refuted empirically given limited and noisy data (Carey and Gordy, 2004).

The recent heightened focus on LGD is evidenced the recent flurry of research into the relatively neglected area of LGD (Acharya et al (2005), Carey and Gordy [2004, 2005], Altman et al [1996, 2001, 2004], Gupton et al [2000, 2001], Araten et al [2003], Frye [2000 a,b,c], Jarrow [2001]). This has been motivated by the large number of defaults and near simultaneous decline in recovery values observed at the trough of the last credit cycle circa 2000-2002, regulatory developments (Basel) and the growth in credit markets. However, obstacles to better understanding and predicting LGD, including dearth of data and the lack of a coherent theoretical underpinning, have continued to challenge researchers. In this paper, we hope to contribute to this effort by synthesizing advances in financial theory, econometric methodology and data acquisition in order to build an empirical model of LGD that is consistent with a priori expectations and stylized facts, internally consistent and amenable to rigorous validation. In addition to answering the many questions that academics have, we further aim to provide a practical tool for risk managers, traders and regulators in the field of credit. LGD may be defined variously depending upon the institutional setting or modeling context, or the type of instrument (traded bonds vs. bank loans) versus the credit risk model (pricing debt instruments subject to the risk of default vs. expected losses or credit risk capital. In the case of bonds, one may look at the price of traded debt at either the initial credit event3 or the value of instruments received in settlement of a bankruptcy proceeding 2 This is equivalent to one minus the recovery rate, or dollar recovery as a proportion of par. We will speak in terms of LGD as opposed to recoveries with a view toward credit risk management applications. 3 By default we mean either bankruptcy (Chapter 11) or other financial distress (payment default). In a banking context, this defined as synonymous with respect to non-accrual on a discretionary or non-discretionary basis. This is akin to the regulatory definition of default (Basel).

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(Keisman et al, 2000; Altman et al, 1996). When looking at loans that may not be traded, the eventual loss per dollar of outstanding balance at default is relevant (Asarnow et al, 1995; Araten et al, 2003). There are two ways to measure the latter – the accounting LGD refers to nominal loss per dollar outstanding at default4, while the economic LGD refers to the discounted cash flows to the time of default taking into consideration when cash was received.5 The former is used in setting reserves or a loan loss allowance, while the latter is an input into a credit capital allocation model.

An aspect of LGD modeling deserving of special attention, until recently neglected altogether or grossly simplified, is the distributional characterization of this quantity. While the available theory and evidence suggests it to be stochastic and predictable with respect to other variables, LGD has been treated as either deterministic or as an exogenous stochastic process. Such assumptions are made for tractability and in practical application results in understated capital, mispricing and unrealistic dynamics of model outputs. We will contribute to resolving such deficiencies by attempting to model the ex ante distribution of LGD as a function of empirical determinants – contractual features, borrower characteristics and systematic factors. However, we will not directly model the interdependency between LGD and other parameters of interest, such as probabilities of default, by either estimating a structural or reduced form model in which they are determined simultaneously6.

4 In the context of bank loans, this is the cumulative net charge-off as a percent of book balance at default (the net charge-off rate). 5 There is debate surrounding the appropriate choice for a discount rate. Bank studies (Araten et al, 2003) have put forward arguments for a punitive rate as consistent with the “low end” of what buyers of distressed assets look for as overall return, the uncertainty of recoveries (with the standard deviation about equal to the average), the rates used by commercial loan pricing models, and consistency with “peer practice”. A competing argument among academics (Acharya et al, 2004) as well as practitioners (Friedman et al 2003) and that it is proper to discount ultimate recoveries using the coupon on the debt prior to default. Finally, some have argued in favor of discounting recoveries at the default risk-free Treasury term structure (Carey and Gordy, 2005). We do not address this issue directly in this paper – however, to the extent that one can jointly forecast time-to-resolution and the ultimate recovery, an implicit estimate of the proper actuarial discount rate can be formulated based upon this research. 6 Altman et al (2003) offers an extensive review of the theory and empirical evidence regarding the relationship between LGD and PD, and further documents the influence of the economic state on recovery values and hence the LGD estimate.

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2. Review of the Literature

In this section we will examine the way in which different types of theoretical credit risk models have treated LGD – assumptions, implications for estimation and application. We will then turn to the empirical evidence, both on the estimation of LGD, and on the performance of these various models. Finally, we will look at some of the stat-of-the-art and vendor models of LGD, and how they have attempted to incorporate lessons learned. 2.1 Treatment of LGD in Theoretical Credit Risk Models

Credit risk modeling was revolutionized by the approach of Merton (1974), who built a predictive theoretical model in the option pricing paradigm of Black and Scholes (1973), which has come known to be the structural approach. Equity is modeled as a call option on the value of the firm, with the face value of zero coupon debt serving as the strike price, which is equivalent to shareholders buying a put option on the firm from creditors with this strike price. Given this capital structure, log-normal dynamics of the firm value and the absence of arbitrage, closed form solutions for the default probability and the spread on debt subject to default risk can be derived. The LGD can be shown to depend upon the parameters of the firm value process as is the PD, and moreover is inversely related to the latter, in that the expected residual value to claimants is increasing (decreasing) in firm value (asset volatility or the level of indebtedness). Therefore, LGD is not independently modeled in this framework; this was addressed in much more recent versions of the structural framework (Frye [2000], Dev et al [2002[, Pykhtin [2003]), to be discussed in more detail later.

Many extensions of Merton (1974) that relaxed many of the simplifying assumptions. Complexity to the capital structure was added by Black and Cox (1976) and Geske (1977), with subordinated and interest paying debt, respectively. The distinction between long- and short-term liabilities in Vasicek (1984) was the precursor to the KMV model. However, these models had limited practical applicability, the standard example being evidence of Jones, Mason and Rosenfeld (1984) that these models were unable to price investment grade debt any better than a naïve model with no default risk. Further, empirical evidence in Franks and Touros showed that the adherence to absolute priority rules (APR) assumed by these models are often violated in practice, which implies that the mechanical negative relationship between expected asset value and LGD may not hold. Longstaff & Schwartz (1995) incorporate into this framework a stochastic term structure with a PD-interest rate correlation. Other extensions include Kim at al (1993) and Hull & White (1995), who examine the effect of coupons and the influence of options markets, respectively.

Partly in response to this, a series of extensions ensued, the so-called “second generation” of structural form credit risk models (Altman [2003]). The distinguishing characteristic of this class of models is the relaxation of the assumption that default can only occur at the maturity of debt – now default occurs at any point between debt issuance and maturity when the

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firm value process hits a threshold level. The implication is that LGD is exogenous relative to the asset value process, defined by a fixed (or exogenous stochastic) fraction of outstanding debt value. This approach can be traced to the barrier option framework as applied to risky debt of Black and Cox (1976).

All structural models suffer from several deficiencies which. First, reliance upon an unobservable asset value process makes calibration to market prices problematic and invites model risk. Second, the limitation of assuming a continuous diffusion for the state process implies that the time of default is perfectly predictable (Duffie and Lando [2000]). Finally, the inability to model spread or downgrade risk distorts the measurement of credit risk. This gave rise to the reduced form approach to credit risk modeling (Duffie and Singleton, 1999), which instead of conditioning on the dynamics of the firm, posit exogenous stochastic processes for PD and LGD. These models include Litterman & Iben (1991), Madan & Unal (1995), Jarrow & Turnbull (1995), Jarrow et al (1997), Lando (1998), Duffie (1998). The primitives determining the price of credit risk are the term structure of interest rates (or short rate), a default intensity and an LGD process. The latter may be correlated with PD, but this is exogenously specified, with the link of either of these to the asset value (or latent state process) not formally specified. However, the available empirical evidence (Duffie and Singleton [1999], Lando and Turnbull [1997]) has revealed these models deficient in generating realistic term structures of credit spreads for investment and speculative grade bonds simultaneously. A hybrid reduced – structural form approach of Zhou (2001), which models firm value as a jump diffusion process, has had more empirical success, especially in generating a realistic negative relationship between LGD and PD (Altman et al 2001, 2003).

The fundamental difference of reduced with structural form models is the unpredictability of defaults: PD is non-zero over any finite time interval, and the default intensity is typically a jump process (e.g., Poisson), so that default cannot be foretold given information available the instant prior. However, these models can differ in how LGD is treated. The recovery of treasury assumption of Jarrow & Turnbull (1995) assumes that an exogenous fraction of an otherwise equivalent default-free is recovered at default. Duffie and Singleton (1999) introduce the recovery of market value assumption, which replaces the default-free bond by a defaultable bond of identical characteristics to the bond that defaulted, so that LGD is a stochastically varying fraction of market value of such bond the instant before default. This model yields closed form expressions for defaultable bond prices and can accommodate the correlation between PD and LGD; in particular, these stochastic parameters can be made to depend on common systematic or firm specific factors. Finally, the recovery of face value assumption (Duffie [1998], Jarrow et al [1997]) assumes that LGD is a fixed (or seniority specific) fraction of par, which allows the use of rating agency estimates of LGD and transition matrices to price risky bonds.

It is worth mentioning the treatment of LGD in credit models that attempt to quantify unexpected losses analogously to the Value-at-Risk (VaR) market

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risk models, so-called credit VaR models (Creditmetrics™ [Gupton et al, 1997], KMV CreditPortfolioManager™ [KMV Corporation, 1984], CreditRisk+™ [Credit Suisse Financial Products, 1997], CreditPortfolioView™ [Wilson, 1998]). These models are widely employed by financial institutions to determined expected credit losses as well as economic capital (or unexpected losses) on credit portfolios. The main output of these models is a probability distribution function for future credit losses over some given horizon, typically generated by simulation of analytical approximations, as it is modeled as a highly non-normal (asymmetrical and fat-tailed). Characteristics of the credit portfolio serving as inputs are LGDs, PDs, EADs, default correlations and rating transition probabilities. Such models can incorporate credit migrations (mark-to-market mode - MTM), or consider the binary default vs. survival scenario (default mode - DM), that principle difference being that in addition an estimated transition matrix needs to be supplied in the former case. Similarly to the reduced form models of single name default, LGD is exogenous, but potentially stochastic. While the marketed vendor models may treat LGD as stochastic (e.g., a draw from a beta distribution that is parameterized by expected moments of LGD), there are some more elaborate proprietary models that can allow LGD to be correlated with PD.

We conclude our discussion of theoretical credit risk models and the treatment of LGD by considering recent approaches, which are capable of capturing more realistic dynamics, sometimes called “hybrid models”. These Frye (2000a, 2000b), Jarrow (2001), Jokivuolle et al (2003), Carey & Gordy (2003), Pykhtin (2003) and Bakshi et al (2001). These models share in common the feature that dependence upon one or a set of systematic factors can induce an endogenous correlation between PD & LGD. In the model of Frye (2000a, 2000b), the mechanism that induces this dependence is the influence of systematic factors upon the value of loan collateral, leading to a lower recoveries (and higher loss severity) in periods where default rates rise (since asset values of obligors also depend upon the same factors). In a reduced form setting, Jarrow (2001) introduced a model of co-dependent LGD and PD implicit in debt and equity prices.7

2.2 Empirical Evidence on LGD and Tests of Credit Models

In this section we focus on the application of credit models and estimation of LGD from data. This ranges from simple quantification of LGD, calibration of credit models embedding LGD assumptions, and finally to empirical or vendor models of LGD.

There is a long tradition of actuarially estimating loss severities from bond or loan data, independent of any credit modeling framework and allied parameters such as PD. These have been conducted by academics, banks and rating agencies. The earliest studies relied exclusively on secondary market prices of bonds or loans. Altman & Kishore (1996) estimate LGDs for 300 defaulted senior secured and senior unsecured bonds from 1978-1995, 7 Jarrow (2001) also has the advantage of isolating the liquidity premium embedded in defaultable bond spreads.

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yielding estimates ranging from 10% to 70% that could be statistically distinguished among various industry groups. In the ZETA™ model of Altman, Haldeman and Narayanan (1977), a 2nd generation of the Altman (1967) Z-Score PD estimation model, loan LGD estimates were based on a workout department survey. Later studies looked at ultimate recoveries on defaulted loans or bonds, either the nominal or discounted price at emergence from bankruptcy. Altman and Eberhart (1994) and Fridson et al (Merrill Lynch 2001) provided evidence that more senior significantly outperformed more junior bonds in the post-default period. Altman and Kishore (1996) find statistically different LGDs across broad industrial sectors.

LGD in bank loans have been studied by banks, rating agencies and academics. Bank studies focusing on internal loan data include Citigroup (Asarnow & Edwards, 1995), Chase Manhattan Bank (1996) and JP Morgan Chase (Araten et al, 2003)8. Average LGDs of 35% (861 large corporate obligors 1979-1993), 36% (412 large corporate obligors 1986-1993) and 40% (3800 wholesale loans 1982-2000) for were found in the Citigroup, Chase and JPMC studies, respectively. Finally, among those conducting historical analysis, some recent rating agency studies are worthy of note. Moody’s (Hamilton et al, 2001) reports an implied mean LGD of 30.3% (47.9%) for 121(181) senior secured (senior unsecured) secondary market loan prices a month after default. Various consortia of banks have published composite loss severity statistics from member banks, including Loan Pricing Corporation (2001; LPC) and the Risk Management Association (2000; RMA)9; however, the degree of segmentation by borrower and instrument characteristics is limited in these, and there are issues associated with normalizing data across banks. Standard and Poors (Keisman et al, 2000) presents empirical results from the LossStatsTM database. Analysis of 264 (690) bank loans (senior unsecured bonds) from 1987-1996 yields an average LGD of 16% (34%). This study also documents the independent influence of position in the capital structure (i.e., the proportion of debt above or below a claimant in bankruptcy), apart from collateral and seniority, in determining loss severities. Emery (2003) and Altman and Fanjul (2004) compare LGDs, as inferred from the prices of the traded instruments at default in a Moody’s database, on bank loans and bonds, respectively. A comparison of results reveals that loans experienced lower loss severity when controlling for seniority.10 Varma et al (2003) document similar findings for corporate bonds as Altman and Fanjul (2004). Additionally, Altman and Fanjul (2004) document a differential LGD by rating at origination, such that “fallen angels” of the same seniority have significantly lower LGDs.11 Several recent empirical studies of LGD by academics have put more structure around this exercise, either by building predictive econometric 8 Average LGDs of 35% (861 large corporate obligors 1979-1993), 36% (412 large corporate obligors 1986-1993) and 40% (3800 wholesale loans 1982-2000) for were found in the Citigroup, Chase and JPMC studies, respectively.9 LPC (RMA) find an average accounting LGD of 30% (27%) for 2,534 (977) loans, both in the 1998-2001period.10 In a comparable period, both authors find median LGDs on senior secured loans, senior secured bonds, unsecured loans and senior unsecured bonds were found to be 27.0%, 45.5%, 49.5% and 57.7%. 11 Median LGDs of 49.5% and 66.5% for defaulted issuers originally investment and speculative grade, respectively.

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models, or by attempting to directly test models. Frye (2000b) examines the LGD-PD correlation in 1982-1997 using the Moody’s Default Risk Service [DRSTM], finding a significant negative relationship at various levels of aggregation, consistent with the recent market experience in the 2001-2002 turn in the credit cycle. Hu and Perraudin (2002) also examines this relationship with Moody’s DRSTM for the 1983-2000 period, standardizing the data by transforming all borrowers to senior unsecured, thereby isolating the influence of systematic factors. They find LGD-PD correlations on the order of 0.2. Carey and Gordy (2004) analyze the correlation of LGD and PD in a combined database of defaults in 1970-199912. Examining aggregated quarterly data at the obligor level, while they find almost negligible correlation with PD over the entire sample, in 1988-1998 there is a significant relationship that is in line with Frye’s (2000b) results13. However, they document that LGDs tend to rise more in recessionary periods than they fall during expansions, suggesting that more is at play than a macroeconomic factor influencing the value of collateral.14 In the Araten et al (2001) bank study, unsecured U.S. large corporate borrower level LGDs are regressed average Moody’s All-Corporate default rate for the period 1984-1999 on an annual basis, yielding an r-squared of 0.2, in line with Carey and Gordy (2004) for their restricted sample, yet significantly higher than Hu and Peraudin (2002). Altman et al (2001,2004) find an that LGDs increase as the credit cycle worsens, going from 75% in 2001-2003 to 55% in 2003 as default rates decreased beneath their long run average of 4.5%. This is verified by Keisman (2003), who finds that LGDs of all seniorities rise during this stress period, in the S&P LossStatsTM database. However Altman (2004) finds that a systematic variable has no effect on LGD when bond market conditions (e.g., supply-demand imbalances) are accounted for. However, Acharya et al (2005) examine the same data as Keisman (2003) for the period 1982-1999, and while they verify that seniority and security are key determinants of LGD, in addition they find industry specific factors influencing LGD independently of the macroeconomic state and bond market conditions seen in Altman (2004). In particular, they find elevated LGDs in distressed industries (less redeployable assets, greater leverage and lower liquidity), after controlling for firm / contract systematic factors. This constitutes a test of the Schleifer and Vishny (1992) “fire-sale” hypothesis – an industry equilibrium phenomenon in which macro and bond market variables are spuriously significant due to omitting an industry factor.

Finally, we may mention vendor models of LGD, which incorporate approaches taken in the academic and agency literature, in addition applying proprietary methodologies and data sources. S&P (Friedman & Sandow, 12 Moody’s DRSTM, S&P’s LossStatsTM and S&P’s CreditprioTM , and the Society of Actuaries private placements database.13 Correlations of 0.45 (0.80) for senior (subordinated) debt.14 Carey ands Gordy (2004) argue for a 2 stage approach to measuring LGD, first estimating an “estate LGD” at the obligor level, and then treating instrument level LGDs according to a contingent claims approach, as under the Absolute Priority Rule (APR) such recoveries can be viewed as collar options on residual value of the firm. However, they argue that the endogeneity of the bankruptcy decision will result in a measurement problem in the 1st stage borrower level. Furthermore, an extensive literature on violations of APR suggests a similar problem in the 2nd stage instrument level (Hotchkiss [1993], Eberhart et al [1989], Weiss [1990]).

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2003) applies a Kulback-Leibler maximum entropy non-linear regression model to the LossStatsTM database, which incorporates Bayesian style prior information (point masses at 0 and 100%) to produce predictive densities of LGD. Moody’s LoosCalc2™ (Gupton, 2004) applies an econometric based models (local regression) to KMV’s proprietary LGD database.

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Econometric Models

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Data and Summary Statistics

We have built a database of defaulted firms (bankruptcies and out-of-court settlements), all having rated instruments (S&P or Moody’s) at some point prior to default. It contains data on 2,732 defaulted instruments from 1986-2003 for 650 borrowers, or which there is information on all classes of debt. All instruments are detailed by type, seniority, collateral type, position in the capital structure, original and defaulted amount, resolution type, instrument price at emergence from as well as the value of securities received in settlement from bankruptcy.

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Estimation Results

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Summary and Conclusions

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Appendix – Tables and Figures

LGD at Default1

Discounted LGD2

Numer of Creditor Classes3

Principle at Default4

Time-to-Resolution5

LGD at Default

Discounted LGD

Numer of Creditor Classes

Principle at Default

Time-to-Resolution

LGD at Default

Discounted LGD

Numer of Creditor Classes

Principle at Default

Count 846 150 996Average 63.20% 51.09% 2.4309 151,750 1.5347 61.12% 45.59% 2.4597 113,001 1.2248 62.89% 50.18% 2.4357 145,309Median 70.00% 57.20% 2.0000 83,410 1.3111 68.69% 51.97% 2.0000 70,000 1.1514 69.62% 56.80% 2.0000 80,386Standard Deviation 28.65% 39.61% 0.8828 250,787 1.0836 27.07% 42.70% 1.0721 146,925 0.7943 28.42% 40.18% 0.9168 237,115Minimum -12.00% -107.20% 1.0000 0 0.0556 2.52% -124.19% 1.0000 0 0.0472 -12.00% -124.19% 1.0000 05th Percentile 8.14% -4.88% 1.0000 4,500 0.2250 12.42% -10.58% 1.0000 2,023 0.1614 9.28% -5.23% 1.0000 4,02495th Percentile 97.59% 100.00% 4.0000 500,000 3.6076 95.99% 100.00% 5.0000 364,102 2.5896 97.51% 100.00% 4.0000 500,000Maximum 99.80% 100.00% 6.0000 4,600,000 6.8667 99.75% 100.00% 5.0000 1,225,000 4.9917 99.80% 100.00% 6.0000 4,600,000Count 104 18 122Average 45.73% 18.72% 2.4659 146,524 0.2417 47.04% 9.93% 2.4405 104,319 0.3140 45.92% 17.22% 2.4615 139,347Median 45.00% 0.03% 2.0000 63,529 0.0028 54.75% 0.03% 2.0000 50,000 0.0028 65.44% 39.25% 2.0000 63,966Standard Deviation 26.74% 32.21% . 256,479 0.6130 29.00% 30.05% 0.7968 177,189 0.5673 26.96% 31.99% 0.8880 245,175Minimum -1.00% -70.89% 1.0000 0 0.0028 -7.87% -99.35% 1.0000 801 0.0028 -7.87% -99.35% 1.0000 05th Percentile 3.62% -4.54% 1.0000 1,623 0.0028 -1.18% -24.03% 1.0000 3,130 0.0028 10.61% -15.80% 1.0000 2,10295th Percentile 89.15% 85.85% 4.0000 523,235 1.3111 84.17% 54.62% 4.0000 342,500 1.9472 96.10% 100.00% 5.0000 360,139Maximum 98.00% 100.00% 5.0000 2,250,000 5.6444 97.47% 99.00% 4.0000 1,350,000 1.9472 98.00% 100.00% 5.0000 2,250,000Count 950 168 1118Average 61.29% 45.26% 2.4372 150,808 1.3018 59.61% 39.02% 2.4561 111,401 1.0570 61.04% 44.22% 2.4403 144,231Median 68.52% 47.74% 2.0000 80,124 1.0986 65.44% 39.25% 2.0000 63,966 0.9611 68.41% 46.09% 2.0000 76,433Standard Deviation 28.96% 40.34% 0.8870 251,773 1.1301 27.54% 42.93% 1.0262 152,775 0.8355 28.74% 40.84% 0.9116 238,558Minimum -12.00% -107.20% 1.0000 0 0.0028 -7.87% -124.19% 1.0000 0 0.0028 -12.00% -124.19% 1.0000 05th Percentile 7.59% -4.83% 1.0000 3,625 0.0028 10.61% -15.80% 1.0000 2,102 0.0028 8.11% -5.96% 1.0000 3,33695th Percentile 97.26% 100.00% 4.0000 506,125 3.4222 96.10% 100.00% 5.0000 360,139 2.3833 97.10% 100.00% 4.0000 500,000Maximum 99.80% 100.00% 6.0000 4,600,000 6.8667 99.75% 100.00% 5.0000 1,350,000 4.9917 99.80% 100.00% 6.0000 4,600,000Count 315 77 392Average 65.44% 53.62% 2.2251 670,990 1.5312 63.68% 53.40% 2.1273 382,212 1.3560 65.10% 53.57% 2.2049 611,280Median 69.00% 56.73% 2.0000 291,175 1.3639 65.66% 53.51% 2.0000 209,000 1.1736 68.69% 55.74% 2.0000 262,778Standard Deviation 23.85% 29.40% 0.8631 1,806,477 1.0040 21.76% 28.46% 1.0414 696,960 0.8841 23.44% 29.18% 0.9027 1,643,396Minimum -5.52% -37.87% 1.0000 11,531 0.0556 9.29% -12.07% 1.0000 17,611 0.0889 -5.52% -37.87% 1.0000 11,5315th Percentile 16.86% 0.81% 1.0000 48,334 0.2754 14.50% 3.44% 1.0000 49,431 0.1825 15.79% 0.85% 1.0000 48,76895th Percentile 93.07% 96.12% 4.0000 1,966,962 3.3893 94.61% 95.69% 4.0000 1,131,799 2.8575 93.48% 95.91% 4.0000 1,921,658Maximum 99.00% 100.00% 6.0000 ######## 6.8667 98.29% 99.88% 5.0000 6,415,738 4.9917 99.00% 100.00% 6.0000 ########Count 55 13 68Average 54.39% 27.11% 2.2551 613,007 0.4523 52.64% 12.27% 2.4000 438,140 0.4378 54.06% 24.60% 2.2797 583,369Median 68.46% 21.65% 2.0000 225,946 0.0792 62.00% 14.35% 2.0000 260,296 0.2097 66.45% 21.38% 2.0000 246,655Standard Deviation 25.25% 28.78% 0.8653 2,013,300 0.8285 22.49% 27.53% 0.8208 537,950 0.5690 24.60% 29.00% 0.8562 1,847,114Minimum 5.29% -64.89% 1.0000 14,495 0.0028 21.00% -47.02% 1.0000 75,840 0.0028 5.29% -64.89% 1.0000 14,4955th Percentile 20.77% -9.86% 1.0000 43,696 0.0028 20.74% -34.57% 1.0000 106,487 0.0028 16.72% -14.31% 1.0000 48,42195th Percentile 93.85% 72.53% 4.0000 1,502,341 1.8528 89.80% 50.54% 4.0000 1,337,473 1.4854 93.29% 71.96% 4.0000 1,502,341Maximum 92.77% 94.01% 5.0000 ######## 5.6444 97.47% 50.99% 4.0000 2,375,000 1.9472 97.47% 94.01% 5.0000 ########Count 370 90 460Average 63.80% 48.62% 2.2308 660,063 1.3279 62.09% 47.08% -2.1692 -390,817 -1.2147 63.46% 48.31% 2.2185 606,213Median 68.79% 51.19% 2.0000 278,875 1.1667 65.31% 48.07% 2.0000 223,110 1.0681 68.22% 50.44% 2.0000 261,291Standard Deviation 24.35% 31.04% 0.8627 1,845,329 1.0604 -22.09% -31.91% -1.0126 -673,406 -0.9048 23.91% 31.20% 0.8942 1,680,742Minimum -5.52% -64.89% 1.0000 11,531 0.0028 -9.29% 47.02% -1.0000 -17,611 -0.0028 -5.52% -64.89% 1.0000 11,5315th Percentile 16.63% -1.06% 1.0000 45,283 0.0028 14.50% -4.78% 1.0000 49,950 0.0750 15.41% -1.18% 1.0000 48,58595th Percentile 93.48% 93.24% 4.0000 1,946,021 3.2718 93.65% 95.44% 4.0000 1,195,574 2.8211 93.53% 94.65% 4.0000 1,906,259Maximum 99.00% 100.00% 6.0000 ######## 6.8667 -98.29% -99.88% -5.0000 -6,415,738 -4.9917 99.00% 100.00% 6.0000 ########

4 - The total instrument outstanding at default.5 - The time in years from the instrument default date to the time of ultimate recovery.

532

1182098

520 130 650

1 - One miunus the price of defaulted debt at the time of defulat

422 110

2 - The ultimate dolloar loss-given-default on the defaulted debt instrument = 1 - (recovery at emergence from bankruptcy or time of final settlement as a percent of par). Alternative ly, this can be expressed as (outstanding at default - total ultimate dollar recovery) / (outstanding at default). 3 - Major creditor classesa as defined by the bankruptcy court or by mutual agreement in the out-of-court settlement.

Cha

pter

11

Out

-of-C

ourt

Tota

l

1.2

- Obl

igor

Lev

el O

bser

vatio

ns

Table 1 - Characteristics of LGD Observations by Default Type and Availability of Financial Statement Data (S&P and Moody's Rated Defaults 1985-2003)

Cha

pter

11

Out

-of-C

ourt

Total

2238

49484410

1.1

- Ins

trum

ent L

evel

Obs

erva

tions

2276 456

Tota

l

2732

Compustat Non-Compustat

1866 372

15

Figure 1.1: Instrument vs. Firm Level Distributions of Discounted LGD (Defaulted S&P and Moodys Rated Bonds and Loans 1985-2003)

0.0000000.0100000.0200000.0300000.0400000.0500000.0600000.0700000.0800000.090000

LGD

-0.45865

4309

-0.33181

4804

-0.23668

5175

-0.10984

567

-0.04642

5917

0.016

9938

35

0.080

4135

88

0.143

8333

4

0.207

2530

93

0.270

6728

45

0.334

0925

98

0.397

5123

51

0.460

9321

03

0.524

3518

56

0.587

7716

08

0.651

1913

61

0.714

6111

13

0.778

0308

66

0.841

4506

19

0.904

8703

71

0.968

2901

24

LGD.Instr.Frequ LGD.Oblg.Frequ

Figure 1.2: Instrument vs. Firm Level Distributions of Discounted LGD (Bankrupt S&P and Moodys Rated Bonds and Loans 1985-2003)

00.020.040.060.08

0.10.120.140.160.18

0.2

LGD

-1.05

1066

94

-0.71

7172

321

-0.57

4074

628

-0.43

0976

935

-0.33

5578

472

-0.24

0180

01

-0.14

4781

548

-0.04

9383

085

0.046

0153

77

0.141

4138

39

0.236

8123

02

0.332

2107

64

0.427

6092

26

0.523

0076

88

0.618

4061

51

0.713

8046

13

0.809

2030

75

0.904

6015

38

LGD.Borr.Frequ LGD.Borr.Frequ

16

Number of Defaults

Average Discounted LGD1

Total Defaulted Amount ($MM)2

Average Time-to-Resolution (Yrs.)3

Proportion of Chapter 11 Filings

Number of Defaults

Average Discounted LGD1

Total Defaulted Amount2

Average Time-to-Resolution3

Proportion of Chapter 11 Filings

1985 2 82.70% 486 5.8653 100.00% 1 82.59% 486 5.9278 100.00%1986 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A1987 43 51.86% 2,737 1.1458 39.53% 9 48.57% 2,907 1.6454 55.56%1988 95 45.28% 5,008 2.3487 85.26% 21 56.22% 5,532 1.9657 76.19%1989 99 59.88% 10,618 1.9773 74.75% 25 55.69% 11,247 1.3807 68.00%1990 228 41.59% 26,633 1.6169 77.19% 62 41.72% 32,080 1.8004 77.42%1991 287 35.61% 27,843 1.4966 72.13% 66 39.50% 26,213 1.5068 74.24%1992 120 38.53% 10,554 1.6360 80.00% 27 45.67% 7,939 1.4727 85.19%1993 121 34.33% 7,740 0.9837 82.64% 27 37.39% 5,516 1.2214 74.07%1994 66 26.41% 4,670 0.8774 74.24% 25 41.02% 4,578 1.0739 80.00%1995 93 36.28% 7,728 1.2872 95.70% 33 42.34% 7,791 1.3519 93.94%1996 72 34.54% 5,068 1.1723 94.44% 22 43.32% 6,156 1.4910 95.45%1997 60 40.63% 6,752 1.6031 100.00% 15 52.48% 5,846 1.4224 100.00%1998 66 64.99% 6,935 1.4139 100.00% 23 60.09% 8,214 1.4135 100.00%1999 163 44.10% 26,518 1.3727 93.87% 48 49.46% 27,164 1.3063 93.75%2000 237 54.59% 33,378 1.4834 98.73% 56 58.84% 37,876 1.3956 96.43%2001 354 55.22% 57,611 1.1741 92.09% 81 59.74% 68,374 1.1896 83.95%2002 446 47.51% 134,694 0.7761 73.54% 73 49.56% 118,725 0.8119 75.34%2003 163 26.90% 17,887 0.3834 66.26% 33 35.02% 16,376 0.4079 63.64%2004 17 6.86% 1,179 0.0237 23.53% 3 16.30% 1,017 0.0028 0.00%Total 2,732 44.22% 394,039 1.2609 81.92% 650 48.31% 394,039 1.3052 81.85%

3 - The time in years from the instrument or firm default date to the time of ultimate recovery.

Instruments Obligors

Table 2 - LGD, Dollar Loss, Duration and Court Filing of Defaulted Instruments and Obligors by Cohort Year (S&P and Moody's Rated Defaults 1985-2003)

Year

1 - The ultimate dolloar loss-given-default on defaulted debt instrument or obligor = 1 - (recovery at emergence from bankruptcy or time of final settlement as a percent of par). Alternative ly, this can be expressed as (outstanding at default - total ultimate dollar recovery) / (outstanding at default). 2 - The total instrument or obligor outstanding at default.

Figure 2.1: Percentiles of Instrument Discounted LGD by Year (Moody's and S&P Rated Bonds & Loans 1985-2003)

-1.5

-1

-0.5

0

0.5

1

1.5

Year 1985 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Year

LGD

1st Perc 5th Perc 25th Perc Median 75th Perc 95th Perc 99th Perc

17

Number of Defaults Average Median

Standard Deviation

5th Percentile

95th Percentile

Number of Defaults Average Median

Standard Deviation

5th Percentile

95th Percentile

Aerospace / Auto / Capital Goods / Equipment 218 38.08% 33.79% 41.12% -16.39% 100.00% 57 48.77% 54.37% 28.98% -0.03% 89.74%Consumer / Service Sector 635 43.96% 47.80% 42.16% -10.75% 100.00% 161 45.51% 46.99% 30.89% -1.06% 91.17%Energy / Natural Resources 204 45.34% 45.38% 36.43% -1.41% 98.34% 53 44.52% 46.97% 29.12% 1.49% 92.13%Financial Institutions 124 40.48% 47.12% 39.39% -5.12% 99.97% 28 54.45% 56.76% 36.52% -7.16% 99.67%Forest / Building Prodects / Homebuilders 151 37.38% 49.95% 36.44% -5.95% 100.00% 29 44.96% 40.19% 26.12% 7.25% 86.14%Healthcare / Chemicals 198 42.10% 36.32% 41.59% -5.50% 99.20% 49 46.79% 50.44% 30.07% 3.78% 91.57%High Technology / Telecommunications 528 55.31% 69.11% 40.36% -1.35% 100.00% 104 60.77% 67.61% 30.74% 1.22% 98.26%Insurance and Real Estate 84 52.09% 57.07% 37.40% -9.13% 99.57% 22 52.76% 55.88% 31.16% 3.47% 90.72%Leisure Time / Media 394 39.70% 39.60% 41.26% -11.21% 99.42% 109 44.32% 43.96% 29.59% -3.74% 89.15%Transportation 113 49.20% 54.73% 43.91% -14.58% 100.00% 25 47.68% 50.23% 34.43% -6.09% 98.62%Utilities 83 18.78% 17.13% 24.49% -5.24% 49.73% 13 24.02% 27.48% 40.04% -28.77% 90.30%Grand Total 2,732 44.22% 46.09% 40.84% -5.96% 100.00% 650 48.31% 50.44% 31.20% -1.18% 94.65%

1 - The ultimate dolloar loss-given-default on defaulted debt instrument or obligor, discounted at the coupon rate on defaulted debt just prior to default = 1 - (discounted recovery at emergence from bankruptcy or time of final settlement as a percent of par).

Instruments ObligorsTable 3 - Discounted LGD1 by Industry Group (S&P and Moody's Rated Defaults 1985-2003)

Industry Group

Count / Stdev

Average / Median

Count / Stdev

Average / Median

Count / Stdev

Average / Median

Count / Stdev

Average / Median

Count / Stdev

Average / Median

Count / Stdev

Average / Median

Count / Stdev

Average / Median

Count / Stdev

Count / Average 115 1.31% 6 0.63% 0 N/A 0 N/A 1 96.98% 0 N/A 3 0.03% 125Stdev / Median 14.46% -0.18% 13.72% 0.03% N/A N/A N/A N/A N/A 96.98% N/A N/A 0.90% 0.04% 33.24%Count / Average 599 20.25% 71 29.51% 0 N/A 1 42.51% 1 75.28% 0 N/A 1 -0.60% 673Sstdev / Median 33.33% 3.33% 31.35% 25.04% N/A N/A N/A 42.51% N/A 75.28% N/A N/A N/A -0.60% 33.24%Count / Average 83 17.41% 50 33.45% 0 N/A 0 N/A 1 96.98% 0 N/A 0 N/A 134Stdev / Median 28.11% 1.07% 30.70% 34.69% N/A 34.69% N/A N/A N/A 96.98% N/A N/A N/A N/A 30.58%Count / Average 124 27.46% 90 40.47% 0 N/A 2 84.05% 0 N/A 0 N/A 0 N/A 216Stdev / Median 32.11% 13.93% 33.44% 39.56% N/A N/A 17.66% 84.05% N/A N/A N/A N/A N/A N/A 33.46%Count / Average 13 52.52% 27 36.80% 1 18.08% 7 30.37% 2 76.33% 0 N/A 0 N/A 50Stdev / Median 44.57% 67.67% 32.74% 49.32% N/A 18.08% 27.61% 22.85% 13.82% 76.33% N/A N/A N/A N/A 35.71%Count / Average 3 -0.85% 12 58.73% 0 N/A 0 N/A 0 N/A 0 N/A 0 N/A 15Stdev / Median 0.65% -0.81% 43.51% 64.98% N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 45.78%Count / Average 0 N/A 2 70.65% 0 N/A 0 N/A 0 N/A 0 N/A 0 N/A 2Stdev / Median N/A N/A 6.54% 70.65% N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A 6.54%Count / Average 82 35.06% 1 98.98% 596 55.03% 423 67.77% 369 67.22% 45 78.67% 1 98.58% 1517Stdev / Median 45.67% 26.72% N/A 98.98% 36.56% 62.47% 35.17% 81.66% 39.13% 82.84% 33.54% 95.25% N/A N/A 38.32%Count / Average 1019 20.30% 259 36.11% 597 54.96% 433 67.18% 374 67.45% 45 78.67% 5 19.62% 2732Stdev / Median 33.67% 2.56% 33.49% 32.77% 36.56% 62.43% 35.27% 81.48% 38.95% 82.86% 33.54% 95.25% 44.15% 0.04% 40.84%

1 - The ultimate dolloar loss-given-default on defaulted debt instruments, discounted at the coupon rate on defaulted debt just prior to default = 1 - (discounted recovery at emergence from bankruptcy or time of final settlement as a percent of par).

Senior Subordinated

Bonds

2nd Lien

Plant, Property & Equipment

Intellectual Property

Cash / Inventories / Receivables / Guarantee

All or Non-Current Assets / Oil & Gas Reserves

Unsecured

Total InstrumentSubordinated

Bonds

Total Collateral

Revolving Credit / Term Loan

Table 4 - Discounted LGD1 by Instrument and Collateral Types (S&P and Moody's Rated Defaults 1985-2003)

Senior Unsecured Bonds

Junior Subordinated

Bonds Other

Capital Stock / Inter-company Debt

Senior Secured Bonds

Most Assets / Real Estate

18

Cat

egor

y

Variable Count1st Percentile

25th Percentile Median Mean

75th Percentile

99th Percentile

Standard Deviation

Correlation with Obligor LGD

Correlation with Instrument LGD

Leverage Ratio (Book Value) 440 0.3463 0.7925 0.9508 1.0616 1.1373 3.1087 0.6489 -1.79% 1.46%Debt to EAAuity Ratio (Market) 330 0.1806 0.7383 0.8705 0.8126 0.9452 0.9999 0.1856 0.54% -10.55%Change in Leverage 428 -0.2318 0.0198 0.0962 0.2064 0.2219 1.6104 0.4645 -3.55% 2.87%Net Sales 441 0.1144 182.35 401.91 993.24 897.53 7911.76 2776.08 60.97% 3.31%Book Value 440 36.1991 206.88 454.95 1035.07 1143.92 9114.56 1566.69 69.41% 9.80%Market Value 329 -0.9111 1.34 1.79 1.79 2.25 3.90 0.84 36.70% 10.71%Tobin's AA 299 0.0220 0.5194 0.7494 0.9255 1.1081 3.5784 0.7124 11.89% 13.40%Quick Ratio 396 0.0497 0.2944 0.6634 0.8105 1.0564 3.2325 0.7152 -6.81% 2.84%Working Capital / Total Assets 424 -0.7045 0.0099 0.1118 0.1135 0.2264 0.6542 0.2207 -10.53% -7.12%Operating Cash Flow 411 -0.4217 -0.0619 0.0030 -0.0090 0.0392 0.2823 0.1370 14.37% -15.52%Cash Flow to Current Liabilities 384 -2.2322 -0.1586 0.0060 -0.0378 0.1309 1.5102 0.6012 10.24% -13.01%Return on Assets 427 -1.3696 -0.2259 -0.0878 -0.1786 -0.0221 0.0600 0.2637 7.29% -7.81%Number of Instruments 650 1.0000 2.0000 3.0000 4.2031 5.0000 31.0000 3.2816 3.52% 10.72%Number of Creditor Classes 650 1.0000 2.0000 2.0000 2.2185 3.0000 6.0000 0.8942 -5.58% -2.54%Percent Secured Debt 650 0.0000 0.0858 0.3767 0.4167 0.6737 1.0000 0.3448 -19.78% -4.84%Percent Bank Debt 650 0.0000 0.0344 0.2717 0.3237 0.5236 1.0000 0.2970 -23.48% -2.12%Percent Subordinated Debt 650 0.0000 0.0000 0.1935 0.3347 0.6740 1.0000 0.3671 13.75% 7.34%Altman Z-Score 295 -11.6200 -0.4078 0.6863 0.2811 1.5194 4.6266 2.6240 -6.44% -4.60%Number of Downgrades 364 0.0000 0.0000 1.0000 1.5797 2.0000 7.3700 1.6403 23.13% -11.12%Credit Spread - Obligor 650 0.0505 0.0877 0.1027 0.2874 0.1212 118.6156 4.6485 6.54% 1.59%LGD at Default - Obligor 460 -0.0073 0.4919 0.6822 0.6346 0.8193 0.9900 0.2391 49.08% 33.88%Credit Spread - Instrument 2687 0.0000 0.0250 0.0750 0.0750 0.1125 0.1695 0.0860 4.21% 19.43%LGD at Default - Instrument 1118 -0.0177 0.4063 0.6841 0.6841 0.8570 0.9900 0.2874 46.96% 66.69%Cumulative Abnormal Returns 200 -1.2779 -0.4638 -0.1222 -0.1153 0.1759 1.7470 0.5648 -19.60% -27.09%Seniority Rank 2732 1.0000 1.00 1.00 1.00 2.00 4.00 0.81 -4.13% 37.39%Collateral Rank 2732 1.0000 2.0000 8.0000 8.0000 8.0000 8.0000 2.8114 7.21% 48.68%Percent Debt Below 2732 0.0000 0.00 0.09 0.09 0.47 0.95 0.29 -0.88% -48.86%Percent Debt Above 2732 0.0000 0.0000 0.0000 0.0000 0.4111 0.9729 0.3005 -5.14% 38.77%Time Between Defaults 2732 0.0000 0.0000 0.0000 0.0000 0.0959 1.7725 0.3871 -5.80% -12.50%Time Since Issue 2364 0.0740 1.5911 2.6849 2.6849 4.4932 20.5112 3.5712 3.67% 10.25%Time-to-Maturity 2404 -0.2601 2.2486 4.5096 4.5096 7.0055 23.6050 4.6734 27.03% 27.21%Moody's All-Corporate Default Rate 650 0.0069 0.0169 0.0284 0.0291 0.0412 0.0534 0.0137 0.18% 2.75%Moody's Speculative Default Rate 650 0.0178 0.0421 0.0639 0.0687 0.0951 0.1300 0.0312 -1.76% 1.97%S&P 500 Return 650 -0.0223 -0.0069 0.0096 0.0057 0.0161 0.0340 0.0141 -7.29% 0.00%M

acro

econ

om

icTable 5 - Summary Statistics on Selected Variables and Correlations with Discounted LGD1(S&P and Moody's Rated Defaults 1985-2003)

Cap

ital

Stru

ctur

eC

ontra

ctua

l Fe

atur

esFi

nanc

ial V

aria

bles

Cre

dit Q

ualit

y /

Mar

ket

19

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