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Understanding and Predicting the Resolution of Financial Distress Michael Jacobs, Jr.1 Office of the Comptroller of the Currency Ahmet K. Karagozoglu Hofstra University Dina Naples Layish Binghamton University Draft: February 2007 J.E.L. Classification Codes: G33, G34, C25, C15, C52. Keywords: Default, Financial Distress, Liquidation, Reorganization, Bankruptcy, Restructuring, Credit Risk, Discrete Regression, Bootstrap Methods, Forecasting, Classification Accuracy 1 Corresponding author: Senior Financial Economist, Credit Risk Modelling Group, Risk Analysis Division, Office of the Comptroller of the Currency, 250 E Street SW, Suite 2165, Washington, DC 20024, 202-874-4728, [email protected]. The views herein are those of the author 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 the resolution of financial distress, bankruptcy or out-of-court settlement given default, as well as liquidation (Chapter 7) or reorganization (Chapter 11) given bankruptcy. This is done for a sample of 518 S&P and Moody’s rated defaulted firms in the period 1985-2005 for which there is an indication for the type of resolution and financial statement data from Compustat at the time of default. Various qualitative dependent variable models are estimated and compared: ordered logistic regression (OLR), multiple discriminant analysis (MDA), local regression models (LRMs) and feedforward neural network (FNN). Based upon a combination of prior research and exploratory data analysis, we select several accounting and economic variables at the time of default which are expected to influence these outcomes. Estimation results reveal the OLR specification to achieve best balance between in-sample fit, consistency with financial theory and out-of-sample classification accuracy. In predicting liquidation vs. reorganization and bankruptcy filing vs. out-of-court settlement, a stepwise analysis of models in the preferred OLR class shows variables capturing 8 of these dimensions (leverage, tangibility, liquidity, cash flow, proportion of secured debt, abnormal equity returns, proportion of secured debt, number of creditor classes, macroeconomic state, indicator for NY /Delaware filing district or pre-packaged bankruptcy and an auditor’s score) contribute significantly to overall fit joint explanation of liquidation or bankruptcy filing likelihood, having signs consistent with hypotheses. In comparing results to the prior literature regarding the determinants of successful resolution outcomes, we are consistent with White (1983, 1989), Hotchkiss (1993) and Bris (2006) regarding intrinsic value, asset size, respectively; in line (at variance with) with Lenn and Poulson (1989) (Jensen (1991)) regarding cash flow; inconsistent (consistent) on profitability (overall firm quality) with Kahl (2002); consistent with Matsunga et al (1991) and Bryan et al (2001) regarding the interest coverage ratio. Model performance is assessed on the dimensions of discriminatory power, predictive and classification accuracy. The former two are measured by implementing standard tests (power curve analysis and chi-squared tests), while classification accuracy is assessed according to alternative categorization criteria (expected cost of misclassification, minimization of total misclassification and deviation from historical averages) as compared to naïve random benchmarks. While in- and out-of-sample performance along these dimensions exhibits wide variation across models and criteria, the OLR and LRM models are found to perform comparably, while the FNN model is found to consistently underperform. The statistical significance of these results is rigorously analyzed and confirmed through a resampling procedure, yielding estimated sampling distributions of the performance statistics, confirming these observations. 2 Introduction 1. and Summary In situations of default or financial distress, when a private arrangement amongst a firm’s stakeholders cannot be made, firms in the U.S. file for bankruptcy and are placed under court supervision. Filing for corporate bankruptcy is mandatory under Chapter 11 of the 1978 bankruptcy code, where management and owners seek court protection against creditors and other claimants. Bankruptcy is usually settled with a court approved rehabilitation scheme in about 1.5 years from filing. However, the following alternative resolutions may occur: emergence as an independent entity, acquisition by other firms or liquidation of assets and the distribution of proceeds to stakeholders. Since firms filing for bankruptcy or in private workout share similar characteristics (i.e., declining revenues, earnings, asset and equity values), it is more difficult to differentiate between them and classify the final outcome, as compared to predicting financial distress. Consequently, in the prior finance literature, the problem of predicting bankruptcy resolution has not been studied as extensively as that of predicting financial distress. This is one of the first studies to do this in an econometrically rigorous fashion with an application to a current dataset of public defaults. First, we specify variables determining, and postulate relationships to, the likelihood of a defaulted firm in bankruptcy ultimately liquidating versus reorganizing2. Explanatory variables are chosen based upon economic theory, prior empirical results, and exploratory data analysis (all subject to availability). Second, we estimate and compare several qualitative dependent variable econometric models (ordered logistic regression - OLR, multiple discriminant analysis - MDA and feed-forward neural networks FNN), with various combinations of these variables, identifying a candidate models based upon in-sample as well as out-of-sample classification accuracy. Classification accuracy is evaluated by choosing cutoff probabilities that are optimal with respect to various classification criteria – expected cost of misclassification (ECM), unweighted minimization of misclassification (UMM) and deviation form historical averages (DHA). Finally, we conduct a bootstrap experiment in order to assess the out-of-sample predictive capability of the models. This exercise in predicting bankruptcy outcome is not only of academic interest but is of importance to a range of players in this domain of finance: investors in distressed equity and debt may use these results to build strategies; stakeholders in often prolonged court deliberations in developing a plan of negotiation; risk managers in building practical credit risk models; as well as guidance for specialists in banking workout departments. We believe that this modeling exercise can contribute significantly to informed decisions regarding the allocation of scarce resources to an often costly and time consuming process. A brief summary of our methodology, data and results is as follows: Theory, exploratory data analysis and estimation results reveal that ten variables satisfactorily explain bankruptcy resolution: higher interest coverage ratio, greater percent secured debt, higher spread on debt at default, or adjudication in certain filing districts is associated with a greater likelihood of liquidation versus reorganization; whereas greater asset size, higher leverage, increased free cash flow, more intangibles to total assets, longer time debt outstanding or a prepackaged bankruptcy decreases this probability. Stepwise regression procedures show that classes of debt, profit margin, industry indicator or macroeconomic state do not contribute, whereas all the other variables do contribute, significantly to the joint explanation of the liquidation probability. 2 Reorganization includes acquisition by another entity as well as emergence as a new entity. See Barniv et al (2003) for a three-group classification. 3 2. The OLR model is found to be superior to either the MDA or FNN models in terms of consistency with hypotheses, fidelity to the data and classification accuracy. In the preferred OLR model excluding assets, 10 (5) out of 14 variables jointly (individually) significant, pseudo r-squared is 18.6% and overall classification accuracy (depending upon classification criteria) ranges from 70-83%. While the FNN model has superior in-sample fit (pseudo r-squared of 19.3% and classification accuracy of 63-83%), coefficient estimates are not consistent with theory and out-of-sample performance is significantly worse than alternative models, at a much greater computational cost. While the MDA model exhibits comparable out-of-sample classification performance to the OLR model, signs of coefficient estimates are not consistent with theory, and in-sample fit is significantly worse than competing models (7.0% rsquared and classification accuracy of 50-81%). In comparing results to the prior literature regarding the determinants of successful resolution outcomes, we are consistent with White (1983, 1989) and Hotchkiss (1993) regarding intrinsic value and asset size, respectively; in line (at variance with) with Lenn and Poulson (1989) (Jensen (1991)) regarding cash flow; inconsistent (consistent) on profitability (overall firm quality) with Kahl (2002); consistent with Matsunga et al (1991) and Bryan et al (2001) regarding the interest coverage ratio. Out-of-sample analysis of classification accuracy reveals that while the models can generally beat random benchmarks, there is much variation in model performance depending upon classification criteria employed. As out-of-sample results on a split sample basis are not conclusive, we implement a bootstrap procedure, to measure the statistical significance of classification accuracy statistics relative to random benchmarks. The resampling experiment leads to sharper conclusions than the split sample exercise: under the ECM criterion, the MDA model outperforms OLR in overall classification accuracy, while OLR is better in classifying liquidation outcomes. Under the UMM or DHA criteria, this is reversed. Across classification criteria and outcome, it is found that the FNN model consistently under-performs competing models in out-of-sample classification accuracy. Future directions for this research include exploring different variables (accounting, economic or financial market), further variations on econometric models, extension of the data-set and joint prediction of with other quantities of interest (e.g., loss severity or time-to-resolution) Review of the Literature This purpose of this paper is to evaluate the outcome and resolution of financial distress. While the path to financial distress will reflect similar trends - decline in profits, decline in 4 cash flows, loss of revenues, etc. - the outcome of the distress can follow several paths. Once a firm is in default there are only two possible paths, either the firm will file for bankruptcy reorganization or the firm will resolve the financial distress out of court. This paper will attempt to classify these two types of firms according to which path is followed. Once this choice is made, there are several possible outcomes of the negotiation (either in or out of court). In either case, we see firms that are acquired or firms that emerge as an independent entity. There is a third possible outcome for firms that file for bankruptcy: liquidation. So, in general, we see five paths that a financially distressed firm can follow (see Figure A1). Using the S&P LossStatsTM database we are able to obtain detailed information about the financial distress and the resolution of this distress on 519 publicly traded firms. The S&P LossStatsTM database is one of the most extensive loss severity database of public defaults (Keisman et al, 2001). It contains data on 2,102 defaulted instruments from 1986 – 2003 for 560 borrowers, having some publicly traded debt and for which there is information on all classes of debt. All instruments are detailed by type, security, collateral type, position in the capital structure, original and defaulted amount resolution type, instrument price at emergence from as well as the value of the securities received in settlement from bankruptcy. Most of the firms in the sample file for bankruptcy and successfully emerge as an independent entity (see Table 1). For the firms that are able to resolve their financial distress outside of the court system, most firms (94%) emerge as an independent entity. A smaller percentage of the firms that file for bankruptcy are able to remain independent, only 74% of the firms that file for bankruptcy are able to successfully resolve the financial distress. The remaining firms are either acquired (9.5%) or liquidated (16.5%). We also see that no matter which path is followed, in court or out of court negotiations, most firms (78%) remain independent following the resolution of the financial distress. And the likelihood of remaining an independent firm increases with an out of court restructuring. In evaluating the outcomes of financial distress this paper will answer three main questions. The first question will examine the characteristics of firms that are able to resolve their financial distress out of court compared to firms that aren’t and file for bankruptcy. Specifically, we will attempt to determine what is different about the firms that are able to restructure privately. The second question will focus on firms that file for bankruptcy. In this sample of firms, we will examine what determines the outcome. For example, are there any indicators that separate firms that are able to emerge as independent going concerns with firms that are acquired and/or firms that are liquidated. And the third question will examine the five paths following financial distress (see Figure A1). Are there any firm characteristics that can predict which path a financially distressed firm will follow? See Table A2 for a breakdown of the possible paths a financially distressed firm can follow. Capital structure theory, under very strict assumptions of firm behavior and market conditions, assumes away the costs of bankruptcy. Miller and Modigliani (1958 and 1963) assume firms can costlessly enter bankruptcy. This theory provides an excellent foundation for understanding the decisions of firms that are far enough away from financial distress. It is safe to assume that firms that are not in danger of filing for bankruptcy do indeed have very small, almost zero, costs of bankruptcy. But for firms that are in danger of filing for bankruptcy, the costs, both explicit and implicit, of bankruptcy is substantial. As the probability of bankruptcy increases, bankruptcy costs become significant and we may see a shift in the goals of the firm. 5 The cost to society of firms that file for bankruptcy can also be substantial. The loss of employment, equity value and confidence in business can impose substantial hardship on those directly involved, as well as on society as a whole. Recent bankruptcies, such as Enron and WorldCom, clearly show the impact bankruptcy can have on society. As a result of this impact, in 2002 the Sarbanes-Oxley Act became a federal law that heightened accountability standards for individuals responsible for documenting and reporting the financial health of a publicly traded firm. We have seen a general decline in the overall trust and confidence placed in the financial reporting of publicly traded firms as a result of these highly publicized bankruptcies. While one would expect managers of all firms to attempt to maximize the value of the firm, firms that are in financial distress may not make the same decisions as a firm that is not in financial distress, further imposing costs on society. One can argue that due to the small probability of filing for bankruptcy (less than 1% of all firms file) the costs of bankruptcy are also very small. But for the subset of the population that does file for bankruptcy, bankruptcy costs are substantial. Firms in financial distress experience significant loss in value prior to, during and following the resolution of the financial distress, imposing significant costs on all of the claimants of the firm and society in general. Bris, Welch and Zhu (2004) find that bankruptcy costs can be as high as 20% of the firm’s value prior to the bankruptcy filing. The resolution of financial distress can take two general forms: an out-of-court restructuring or a bankruptcy filing through legal channels. Most bankruptcy filings begin as an out of court restructuring with the firm only filing for bankruptcy when the negotiations fail or to facilitate the prefiling negotiations, more commonly known as a prepackaged bankruptcy. In the United States, once a firm decides to file for bankruptcy it can decide whether to reorganize under the Chapter 11 procedure or to liquidate under the Chapter 7 procedure . Under Chapter 11, the court provides an automatic stay on the firm’s assets, that is the firm is protected against creditors, secured and unsecured, attempting to force repayment. In almost all Chapter 11 cases, the firm’s existing management remains in control of the firm, as debtor in possession, and continues to make operating decision for the firm and deal with the reorganization procedure. Under Chapter 7, the firm is liquidated. A trustee is assigned to the case and is responsible for selling the assets of the firm and repaying creditors according to the priority structure of the firm’s capital structure. There is considerable debate in the literature about the most efficient bankruptcy procedure. The purpose of any bankruptcy code is to facilitate the redistribution of assets to their best use. Two distinct types of bankruptcy codes exist in the world today, creditor based and debtor based. Creditor based systems, found in Japan and Germany, automatically remove the firm’s management and install a bankruptcy trustee who is responsible for determining the final outcome of the procedure. Debtor based systems, found in the United States and Canada, allow existing management to stay in control of the firm’s operating decisions. Arguments have been made both for and against these two opposing systems. Critics of the current bankruptcy laws in the United States argue that the system is pro-debtor, allowing for the reorganization of inefficient firms while incumbent management remains in control of the firm’s assets, for example Jensen (1991), Baird (1986) and Bradley and Rosenzweig (1992). Whereas, Berkovitch, et al. (1998) argue that it is essential that bankruptcy laws are pro-debtor in order to properly incentivize managers to maximize firm value, even when facing financial distress. While several authors argue for an auction-like system (see Baird (1993) and Easterbrook (1990)) to better redistribute assets, Stromberg (2000) shows that, in Sweden, the auction system does not eliminate the agency problem among claimants in a financially distressed firm. He further reports that the cash auction system currently operating in Sweden, looks more like the US reorganization procedure, with similar advantages and disadvantages. Theoretically an auction system may allow assets to be redistributed to their best use, but practically implementing such a system is extremely difficult. 6 While, Kahl (2002) finds that correctly separating efficient firms from inefficient firms is extremely difficult and the continuation of inefficient firms is necessary in order to eventually find the efficient firms. While debate over the efficiency of the bankruptcy laws have important public policy implications, inquiry that tries to understand how economic fundamentals interact with the rules of the game to determine outcomes of the process has an equal place. This is research that develops tools to help investors and risk managers use the rules to their advantage, to either avoid losses or even profit from financial distress, which promotes efficiency in its own right, and ultimately leads to evolution of the legal system towards a form that facilitates a more efficient distribution of scarce resources. The purpose of this paper is not to debate the efficacy of bankruptcy laws and to propose an efficient bankruptcy procedure. Rather we focus on determining which types of firms are able to survive financial distress and successfully remain as an independent entity following this resolution. By examining pre-distress firm characteristics, we hope to be able to properly predict the five possible outcomes of financial distress, as defined in Table A2 and Figure A1. This exercise in predicting bankruptcy outcome is not only of academic interest but is of importance to a range of players in this domain of finance: investors in distressed equity and debt may use these results to build strategies; stakeholders in often prolonged court deliberations in developing a plan of negotiation; risk managers in building practical credit risk models; as well as guidance for specialists in banking workout departments. We believe that this modeling exercise can contribute significantly to informed decisions regarding the allocation of scarce resources to an often costly and time consuming process. 3. Testable Hypotheses Several theories have been developed to predict the resolution of financial distress (White (1983, 1989) and Hong (1984)). We have used these theories to develop our testable hypotheses. H1. Larger firms will be more likely to successful emerge from financial distress (Hotchkiss, 1993) H2. A firm will be more likely to successful emerge from financial distress the greater the value of the firm’s intangible assets (Hong, 1984) H3. A firm will be more likely to successful emerge from financial distress if prior negotiations with lenders occurred (prepacks). H4. A firm will be more likely to successful emerge from financial distress that have greater managerial stock ownership (Casey et al, 1986). H5. A firm will be more likely to successful emerge from financial distress that has greater profitability (Kahl, 2002). H6. A firm will be more likely to successful emerge from financial distress that is more diversified (more room to divest underperforming assets). H7. A firm will be more likely to successful emerge from financial distress if it has more free cash flow (Lehn & Poulson, 1989). This can be considered either positively or negatively 7 related to reorganization. Firms with more free cash flow should be in a better position to restructure their capital structure and get out of bankruptcy successfully. Alternatively, agency problems are greater for firms with greater free cash flow (Jensen, 1991), so these firms may be more likely to be liquidated. H8. A firm will be more likely to successful emerge from financial distress if tenure of existing management is longer. Although most managers are replaced, managers who have been with the company a longer time will be more partial to reorganization. They would have more human capital or wealth tied in the firm (White 1983,1989). H9. A firm will be more likely to successful emerge from financial distress in certain filing districts – the Southern District of New York is notoriously pro-debtor, so these firms are more likely to be reorganized, no matter what. H10. A firm will be more likely to successful emerge from financial distress that has greater free assets (unsecured – secured debt vs. total assets). H11. It is expected that higher industry leverage will affect the firm chances of being acquired or liquidated. Hotchkiss (1993) argues that higher industry leverage will increase the probability of reorganization. However, along the lines of Shleifer & Vishny (1992), firms that would be in the market to buy the assets of the bankrupt firm will not be able to (using debt financing) if they have too much debt. H12. Industry concentration as measured by the Herfindahl index (Lang & Stulz, 1992). According to Hotchkiss (1993), firms in more concentrated industries have less potential buyers so the firm is more likely to be reorganized (I am not sure if I agree with that theory). H12. Long term vs. short term debt ratios: Firms with more short term debt are much closer to the insolvency region than those with more long term debt. It might be easier to renegotiate debt that is not supposed to mature immediately. H14. Free assets, unsecured – again from Hong’s dissertation. The greater the firm’s free assets the better its ability to borrow (using these assets as security) to improve its financial condition. This probably should be compared to existing debt levels. H15. Change in total assets, prior to filing – Casey et al (1986) measure this 3 years prior to filing. White (1983, 1989) predicts that size is related to borrowing capacity, so larger firms should be better able to reorganize. Firms that are shrinking will not be able to borrow. We could also look at this measure at the industry level. H16. Macroeconomic factors will play a role in the reorganization/liquidation outcome. The arguments here are 1-In a downturn, creditors are less likely to sell assets when asset values are depressed, hence more likely to attempt a reorganization, 2 - Failing during an expansion sends a different signal about ultimate quality of the business than during an downturn (a “signaling story”). In a model by Brown et al (2004), which is developed and tested empirically on real estate data, in a owner managed and endogenous default setting, when industry wealth is low in all cases there is restructuring (regardless of the realization of random project value, another variable in the model). H17. Interest coverage ratio – Matsunga, Shevlin & Shares (1992) argue that this measure proxies for the distance a firm is from violating a debt covenant, hence if this is lower it may be a signal that the default is technical in nature, and therefore that liquidation is less likely there (Bryan et al, 2001). 8 4. Econometric Models and Measurement of Classification Accuracy Various techniques have been employed in the finance and economics literature to classify data in models with qualitative dependent variables. Maddala (1983, 1981), Ohlson (1980), Lo (1986) and Venables and Ripley (1999) introduce, discuss and formally compare the different models. Classes of models employed in the literature span linear (e.g., multiple discriminant analysis-MDA), generalized linear (e.g., multinomial logistic resgression-MLR), generalized additive (local regression models-LRMs) non-linear models (multi-perceptron neural networks-MNN). Following the seminal work by Altman (1968) in classifying healthy vs. financially distressed firms, numerous studies in the finance and accounting literature followed, the early studies primarily deploying versions of MDA. Later studies use generalized linear (GLM), such as logit (Ohlson, 1980) and probit (Zmijewski, 1984).3 Among the first of the few existing studies to deal with the post-bankruptcy scenario, LoPucki (1983) uses linear correlation analysis to examine bankruptcy outcomes for a small sample of firms. Casey et al (1986) build an MDA model to discriminate between a group of liquidated and restructured firms using purely accounting variables. Kim and Kim (1999) apply a similar model to a set of firms in Korea. In a recent study, Barniv et al (2002) apply an OLR4 model to predict a three state resolution (liquidation, acquisition or emergence), to a sample of 237 defaulted firms from 1888 to 1995, using 5 accounting and 5 non-accounting variables. Optimal cutoff points are determined by an empirical quantification of the relative costs of misclassification.5 While signs on and statistical significance of coefficients are not consistent with theory across all specifications, they are able to achieve 70% out-of-sample classification accuracy relative to random classification scheme. Fisher et al (2003) apply a similar model to 640 bankrupt firms in Canada from 1977-1988 with 13 accounting and macroeconomic variables. The authors attempt to directly test the theoretical model of Bulow and Shoven (1978), finding that while the data is generally supportive of the framework, there are other dimensions of resolution determination not captured by the model. 4.1 Alternative Econometric Models In order to probabilistically classify bankruptcy resolution, we propose to compare these three approaches. As the model representative of the GLM class, as well as an overall baseline model, we choose the MLR. This is motivated by the commonness of application in the recent distress and bankruptcy resolution literature, as well as its simplicity and defensibility relative to more computationally intensive approaches, both within and outside of this class.6 MLR assumes that the dependent variable Y can take on r = 1,..,R unordered discrete values (resolution types) for each independent observation i = 1,..,N. Then the random variables Yi is multinomially distributed. OLR models the conditional mean probability of observing resolution r linked to a linear function of explanatory variables through a logistic function7: 3 More recent studies of bankruptcy prediction having a bearing on this current research in terms of methodological issues that include: optimal cutoff points for prediction (Hsieh, 1993), real variables (Platt et al, 1994), intra-industry effects (Akhigbe et al, 1996), loan / default accommodation (Ward et al, 1997), cash management with earnings retention (Dhumale, 1998) and the impact of audit reports (Lennox, 1999). 4 Also called “polychotomous dependent variable regression”. 5 Based upon the analysis of cumulative abnormal returns (CARs) through the bankruptcy period, the authors claim that it is 3 times more costly to misclassify a liquidation as either an acquisition or emergence than it is to misclassify the latter two. 6 Triguerios and Taffler (1996) demonstrate the pitfalls in applying more elaborate techniques, such as non-parametric MDA and NN, for statistical analysis of this nature. 7 This is also known as the link function in the terminology of the statistics literature. 9 exp βTr Xi + ri Pr(Yi = r | Xi ) = F β 2 ,.., β R , Xi = exp R 1+ βTj Xi + ji (4.1.1) i = 1,..N;r = 2,.., R j=2 For the baseline category, r = 1, we have: 1 Pr(Yi =1| Xi ) = F β 2 ,.., β R , Xi = exp R 1+ βTj Xi + ji (4.1.2) i = 1,..N j=2 Where Pr(.) denotes probability, F(.) is a cumulative distribution function, βr βr1 ,..,βr k is T a vector of regression coefficients for the rth resolution type, and Xi Xi1 ,..,Xik is a T vector of explanatory variables for the ith observation. Category 0 is known as the baseline category, in that the relative likelihood of any outcome can be represented relative to this one. This can be arbitrary, but generally we try to give this some meaning, here being the most likely outcome. 8 We can express this model in terms of a logit transformation of the dependent variable as the log odds ratio of any outcome relative to the baseline: Pr(Yi = r | Xi ) T log β r Xi + ri Pr(Yi =1| Xi ) i = 1,..N;r = 2,..,R (4.1.3) This can estimated by maximum likelihood (ML) in most standard statistical packages.9 We define the dummy variables: 1 if Yir =1 d ir = 0 otherwise (4.1.4) i =1,.., N;r = 1,.., R Then the log-likelihood function can be written as: Log L β1 ,.., β R ; X1 ,.., X n , Y1 ,.., Yn N R d ir Pr(Yi = r | Xi ) (4.1.5) i=1 r=1 The second linear qualitative dependent model that we implement, in the generalized linear model class, is local regression models (LRMs), as discussed in Hastie and Tibshirani (1990), Siminoff 91996) and Bowman and Azzalini (1997). This represents a generalization of GLM framework, in which we replace a linear function by an additive predictor, or a linear combination of smooth functions fi : R R : 8 If we are in a 3-state setting for resolution, we can code the polychotomous dependent as: 0 if reorganization r 1 if acquisition 2 if emergence We implement the model in S-Plus, a scientific computing environment that is equipped with functions calls and specialized diagnostics for an entire suite of models in the GLM class (Venables et al 1999). 9 10 n Pr(Yi = r | Xi ) = L-1 f i Xi + i i=1 where the link function L x (4.1.6) 1 is taken to be the logistic function. In GLM 1 e x terminology, L(.) relates the conditional mean of the dependent variable (i.e, the probability of occurrence) to a linear function, which is extended in this context to a sum of arbitrary functions satisfying certain regularity conditions. While not directly a non-linear parameterization, this allows specifying non-linear transformations of the independent variable.10 In the class of neural networks, we consider the feed-forward neural network model (FNN): k Pr(Yi 1| Xi ) F βT Xi 0 0 j j βTj Xi i j 1 (4.1.7) Where φ x 1 exp x is taken to be the logistic function, φ 0 . is the activation function 1 in the outer layer, α0 is the bias in the hidden layer, φ j . is the jth activation function (output unit) in the hidden layer, αj is the weight on the jth activation function, β j is the coefficient vector in the jth output unit in the input layer with first element βj0 the corresponding bias and k is the total number of output units. Motivated primarily by considerations of tractability, we restrict ourselves to a FNN’s having single hidden layers, but possibly different numbers of output units in this single layer. 4.2 Measures of Model Performance Measuring model performance in this context can be accomplished in several ways. There are dimensions along which we may measure model performance, corresponding to competing objectives in how a model is to be implemented. These correspond to 2 notions of accuracy - classification accuracy versus predictive accuracy. Classification accuracy is the ability of the model to discriminate amongst outcomes, or in the parlance of credit risk modeling, quantify risk in a relative sense. This means that the model tends to identify observations that will be in the categories modeled. 11 Predictive accuracy is the ability of the model to forecast the level of the response variable in an absolute sense, or to measure risk cardinally. In probabilistic modeling, for default frequency or in the present context of resolution of default, this represents the ability to produce an estimated probability that is correct most of the time on average.12 4.2.1 Classification Accuracy This is closely related to the method of splines (Green and Silverman, 1994). Although the values of the estimated probabilities may fall far from the observed frequencies (e.g., a model that process a “pass/fail” signal and is correct ex post will classify perfectly, but will be predictively inaccurate, in that forecasted probabilities are never close numerically to actual ones.) 12 Operationally, this means that forecasted probabilities conditional on certain characteristics tend to closely match observed frequencies in repeated sampling. 10 11 11 There are various ways in which this may be measured. First we consider the more traditional approach taken in the finance and biostatistics literature, the analysis of classification accuracy, which centers upon the choice of a cutoff probability for optimal classifying an observation. In this framework, we follow the approach of choosing a cutoff point that minimizes some measure of misclassification (Altman, 1968), both within and out-of-sample.13 In the formulation of the first objective function considered, we minimize an expected cost of misclassification (ECM) function (Frydman et al, 1985): K n r Xi , βˆ , M, c r 1 Nr ECM X i , βˆ , M, c Pr Cq|r (4.2.1.1) Where r = 1,..,K is a type of resolution, Pr is the prior probability of observing the rth resolution, q|r is the set of all resolutions not equal to r, Cq|r is the cost of misclassifying the rth type of resolution, Nr is the number of resolutions of type r in the sample and nr(c) is the number of misclassifications for the rth resolution as a function of the cutoff c. We consider two special cases of (5). First, we follow Barniv et al (2003), who present empirical evidence that the costs of misclassifying a liquidated firm is about 3 times that of misclassifying other resolution types (emergence or acquisition in their 3 state framework). 14 Therefore, for K = 2 , Cr|l = 3 and Cl|r = 1 (5) becomes: ECM0 Pr nr c n c 3Pl l Nr Nl (4.2.1.2) Where Pr (Pl) is the prior probability in the broader universe, Nr (Nl) is the actual number and nr (nl) is the number misclassified in the estimation sample, of reorganizations (liquidations).15 Given a set of estimated parameters in (1), the optimal cutoff c* is the value such that a larger predicted probability of liquidation results in classification as such, which minimizes the value of the criteria given by (9)-(11): c*M argmin ECM c | Xi , βˆ , M, Pr , Pl , N r , N l c (4.2.1.3) Based upon the results of this optimization, we can conduct two kinds of analysis regarding the predictive power of the model. First, we can compute (5) using the estimation results using the entire sample, and then measure the proportions correctly predicted within-sample. Second, we can perform an out-of-sample analysis of predictive ability by estimation of a model (4)-(6) and a corresponding optimal cutoff (5) on a subsample, and then classification of a holdout sample. We propose extending the latter through a resampling (or bootstrap) procedure, in which we build the model and predict The Lachenbruch (1967) “U-technique” can be thought of as a hybrid of in- and out-of-sample evaluation, in which the model is estimated leaving out one observation at a time, and then classifying the holdout, until all observations have been classified in this way. Then the distribution of proportions correctly predicted in each category can be analyzed. However, evidence suggests that this yields assessments very close to in-sample prediction, in which each observation is classified with the models as built on the full sample (Barniv et al, 2003). 14 This is based upon analysis of cumulative abnormal returns (CARs) for equity prices of defaulted firms through the resolution period. 15 The prior probabilities are given by the frequencies of liquidated/reorganized firms in the entire LossStats™ database (Pr = 86.6%, Pl = 13.4%) and the respective numbers of resolution type are given by the counts in the estimation sample (Nr = 44, Nl = 220). 13 12 out-of-sample many times on randomly sampled (with replacement) estimation and testing samples. This is a simple way to measure the confidence around statistics of interest in out-of-sample predictions, such as liquidation or reorganization resolutions correctly classified, for which we have no distribution theory16 (Efron, 1979; Efron et al, 1986; and Davison et al, 1997). In addition to the ECM approach, we will evaluate the classification accuracy of these models according to other commonly employed metrics, Kolmogorov-Smirnov (KS) and Area Under the Receiver Operating Characteristic (AUROC) statistics. Let F(Pˆi | X , βˆ ,Yi = j,M) denote the cumulative distribution function of the predicted i probability (or “score”) for outcomes j=0,1 (reorganization, liquidation), where M denotes the model under consideration (logistic, local regression or neural network). The KS statistic is the maximum distance between the cumulative distributions for the given outcomes: KS arg minF(Pˆ i P̂i | X , βˆ ,Yi = 1,M) F(Pˆi | X , βˆ ,Yi = 0,M) i i (4.2.1.4) This criterion favors the model which gives rise to the greatest degree of separation between the distributions of the liquidated and non-liquidated populations. The AUROC statistic is derived from the receiver operating characteristic (ROC) curve. In the classic representation of signal detection theory, the ROC is a graph of the proportion of the sample that the model predicts will have a characteristic (e.g., a liquidation), as the classification threshold (i.e., the cutoff probability) is varied, versus the true proportion at each of these levels. In the commonly used version of this, the scale of the x-axis is transformed from the sample proportion into the cutoff probability, giving rise to the following notation: let the complement of the cumulative distribution function of the fitted probability in model M be given by a decreasing function of the cutoff c: F(c | X , βˆ ,Pˆi ,M) 1 F(c | X , βˆ ,Pˆi ,M) Pr Pˆi c | X , βˆ ,M i i i (4.2.1.5) This corresponds to a probability of incorrect classification in the target group under the null hypothesis H0 : Yi = 0 17. Against this we graph the probability of correct classification18: (c | X , βˆ ,Pˆi ,M) Pr Yi 1| F(c | X , βˆ ,Pˆi ,M) i i (4.2.1.6) The AUROC is then the area under this curve and above the 45 line in c-(c|.) space: 1 1 AUROC 2 (u | X , βˆ ,Pˆi ,M)du i 2 0 (4.2.1.7) In the terminology of classical statistical inference, under the null hypothesis of liquidation, reorganizations (liquidations) incorrectly (correctly) classified are false positives (negatives). 17 Also called the probability of a false positive, probability of a Type 1 error under the null hypothesis, or one minus the specificity. Specificity is defined as the probability of correctly failing to reject the null, or a true negative. 18 Also called the probability of a true positive, one minus the probability of a Type 2 error under the null hypothesis, the sensitivity or the power of the test. Sensitivity is defined as the probability of correctly rejecting the null. 16 13 The closer this quantity to unity, the better the model can discriminate between the outcomes of interest. However, this test says nothing about how we would choose the cutoff in implementing the model, nor how the model performs at different ranges of the cutoff. 19 4.2.2 Predictive Accuracy We will consider various measures of predictive accuracy – McFadden Pseudo R-Squared (MP-R2), Pearson Chi-Squared (P-X2), Hoshmer-Lemeshow Chi-Squared (HL-X2) and Le Cessie and Van Houlwelingen Chi-Squared (LCVH-X2). In the context of qualitative dependent variable models, standard measures goodness-of-fit measure – such as a linear r-squared – are difficult to interpret. Let us consider the binary dependent variable case Yi = 0,1 and denote the fitted values, or predicted probabilities, under Model M by F ˆ , Xi ,M = ˆiM . The residual deviance of the model, also twice the maximized loglikelihood, can be written as: n Y DM 2 Yi log iM ˆ i 1 i 1Y i 1 Yi log ˆ M i n ˆ M i 2 log 1 ˆ M i 1 i ~ 2 n k (4.2.2.1) a This has an interpretation analogous to a sum-of-squared residuals, in that a large value indicates a lack of fit, but taking this analogy too far can be dangerous in this context.. Under certain assumptions and in large enough samples, (1.1) follows a chi-squared distribution, but in most practical situation this is far from reality. The MP-R2, commonly reported in the finance literature, compared the deviance in a “Model 0” having only an intercept (the null-deviance D0) to (1.1): RM2 1 DM LR M : 0 D0 D0 (4.2.2.2) where the numerator is the likelihood ratio statistic that tests the restriction of sub-model 0 with respect to Model M, normalized by the residual deviance. The closer that (2.2) is to unity, the better the fit of the model, in analogy with the linear r-squared of OLS regression. A closely related statistic is the P-X2, the sum of the squared generalized residuals Yi ˆiM scaled by the estimated standard deviations Y ˆ rˆ ~ n k 1 ˆ ˆ n PM ˆiM 1 ˆiM : i 1 M i 2 n 2 i M M i i i i 1 (4.2.2.3) 2 a Where we define the standardized generalized residuals by rˆi Yi ˆ M 1 ˆ i M i ˆ M i 1,.., n . i 19 It can be shown that the AUROC is related to the Mann-Whitney U-Statistic, a non-parametric test of the difference in medians between independent random variables measured on a least an ordinal scale. In the current context, the Ustatistic would be computed by looking at all comparisons of predicted probabilities in the 2 groups, and this would be scaled by all possible comparisons (the product of the sample sizes), to produce a quantity that we could interpret as the probability that the fitted probability of liquidation is greater than that or reorganization under the model being estimated. 14 As noted by Hosmer et al (1997), only under three assumptions are these tests of predictive accuracy valid: the link function F(.) must be correct (e.g., logistic), the linear predictor βT Xi must be correctly specified (i.e., no non-linear transformations of the covariates or interaction terms), and (in the binary case) the variance must be Var Yi | Xi ˆiM 1 ˆiM (i.e., Bernoulli). However, even if these assumptions 20 hold, the p-values from these test statistics are likely to be highly inaccurate in finite samples. Hoshmer and Lemeshow (1980) propose a test statistic that is more robust to small samples and violations of any of these conditions, the Hoshmer-Lemeshow C-Statistics (HL-C), which groups the observations into G risk buckets based upon the predicted probability.21 O n 1 G HLM g M g g 1 where Og g M g M g 2 ~ 2 n 2 (4.2.2.4) a ng Y is the number of occurrences of the event of interest n i g is the sample size i 1 such that n G n g 1 g , and ng gM ˆ M i is the average predicted probability under model M in i 1 the gth group, g = 1,..,G. While this test may have intuitive appeal, a severe limitation is its dependence upon the segmentation scheme. Furthermore, as note by Le Cessie and Van Houlwelingen (1991, 1995; LCVH), this test statistic suffers from low power against several common specifications close to the logistic model, in that the grouping in (1.4) are based upon a grouping strategy in “Y space”, whereas departures from the null in the x space (especially if an alternative configuration gives rise to the same fitted probability) are likely to go undetected. LCVH address this problem by constructing a class of test statistics based upon residuals smoothed according to distance measures in x.22 We follow LCVH by defining the weight function between (a uniform kernel) the ith and jth observation to be: xik xij I cw ˆ k 1 x k p wij (4.2.2.5) 1 x 0 Where I x is the indicator function, ˆ . is the sample standard deviation of the 0 x 0 2 vector x k and the constant cw 1 is taken from LCVH (1991,1995). The LCVH test statistic n2p is given by: i 1 n LCVH M 2 wij rˆj j 1 n n rˆ 2 si (4.2.2.6) i 1 20 Hosmer et al (1997) point out that there must be a fixed number of distinct values that each independent variable can assume, and the sample expectation of these must exceed some minimum number (such as 5) for each value of the binary dependent variable, for the p-values in a these chi-squared tests to be valid. 21 There are variations of this in which these are deciles, based upon the ordered values of the predicted probabilities, or groups of equal numbers also based upon this criterion. 22 This is closely related to the literature on non-parametric regression, see Copas (1980) and Azalini et al (1989). 15 Where the smoothed standardized generalized residuals are defined by rˆSi2 n w rˆ ij j . The j 1 distribution of the test statistic follows from a normal approximation LCVH M LCVH M ~ N 0,1 given in Hosmer et al (1997). LCVH M 16 5. Data, Summary Statistics and Univariate Statistical Analysis 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. We have merged Moody’s ##### V #.# 2006 database with various public sources of information (SEC filing from Edgar, LEXIS/NEXIS, Bloomberg, Compustat and CRSP). It contains data on 2,732 defaulted instruments from 1985-2004 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. Table 1 summarizes resolution processes (out-of-court settlement vs. bankruptcy filing) and outcomes (reorganization vs. liquidation) by year, for the entire database and for the Compustat matched sample (518 out of 650 firms). Overall and by year, it can be seen that the Compustat sample is very representative of the universe of companies in this database. Over 20 years, in the entire database 13.4% (86.6%) of outcomes are liquidation (reorganization), while the corresponding frequencies are 13.3% (86.5%) in the Compustat sample. 81.9% (18.1%) of resolution processes are bankruptcy (out-of-court) in the broad sample, as compared to 81.3% (18.8%) for the Compustat matched firms. There is wide variation across time in the relative frequencies of both outcome and process, a range of 5-27% for liquidation percentages (excluding 1985 and 1987), while bankruptcy frequencies lie between 56% and 100% (excluding 2004). While anecdotal evidence suggests that liquidation has become more common with time, it is difficult to discern this pattern in this data. It is possible that the likelihood of this outcome is also influenced by cyclical factors – we see increases during the 1998 and 1998-2000 periods, preceding a downturns in the economic cycle. We also see the relative frequency of bankruptcy processes increase in benign periods, such as the mid 1990’s. Table 2 presents a breakdown of the database by industry, in entirety and the Compustat matched sample, for resolution and process type within each industry. We use the highest level NAIC classifications, as the data is rather thin at more refined industry levels, in order to make very precise conclusions. The borrowers are spread out among industries in a manner consistent with prior expectations supporting the presumption that this sample is representative of the broader universe of large companies having publicly traded debt. Further, the Compustat matched sample is close in distribution across these groups to the broader database. The top 3 groups (Consumer / Service, High Technology / Telecommunications and Leisure Time / Media) constitute nearly 50% of the database. Among the larger groups for which differences are might be more reliable, liquidation is relatively most likely in Consumer / Service (18.7%), and less likely in Leisure Time / Media (8.2%). No utilities are liquidated, while the greatest proportion of bankrupt Financial Institutions are liquidated (22.2%), but the number of observations in these groups (8 and 18, respectively) are too low to make definitive statements. In the case of the process whereby financial distress is resolved, firms in Insurance / Real Estate are most likely to go through bankruptcy (88.9%), while Utilities are least likely (63.5%), but the same caveat regarding the size of these groups applies. The larger groups are all close to the mean bankruptcy frequency of 81.3%. In order to explain resolution of financial distress, 14 variable groupings were chosen, on the basis of theory or prior empirical results seen in the literature, as well as exploratory statistical analyses. This set is optimal in the sense of balancing performance across models with theoretical considerations. The dimensions that they capture, the empirical 17 proxies used and hypothesized relations to the resolution or process type are listed in Table 3. Among groups of financial statement variables, among those hypothesized to reduce the probability of either or bankruptcy given financial distress, or liquidation given bankruptcy, include measures of leverage (book, long term debt and debt to market value of equity ratios). The rationale is three-fold, in that greater leverage implies lower recovery in liquidation, hence an incentive to attempt a reorganization or avoid bankruptcy, under Chapter 11 if book value is negative then equity is given a greater say and higher leverage is a signal that the fundamental business may be viable in financial distress. Larger size / scale of operations (book value of assets, market value of equity, sales) also reduces the chances of liquidation. Larger scale of operations implies a better candidate for rehabilitating business model and therefore a successful reorganization. The complexity of larger firms and self-selection may make bankruptcy more likely, as bigger firms better candidate for rehabilitating a business model, and therefore a successful reorganization. However, the complexity of larger firms or self-selection may make bankruptcy more likely. Greater tangibility (Tobin's Q, book value ratio of intangible to total assets) is associated with increased likelihood of liquidation, as a greater proportion of intangible assets make a defaulted borrower a more attractive acquisition candidate, or makes liquidation more costly thus lowering the chances of liquidation. However, the sign may go either way with bankruptcy, as the bankruptcy process may be more destructive of value with less tangibility, but this may be countered by self-selection. Cash flow measures (free cash flow and cash flow from operations) and profitability (profit margin, return on equity, retained earnings to total assets, net cash flow to current liabilities) are postulated to be inversely related to either of these events, in that greater cash generating ability indicates better quality of the borrower, ability to restructure and a lower probability of liquidation or bankruptcy. Alternatively, agency problems are greater with more cash (Jensen), but this may not be operative in financial distress. Liquidity variables (interest coverage, free asset, and net working capital to total asset ratios) are though to have either a positive or negative influence on either bankruptcy or liquidation likelihood. While higher greater liquidity implies that a firm is in a better position to keep operating through bankruptcy proceedings, therefore a reorganization is the more likely outcome as well, it is also the case that higher liquidity can facilitate liquidation as the “fire-sale costs” may be lower with increased ease of disposal. The capital structure variables, percent secured debt and number of major creditor classes at default, are thought to be positively related to both the probabilities of bankruptcy and of liquidation. The former is a due to greater bargaining power among secured creditors makes liquidation or bankruptcy filing more likely. The latter is a coordination story, in that more parties involved in resolving financial distress imply greater difficulties in either negotiating a reorganization or negotiating an out-of-court settlement. Borrowers with lower credit quality prior to default (measured by credit spread just prior to default, implied loss-given-default at default on traded debt, investment grade status at origination or the Altman Z-Score a year prior to default) are thought to be more candidates for liquidation or less likely candidates for an out-of-court settlement. This is because higher credit quality might signal assets or a business model more amenable to rehabilitation. While it may be argued, some have found evidence (Brady et al, 2006), 18 that the greater “recovery risk” of fallen angels (i.e., low default likelihood prior to default, but greater uncertainty in the loss rate once default occurs) makes such companies more at risk of being liquidated, we believe that this effect is of second order. The vintage of debt (time since debt issued, to maturity or between instrument defaults, weighed by outstanding at default) is hypothesized to be negatively related to the probability of liquidation or of bankruptcy. The rationale is that borrowers that have been around a longer time, or that have had more time to deal with financial distress between default events, may have more franchise value and therefore be either better reorganization or out-of-court settlement candidates. The macroeconomic state (as measured by either the Moody’s 12 month speculative or all-corporate default, or the S&P 500 equity return) may have either effect. Collateral values are likely to be depressed during recessions, implying that claimants are more likely to attempt reorganization or avoid bankruptcy proceedings. Consistent with the sign implications of this is a signaling story, that failing in better times is a sign of something fundamentally wrong with the business, versus just financial distress. Alternatively, the probability of a new business succeeding might not seem as high in the midst of a recession, and parties may be more likely to "cut their losses" & liquidate. We also examine a set of variables that control for considerations of regulation, policy or the legal environment. Prepackaged bankruptcies are believed to be less likely to result in liquidation, which not only is born out in the data (far fewer prepacks become Chapter 7’s than do failed Chapter 11’s), but is a reasonable prior expectation. However, conditional on a prepack, we would expect there it to be more likely that there is a bankruptcy filing, as opposed to a conversion to an out-of-court settlement (there are very few of these). Similarly, we might expect that in certain legal jurisdictions, liquidation is less likely – therefore, we include a dummy variable for the Southern district of New York and Delaware, which are known to be debtor friendly as compared with other courts. Finally, there are certain industries in which liquidation or bankruptcy would be more or less frequent. We choose indicators for the Utility and High Technology industries in order to capture this effect – for example, we might expect more liquidations or less bankruptcies in the Utility industry, due to various factors (regulation, inability to redeploy assets, favorable recoveries given default). On the other hand, Technology might work either way – for liquidation, lower tangibility of assets reduces, while potentially lower recoveries increases, that probability. Finally, we have the Auditors Opinion, an indicator of the quality of the firm’s financials at the last filing prior to default. This is a numerical score that assesses the quality of the firm's financial statements and controls (0 - Unaudited, 1 - Unqualified Opinion, 2 - Qualified Opinion, 3 - No Opinion, 4 - Adverse Opinion), the less favorable being this assessment, the more likely is either bankruptcy or liquidation. Tables 3.1 (Compustat financial statement) and 3.2 (loss database capital structure, debt and equity market) presents detailed summary statistics and diagnostic tests on candidate explanatory variables. Results in each table are broken down by liquidation vs. reorganization for the bankruptcy sub-sample, and by bankruptcy vs. outof-court settlement for the entire sample. Degree of separation across outcome and process are assessed by Kruskall-Wallace (KW) tests of the sample medians and Kolmogorov-Smirnov (KS) tests of the sample distributions. A range of variables is displayed in each group based upon univariate significance, significance in the multivariate regressions as well as to gain a high level of representation (thereby gaining some comfort that results are not driven by the empirical proxy for a dimension that we happen to 19 choose) in each group. The multivariate regressions, incorporating a further sub-set of these variables in each group, are shown in Tables 4.2 and 4.3 for process and resolution type (6 and 8 models), respectively; the consistency of these results with the univariate tests will be referred to in the discussion of the latter, but a detailed comparison of the models will be deferred to the next section. The top panel of Table 3.1 (“Leverage”) shows the univariate tests are broadly consistent with hypotheses for liquidation vs. reorganization by both KS and KW, yet this is not the case for bankruptcy vs. out-of-court. In the liquidation outcome, sample distributions of Long Term Debt and Long Term Debt to Market Value (this both on an industry adjusted and industry basis) ratios are significantly lower than for reorganization (e.g., mean debt to market value of 30.2% for liquidations vs. 42.2% for reorganizations). Exceptions are the Leverage and Debt to Market Value ratios, as well as the percent change in the long-term debt to market value ratio, which are not significantly in median or sample distribution. While the leverage ratios are in general numerically lower for bankruptcies vs. out-of-court settlements, these differences are generally all statistically insignificant (the exception is Debt to Market value at the industry level, which is significantly lower for bankruptcies, 43.7% vs. 45.8% for out-of-court). However, in most of the multivariate regressions the Leverage Ratio is significantly associated with a lower probability of liquidation or bankruptcy, which illustrates the pitfall of relying on the univariate tests in drawing any conclusions. While the next panel “Size / Scale” of Table 3.1 shows similar results for the size variables, lack of statistical difference for resolution type (and magnitudes contrary to hypothesis), while bankruptcies (except for the Sales) are generally larger (e.g., average log Book Value of 2.71 vs. 2.58); however, only Market Value of Equity is significant in 2 of the regressions for process (Models 1 and 4 of Table 4.2). The exceptions for liquidation vs. reorganization are industry Market Value of Equity and Change in Market value of Equity (only by KW), and each of these relationships (of dubious interpretation) holds up in one of the regressions (Models 2 and 5 of Table 4.3). The 3rd panel down from the top in Table 3.1 examines the distributional properties of the tangibility measures – Tobin’s Q and Intangibles Ratio. While numerically larger for liquidations and bankruptcies (94.4% and 95.3%, respectively) than either reorganizations or out-of-court settlements (92.1% and 76.2%, respectively), at the firm level these counterintuitive results are not statistically different by either the KS or KW statistics. However, in the process regressions Table 4.2 we see that Tobin’s Q is significantly associated with a greater probability of bankruptcy across the board, Models 1-4 having financial statement data; while Tobin’s Q remains insignificant in all regression that it is included in (not shown in Table 4.3). On the other hand, the Intangibles Ratio is numerically higher for reorganizations and out-of-court settlements (18.7% and 19.0%) vs. liquidations and bankruptcies (9.1% and 17.0%), but this is only significant for liquidation vs. reorganization. However, these univariate results generally hold up in the regressions, as in Models 1-5 of Table 4.3 Intangibles Ratio is significantly related to the probability of liquidation, while it is insignificant in any of the bankruptcy vs. out-of-court regressions that it is included in (not shown in Table 4.2). In Table 3.1 Industry Tobin’s Q is significantly greater for bankruptcies vs. out-of-courts’s (100.1% and 85.5%,l respectively), and industry adjusted Intangibles Ratio is significantly greater for reorganizations than liquidations ((4.3% vs. 3.7%, respectively), this does not carry over to the regressions. Regarding the liquidity variables shown in Table 3.1, for liquidation vs. reorganization only the Net Working Capital to Total Assets ratio is significantly grater (-2.1% vs. –10.1%, respectively), a result that holds up in only 2 of the regressions (Models 6 & 7) of Table 4.3 (the industry adjusted version is also significantly greater for liquidations in Table 3.1, but this does not carry over to the regressions.) Quick Ratio is significantly lower for 20 bankruptcies by KW and KS in Table 3.1 on a firm level (78.1 vs. 92.8%, respectively), which carries over to the regressions in Table 4.2, but such is not the case for other liquidity variables; this holds for the industry adjusted version in Table 3.1, but not in any of the regressions. The industry adjusted Free Asset Ratio is significantly higher for both liquidations and bankruptcies in Table 4.1, but not so in the regressions. The second from bottom panel in Table 3.1 shows the cash flow (Free Cash Flow - FCF and Cash Flow from Operations - CFO, on a dollar basis and normalized by assets, and for industry and industry adjusted) to be associated with a greater likelihood of liquidation (significantly more negative), but not bankruptcy, versus the alternatives on a univariate basis. These results carry over to the regressions - significantly negative coefficients on CFO in 5 out of 8 regressions for liquidation vs. reorganization Table 4.3, and in significantly negative coefficients on FCF in all regressions for bankruptcy vs. out-of-court (CFO was more insignificant if included, which is not shown) Table 4.2. In the final set of financial variables considered, characterizing profitability, the tests for means and distributional equality are shown in the bottom panel of Table 3.1. These are generally not very strongly differentiated across outcomes and processes in these tests, only Net Cash Flow to Current Liabilities (NCF/CL) for liquidations vs. reorganization is significantly lower (a sign contrary to hypothesis) for liquidation vs. reorganization, and industry Retained Earning to Total Assets is significantly greater for bankruptcy vs. out-of-court, by both KS and KW tests. However, no profitability variables appear in the regressions for liquidation vs. reorganization (none are significant) in Table 4.3, and Return on Equity is significantly associated with bankruptcy in only one of the process regressions (while the latter is significant in the univariate KS test only) in Table 4.2. Table 3.2 shows the sample characteristics and univariate tests for the financial distress database variables. The top panel displays results for the Capital Structure variables (number of creditor classes or instruments; percent secured, bank or subordinated debt). These are overwhelmingly statistically indistinguishable by either outcome or process for either the KW or KS tests23. Liquidations have lower numbers, or greater proportions, of number classes / instrument or percent secured / bank / subordinated, respectively; while the magnitudes are mixed for bankruptcy vs. out-of-court (lower for number clases as compared to number of instruments and vice versa for percent secure /bank vs. subordinated). However, Table 4.3 shows Number of Creditor classes is significantly and positively related to liquidation likelihood in the 2 out of 8 regressions having no Compustat variables, as is (significantly positive) Proportion of Secured Debt in 6 out of 8 regressions, consistent with hypotheses. Further, in the bankruptcy regressions Table 4.3, these are generally significant and in line with hypotheses: Number of Creditor classes significantly negative in 3, Proportion Secured Debt significantly positive in 4 and Proportion Subordinated Debt significantly negative in 4 out of 6 models. The next category in Table 3.2 in the second panel from the top comprises important group of variables measuring credit quality of the obligor prior to default. The three variables that stand out are the Altman Z-Scrore (AZS), Loss Given Default (LGD) and Cumulative Abnormal Return (CAR). While in the univariate tests AZC is significantly worse for (lower) for liquidation vs. reorganization, although not so for bankruptcy vs. out-ofcourt, these results do not carry over to the regressions in which this variable appears: insignificant in the 2 of 8 models it appears in for liquidation probability (Table 4.3) and significant in the one model it appears in for bankruptcy probability (Table 4.2), the latter 23 The sole exception is a significant KW statistic for Number of Defaulted Instruments for liquidation vs. reorganization, with the direction of implied likelihood opposite expectations, and the KS test insignificant. 21 of the expected sign. LGD is significantly greater for both liquidation outcomes or bankruptcy processes by both KS and KW, but this does not carry over to the 5 of 8 regressions for liquidation likelihood in Table 4.3 it is included in, while this does carry over to the 4 of 6 regressions for l bankruptcy likelihood in Table 4.2 (the latter of theoretically correct sign). CAR is significantly lower for both liquidation outcome or bankruptcy process in Table 3.2, and this comes closest to be completely consistent with the regressions for which it is included in, in 1 (3) out of 3 for outcome (process); and in the case of liquidation vs. reorganization, it is borderline significant in the 2 other regressions. The other variables capturing this dimension do not perform as well. While the Altman ZScore is significantly lower for liquidations by the KS and KW statistics, it is insignificant in Models 1 and 6 of Table 4.3; on the other hand, while it is not statistically different across bankruptcy vs. out-of-court, it is significantly negatively related with the probability of bankruptcy in Model 4 of Table 4.2.24 While Weighted Average Spread is significantly lower (contrary to hypothesis) for bankruptcy by both KS and KW, this variable - along with the others in the group not appearing in Tables 4.2 or 4.3 - are insignificant in any of the trial regressions that we ran. The second from bottom panel of Table 3.2 presents univariate tests for the Vintage variables, representing durations from origination to default, default to maturity, time between defaults, etc. Both Time Since issue - TSI and Time Since Issue as a Percent of Maturity - TSIPM (weighed across instruments by claims at default) are significantly lower for liquidations (but not for bankruptcies) in the univariate tests, in line with expectations if this is taken as a proxy for age of the firm; however, this does not carry over to the regressions in Table 4.3 for resolution for TSI, and TSIPM remains insignificant in the the 2 regressions it is included in Table 4.2 for bankruptcy. The variables measuring duration between default events – Maximum or Average Time between Instrument Defaults (MTID and ATID, respectively, or Time between First Instrument Default and Filing (TFIDF) – are all significantly lower in the KS and KW tests of Table 3.2 for outcome, but not for process (although numerically lower for bankruptcies). However, in the process regress Table 4.2, MTID is significantly negatively related to bankruptcy probability in Model 6 (no financials), consistent with the univariate results, while in Model 2 it is significant but of positive sign. On the other hand, TFIDF is significantly negatively related to liquidation likelihood in 2 out of the 5 regression model for which it is included in Table 4.3. Time-to-Maturity, numerically lower for liquidations or bankruptcies but significantly so, is also never significant in any of the exploratory regressions and hence is not shown in either Tables 4.2 or 4.3 for process or outcome, respectively. The final set of variables in Table 3.2 are measures of the macroeconomic state – the Moody’s default rates25, all-corporate and speculative, and 12-month lagging or coincident; also, the return on the S&P 500 equity index. The lagging (coincident) default rates are numerically lower (higher) for liquidations and bankruptcies, which is consistent (inconsistent) with hypotheses. However, this holds strongly only for the coincident devault rates in process type (KW and KS are significant for the all-corporate and speculative), whereas for outcome only the lagging speculative default rate comes closest to being significant by both tests (only marginally for the KS). However, the speculative default rate is significantly related to liquidation likelihood in only one regression (Model 6 with no financials), and the sign of the coefficient (positive) is counter to the univariate tests and hypotheses; and in the process regression, this same variable is also only significant in one regression, Model 5 (also with no financials), but the sign (negative) is consistent with 24 But it may be argued that we should not be using this variable, as it represents a prediction based upon many of the same financial statement variables that we are already using in the regressions. 25 Aggregate monthly default rate in Moody’s DRS database of rated issuers. 22 hypotheses. On the other hand, the S&P return is significantly higher for liquidations and bankruptcies in all of the univariate test, which carries over to 3 out of 8 of the outcome regressions, but holds in only 1 out of 6 of the process regressions. 6. Estimation Results: Multivariate Regression Model Comparison In this section we compare various multivariate logistic regression models, for explaining bankruptcy vs. out-of-court settlement of financial distress (Table 6), as well as liquidation vs. reorganization outcomes of bankruptcy (Table 7). We present the set of models that is considered best in terms of dimensions of explanatory variables spanned, in- and out-ofsample predictive and discriminatory accuracy as well as economic sensibility (significance, signs and magnitudes of estimates). The coefficient estimates are normalized by the median derivative of the fitted logistic function, representing the partial effect of a change in a dependent variable upon the probability being modeled, evaluated at representative value of the covariates (Greene, 1993). In addition to the usual likelihood ratio statistic, we show 4 measures of predictive accuracy (Pseudo RSquared-PR2, Bias, Hoshmer-Lemeshow - HL and Le Cessie-Van Houlwenigan Chi-Squared - LCVH), and 4 measures of classification accuracy (Area under Receiving Operator Curve – AUROC, Kolmogorov-Smirnov – KS, Spearman Rank Correlation –SRC and Percent Correctly Classified – PCC). 6.1 Regressions Results: Bankruptcy Filing vs. Out-of-Court Settlement In the process regressions Table 6, Models 1-4 contain Compustat and JKL Loss Database variables, while Models 5-6 contain only the latter. The main differences are in the debt or equity market variables that contain information about potential firm viability at default: All models except Models 3 and 4 has the LGD (implied loss rate at default), Model 2 and Model 5 has the CAR as well, M3 has only the CAR, while M4 uses the Altman Z-Score in lieu of these. We have the fairly robust result at greater leverage is associated with going out-of-court, significant in Models 1 through 5, with the partial effects on bankruptcy probability ranging from 0.005% to 3.5%, and significance levels ranging from 0.1% to 10%. This is in line with our hypothesis (see also Bris 2006) that the more underwater you are, the less likely it is that it is economic (vs. only financial) distress, and hence less need for the harsher medicine of going to court. However, industry average leverage (long term debt ratio) is the only one consistently significant (Models 1-5). At the observation level, LTDR is significant in only Model 1. LTD to market value of equity does not cut it in Model 4. (This is consistent with Bris JF June 2006.) Second, we have mixed evidence that larger companies – as measured by the market value of equity - are more likely to file bankruptcy, significant in models 1 and 4 at the 5% and 1% levels (and with partial effects on the order of 0.08% and 0.7%), respectively. It seems that putting CAR in washes this variable out, perhaps a consequence of sample selection as bigger companies that are more likely to have traded equity; however, other measures of size performed even worse that this one in Model 2 and Model 3. A result apparently new to this literature is that the Tobin's Q measure of tangibility is positive and significant across all Compustat models, but with modest significance levels (partial effects) varying in the range 5%-10% (0.04% - 1%). This is consistent with one of our 23 hypotheses, that the serves as a mechanism to ameliorate value destruction, in spite of the alternative story that less tangible obligors would self-select out of this process. The measure of liquidity that contributed most to the joint explanation of process type, industry adjusted Quick Ratio (QR), is significant and negative across all the models, with partial effects ranging from -0.02%-2.0%. We postulated that the opposite might be the case, as more liquid assets might facilitate navigating a bankruptcy, but we also left open the possibility that it might signal better quality and help to stave off court proceedings. The sign on the cash-flow variables are consistently negative, but never significant at better than the 10% level, just shy of that in Model’s 1 and 4. This is contrary to what we postulated, in that it is a reasonable presumption that companies with more viable underlying business's, as evidenced by higher cash generating measures, would be in a better position to avoid filing for bankruptcy. Finally for the financial variables, the best of the profitability measures in combination with other variables, Return on Equity, achieves significance only in Model 2, and with a negative sign contrary to the expectation that greater profitability would imply a lower probability of bankruptcy. However, the partial effect is very small in this model, .000019%, so that this is not of economic significance. Number of creditor classes is significant in only Models 1,2 and 5 at levels of just under 1% to just over 5%, with partial effects in the range of -.00015% to -2.4%. If you take this variable to proxy for coordination problems, this might make sense, as perhaps with more parties it is less likely that an agreement can be reached out of court. This is essentially the argument of Bris (2006), that the court process is more necessary to mitigate these coordination problems if they are present, and that's what he finds. Generally, more secured debt is associated with court filing, in all models but 5, in most cases at better than the 5% level (0.2%-4.8%), with a wide variation in partial effects of 0.008% to 2.7%. This is sensible in secured creditors may prefer a court setting in which there is a higher probability of liquidating their collateral, as opposed to an out-of-court settlement in which restructuring of debt is more likely. In all of the Compustat models 1-4, percent subordinated is significant and with negative coefficients (with significance levels and partials effects approximately the same, ranges of 0.15%-2.2% and -0.006% to -3.7%, respectively), which is consistent with the result for proportion secured debt in that we would expect this class of creditors to have the opposite interests. A robust and intuitive result is that court filing is significantly associated with either higher LGD on debt at default or lower equity CARs, across all models, with the Altman Z-Score in Model 4 consistent with this. Significance levels and partial effects range from 0.05 bps0.03% and 0.0015%-10% (-0.0037 bps-5.3% and 0.01%-4.3%) for LGD (CAR), respectively. This is a reasonable result, taking out-of-court settlements to be the "superior" outcome, if for no other reason that it guarantees continued existence of the firm (either as an independent entity or through acquisition). The "vintage" variables, measuring time between instrument defaults or time since issue, are not very effective. Only in Model s 1 and 6 is the former one of these significant, but at just the 1-5% levels with a small partial effect of only 0.000007% to -1.3%. A possible 24 interpretation is that a longer time to sort things out from the first instrument default leads to a greater possibility of avoiding court26. The macro variables are not significant in any of the Compustat models, except that the Moody’s speculative default rate is marginally significant in Model 3 with a relatively large partial effect of -13.6%. Only in M6, with no financials and LGD but no CAR, is the Moody's default rate (S&P equity return) negatively (positively) related to bankruptcy filing, both at the 5% significance level with partial effects of -16.6% (39.39%), respectively. So in those models, firms tend to go to court in better times, which we have commented previously could be a consequence of that failing during an expansion is a signal that there is something really wrong, as opposed to recession when many firms are in distress. Finally, we turn to the variables describing legal, regulatory and industry factors. In all the Compustat models, filing is significant more likely the Southern District of NY and Delaware jurisdictions, with significance levels ranging in 5%-.0001%, and partial effects ranging in .0003%-24.6%. The indicator for a prepackaged bankruptcy is only significant in Models 3 and 4, at the 1% level with partial effects in the range 2-3%, and there are only 2 cases of pre-packaged bankruptcies that settled out-of-court. Firms in the Technology industry are less likely to file for bankruptcy, in all models for which the variable is included in except for Model 5, with ranges of significance level 0.01%-5% and partial effects -.008 to 1.7%. This is a bit surprising, as there is evidence that recoveries are lower in these industries; however, this may be another case of self-selection. The results for the Utility industry are not as clear-cut: significantly positive (negative) in models 1 and 6 (model 4), significant at the 510% level and partial effects ranging in absolute terms 0.06%-1.6%. Finally, auditor's opinion is only marginally significant (just shy of the 10% level) and negative (partial effect -0.1%) in model 4. In that this is a financial statement quality score, where higher is worse, the interpretation is unclear. The bottom panel of Table 6 compares model diagnostic statistics, both in and out-ofsample. First we consider measures of predictive accuracy (or model fit). Model 2, which has the maximum information (in the sense of including LGD and CAR) but the greatest loss of sample size, achieves the highest (McFadden pseudo) r-squared of 74% (55.1%) insample (out-of) sample. Model 1, having only LGD at default, is only slightly less with rsquared of 68.7% in-sample (51.8% out-of-sample), and is close as well in other measures. The worse models by this measure are the ones with no financials, Model 5 with LGD and Car at 42.9% in-sample (33.4% out-of-sample), plunging to 25.7% in-sample (19.1% out-ofsample) with no CAR in Model 6. Potentially better measures of model fit or (predictive accuracy), the LCVH and HL chi-squared, are all highly insignificant to about the same degree (p-values on the order of 0.9 and 0.5 in-sample, and 0.25 and 0.15 out-of-sample, respectively), which is good in that the opposite implies a precise numerical probability is not being produced. For what it is worth, Model 4 having the Altman Z-Score in lieu of LGD or CAR, has the most insignificant of these statistics. Finally, Model 8 is the most significant in terms of p-value on likelihood ratio (8.81X10-16 and 1.12X10-8 in- and out-ofsample, respectively), followed by Model 1 (6.58X10-12 and 3.91X10-7 in- and out-of-sample, respectively), while Models 4 and 5 are worse by this measure; however, while this measures model “fit”, it is an imperfect measure of predictive accuracy. Turning to measures of model classification or discriminatory accuracy, Models 1 & 2 have the best AUROCs of 92.4% and 91.2% (74.4% and 72.7%) in- (out-)of-sample. Models 3 performs worst by this measure (71.3 and 61.0% in- and out-of-sample, respectively), while 26 In some other related research, this variable is found to be associated with better recoveries or lower ultimate LGD (Carey and Gordy 2005, Jacobs 2006). 25 the other models are in the range of 80-90% in-sample (65-70% out-of-sample), respectively. Models 1 and 2 also perform best according to the Percent Correctly Classified (PCC), 92.4% and 94.8% in-sample (73.6% and 75.9% out-of-sample), respectively. Model 5 has the lowest PCC, 55.3% in-sample (43. 8% out-of-sample). Another related measure, the p-value on the Kolmogorov-Smirnov test (the separation between the filing and non-filing distributions by the models, is highly significant in all models and shows little differentiation in significance levels across models. Regarding measures of predictive accuracy, the Hoshmer-Lemeshow (HL) and Le Cessievan Houwelingen (LCVH) statistics are highly insignificant in all model, with p-values all close to .5 (1) for the HL (LCVH) with little variation across models. These p-values are diminished out-of-sample, but never significant at the 10% level. On the other hand, the more commonly reported yet less meaningful McFadden pseudo r-squared (MPR2) shows greater variation across models, greatest in Model 2 (74.0% and 55.4% in- and out-ofsample, respectively), followed closely by Model 1 (68.7% and 51.8% in- and out-ofsample, respectively). The non-financial statement Models 5 (42.9% and 32.5% in- and outof-sample, respectively) and 6 (25.7% and 20.0% in- and out-of-sample, respectively) are worst by this measure. Finally, Model 6 has the highest likelihood (or equivalently the smallest p-value on the likelihood ratio statistic), followed by Models 1 and 3. This ordering runs counter the other measures of Model performance, in which Model 6 usually ranks on the bottom with Model 5. However, Model 6 results in the least loss of observations, whereas Model 2 (requiring both a CAR and an LGD at default) results in the most. 6.2 Regression Results: Liquidation vs. Reorganization In Table 4.3 the results of the regressions for liquidation versus reorganization are tabulated. There are 8 models shown, each with slight variations in the financial ratios or measure of credit risk at default used (and Model 8 without Compustat data), representing the set of most hopeful candidates. Model 1 can be considered the "base model" built on accounting variables, as it does not utilize the loss rate at default (LGD), but has Z-score instead. In this model, Leverage is captured by the Long Term Debt Ratio (LTDR) at the obligor level and the Long Term Debt to Market value Ratio at the industry level (LTDMV-I), size by the Market Value of Equity at the industry level (MVE-I), Tangibility by the Intangibles ratio (IR), Liquidity by Net Working Capital to Total Assets (NWC/TA), Cash Flow by Cash Flow from Operations (CFO), Capital Structure by Number of (Major) Creditor Classes (NUMCL) and Percent of Secured Debt (PERCSEC), Vintage by Time Since Issue (TSI) and Macroeconomic by the S& Return (S&P). Finally in the Legal / Regulatory realm, all models contain Filing District (FD) and Prepackaged Bankruptcy (PREP), while all but Model 8 contains Auditors Opinion (AUDOP). Across all models, with respect to the financials variables we see, in line with hypotheses, consistently that increased Leverage or Cash Flow, or decreased Tangibility, is associated with a greater probability of liquidation. Further, in general we see across models that Size (improbably with the exception of Models 4 and 5) and Liquidity (except Model 7) are not significantly associated with the likelihood of Liquidation. In the case of Capital Structure, NUMCL is positively and significantly related to liquidation probability only in the Models 7 and 8, as is PERSEC in all except Model 7, the latter in support of hypotheses. The credit quality or risk variables generally play no role, in particular with LGD at default significant in none of the models, the exception being CAR in Model 7 in which it is significantly and 26 inversely related to liquidation likelihood. The latter is not particularly supportive of our hypotheses. In Model 1, both leverage measures LTDR and LTDMV-I are significantly (at the 10% and 5% levels, respectively) and negatively related to liquidation probability (partial effects of 6.7% and -29.5%, respectively). The size measure MVE-I is just shy of significance at the 10% level (p-value of 0.13) and not of much economic significance (the partial effect is a rather small -2.8%). IR is both economically (partial effect -13.5%) and (p-value 0.023) statistically significant. NWCTA is neither economically (partial effect 2.6%) nor (p-value 0.22) statistically significant. CFO is statistically significant at the 5% level (p-value 0.027), and while the partial effect is small (-.015%), we must bear in mind that the units are dollars so that this is of economic significance. For capital structure, NUMCL is highly insignificant in all senses (partial effect 0.15% and p-value 0.45), while PERCSEC is only moderately so (partial effect 3.9% and p-value 0.08). The indicator variable PREP is significant in all senses (partial effect -3.2% and p-value 0.015). Finally, Time Altman Z-Score (ZSC), Since Issue (TMISS), Filing District (FILE) and Auditors Opinion are all highly insignificant on an economic (partial effects -0.025%, -0.00036, 0.34% and -0.043%, respectively) and statistical (p-value’s 0.48, 0.24, 0.36 and 0.49, respectively) basis. In terms of overall model performance, while Model1 has the lowest r-squared of 20.8% (15.8% out-of sample) and second to least significant KS statistics (p-value of 0.093 in-sample and 0.094 out-of-sample), it has among the highest percent correctly classified (81.2% in-sample and 65.1% out-of-sample) and AUROC (56.4% in-sample and 46.0% out-of-sample). While it is positive that Model 1 has highly insignificant HL and LCVH statistics (p-value of 0.06 and 0.58, respectively), this is not meaningfully different than the other models, which are all highly insignificant and which indicate that all candidates are quite accurate. In Model 2 we replace the Altman Z-Score with LGD at default, as well as substitute CFO to assets (CFO/A) for CFO (which, unlike CFO in Model 1, is not statistically significant), and time between 1st and default and bankruptcy filing for time since issue (which is still not statistically significant, like its Model1 counterpart). LGD is not quite significant, having a pvalue of 0.12, and mild partial effect of 3%. The LTDR is no longer statistically significant, and LTDR-I is less potent (partial effect decreases in magnitude from -29.5% to -12.4%) as well as less significant (p-value more than doubles to 0.02). MVE-I is now marginally significant (p-value 0.0997) with a small partial effect of 1.4%. Another major change is that SP is now not only statistically significant (p-value 0.01) and but highly economically significant (partial effect of 8.8%). Further, AUDOP turns significant in a statistical sense (pvalue of 0.05), yet the partial effect is a small 0.35%. Several overall performance measures do improve in Model 2 – increases of r-squared rises to 24.7%, AUROC to 58.4%; decreases in the p-valued on the KS to 0.073; and increases in the p-values for HL and LCVH to 0.93 and 0.70, respectively. However, the percent correctly classified declines to 78.8% in-sample (63.4% out-of-sample). Model 3 is a version of Model 2 with dollar CFO in lieu of CFO/A. While this variable is now significant as in Model 1, albeit with a slightly increased p-value 0.05 and diminished partial effect of -.005%, LTDR is no longer statistically significant. Otherwise, in terms of the statistical and economic significance of other individual variables, Model 3 is not materially different from Model 2. While the r-squared is slightly higher than in Model 2 (25.9% in-sample, 19.6% out-of-sample), the KS statistic ceases to be significant, and the AUROC declines to the level of Model 1 (56.5% in-sample, 44.9% out-of-sample). Model 4 is a variation on Model 3 that tries Long Term Debt to Market Value (LTDMV) in lieu of LTDR. This variable is shy of statistically significant (p-value of 0.12) with a partial effect on the order of that for LTDR in Model 1 (5.6%). Otherwise, there is not much else that 27 distinguishes Model 4 from Model 3. The partial effect of INTA goes up to 11.8% (but is slightly less statistically significant with a higher p-value of .034), while LGD moves far away from being even marginally significant (p-value shooting up to 0.44 and partial effect plunging to 0.65%). However, NUMCL inches toward marginal significance, as the p-value declines to 0.14 and the partial effect rises to 1.3%. unfortunately, SP now falls back into such a marginally significant state from significance in Model 3, having a p-value of 0.15 (yet about the same partial effect of 6.2%). There is quite a bit of loss in sample going from Models 3 to 4 (due to the observations with zero book value with which to normalize CFO), with number of observation going from 193 to 147, reflected in a decreased likelihood ratio (p-value increases 100-fold from 0.000023 to 0.0031). Further, we have declines of rsquared and AUROC, slightly to 23.9% and precipitously to 50.5%, respectively. On the bright side, the KS is now just significant, having a p-value of 0.99, and percent correctly classified holds up at 78.2%. Model 5 substitutes the change in book value of assets (C-BV) for BV, the coefficient on which is negative (partial effect of 3.4%) and marginally significant (p-value of 0.097). This model is on the whole not very different from Model 2. LGD is slightly more significant (pvalue of 0.11 and partial effect slightly higher at 3.1%) and FD is nearly significant (p-value of 0.10 and partial effect slightly higher at 6.4%). However, the overall model diagnostics are almost the same as in Model 2, the only place where is measurable improvement being a slightly more significant KS statistic (p-value decreases from 0.73 to 0.05). Model 6 is a version of Model 1 that incorporates CARs in addition to the other variables appearing in that model. Dramatic loss of sample size makes this not-so-comparable to the other 5 models, most variables are not significant. Particularly damning is the Likelihood chi-squared, it is greater than .01 in the best 2 models I showed (in the others, not significant). In Model 7, we drops LGD at default while retaining CARs, as well as uses the change in the market value of equity (C-MVE) in addition to MVE-I. While the latter measure of Leverage is not statistically insignificant, CAR is at the 10% level (p-value 0.06) with a negative coefficient (but a small partial effect of -0.13%). There are also some notable differences from the other models here. The coefficient on NWCTA is negative and, unlike all other models, significant (partial effect 3% and p-value 0.03). NUMCL now has a significantly (p-value 0.08) positive sign (partial effect 8.5%), but PERC no longer has such. Finally, this is the only model in which filing district is significant at the 10% level (p-value 0.09), having a positive parameter estimate (partial effect 5.9%). While this model has the most individually significant coefficients (7 out of 15), it is not remarkable as measured by overall model performance statistics: the r-squared of 24.1% and PCC of 82.1% are middling; the AUROC of 43.6% is the lowest of the set; and, while highly insignificant, the pvalues on the HL and LCVH are (.46 and 0.50, respectively) also lower than in the other models. However, to its benefit the KS is significant, having a p-value of 6.1% (7.9%) in(out-of) sample. The final candidate Model 8 has no financial variables, and includes all the nonCompustat variables from the other Models except for Altman z-Score (it has both LGD and CAR instead) and AUDOP. Now we find that both NUMCL and PERSEC are significant, albeit at only the 10% and 5% levels, respectively (p-values 5.3% and 4.4%, respectively), and the partial effects are positive and substantial (8.9% and 22%, respectively). In summary, we first note that there is some evidence that leverage is inversely related to the likelihood of liquidation – at the individual level in 3, and at the industry level in 5, out of the 8 candidate models considered. Second, there is not much of a “size effect” – 28 among the Size / Scale variables, only MVE-I is marginally significant in Model 2, which says that companies from industries where companies tend to be large are more likely to liquidate. C-BV is also marginally significant in Model 5, but the economic interpretation of this is questionable, as it says that firms experiencing more growth prior to default are less likely to liquidate; further, this is counter to what has been found in the literature, namely Bris (2206) finds that bankrupt firms filing Chapter 11's are much larger than those filing Chapter 7. Next, we get the relatively robust result that across most regressions (Models 15 with no CAR) firms with more intangibles are less likely to liquidate. This would appear to be a new result to the literature, with the clear economic intuition that there is more deadweight loss in liquidation if assets are tied up in things like human capital, therefore a greater incentive on the part of interested parties to effectuate a reorganization. Another reasonably strong result is that higher cash flow is associated with lower odds of liquidation in all models in which it is measure din dollars, but not when normalized by assets in Models 2 & 5. If cash flow is taken as a sign of fundamental economic viability, there is a compelling economic story here; but the fact that this result obtains only when measured on an absolute basis a may mean that size / scale effects are being picked up as well. The Liquidity dimension, as measured by NWC/ TA, is significant in Model 7, with a positive sign; the only story here, in our minds, is ease of asset disposal. In the case of the capital structure variables, number of creditor classes does not step up to the plate - we were expecting to see more of them lead to liquidation, a "coordination story". Bris finds the opposite and also calls it a coordination story. However, percent secured debt is positive and significant in most models, which makes sense, as you have creditors with clout who can push to get their collateral liquidated. Bris finds the same sign but not significant. Neither LGD nor Z is ever significant as a measure of "credit quality" or "market view" (CAR is just significant in Model 7, and the right sign, the better the abnormal return the lower the chances of Chapter 7). The Time / Vintage variables are generally not significant, the only exception is time between first default & filing in Model 4; a negative relationship has the rationale that a longer time period from the first sign of trouble implies greater opportunity to pre-negotiate before going to court, and hence the greater probability of a successful resolution. There is limited evidence that the macro variables influence bankruptcy resolution. S&P 500 return is significant is on-again / off-again, positive & significant in 3 of the models (but not at high significance levels, with p-value ranging in 0.01-0.09, and modest partial effects, ranging in 2.7%-8.8%). A plausible story here is that in the absence of perfect information, defaulting in a good time conveys a signal of fundamental non-viability, while in a worse time this may be considered a noisy signal, hence a lower probability of liquidating in the latter case. The dummy variable for NY/Delaware jurisdiction is not much of a performer, at best marginally significant and only in Model 7 (p-value 0.09 with partial effect of 6%), which seems to say that more companies get liquidated there; but we have to worry about sample selection bias in the model with CARs.) Prepacks are less likely to be Ch 7's, significant across all models, which I is self explanatory. Finally, Auditors Opinion shows up positive and significant in 4 of the models - as this is a kind of score where higher values mean less reliable financial statements, this makes sense. In comparing results to the prior literature regarding the determinants of successful resolution outcomes, we are consistent with White (1983, 1989) regarding the significance of intrinsic value. However, we are not consistent with Hotchkiss (1993) regarding asset size. We are in line with Lenn and Poulson (1989), but at variance with Jensen (1991), regarding cash flow. Our results are inconsistent on profitability, but consistent on overall firm quality, with Kahl (2002). Finally, these results agree with Matsunga et al (1991) and Bryan et al (2001) regarding the liquidity. 29 7. Model Validation Results: Out-of-Sample and Out-of-Time Classification and Predictive Accuracy In this section we will discuss the results of model validation exercises that attempt to mimic the long-run performance of models employed to classify the mechanism and outcome of financial distress resolution. We perform these experiments for all of the plausible models discussed in the previous section, but present the results for those that perform best over time, Model 2 for prediction of bankruptcy filing and Model 2 for prediction of resolution liquidation.27 This is performed for three estimation techniques: logisitic regression (LR), additive local regression (ALR) and feedforward neural networks (FNN). Tables 8 and 9 present detailed results by year for LR model, for prediction of the process and resolution of financial distress, respectively. Table 10 shows summarized results, out-ofsample results aggregated over years an in-sample results for the entire period available, comparing all three estimations. The technique that we employ is a rolling out-of-time and out-of-sample bootstrap, in which a model is estimated and performance measured repeatedly, for increaesing estimation (or training) periods and rolling 1 year ahead prediction periods. That is, starting with the 1885-94 estimation period and the 1996 prediction period, the sample is re-formed by sampling with replacement in the former period for the in-sample part, and then applied to a resampled 1995 cohort for the out-of sample part. This is done for 100,000 repetitions, then the same for 1985-1996 and 1997 estimation and prediction periods, respectively, and so on until the entire sample corresponds to the estimation period. The distributions of performance measures can then be analyzed, which can give us an idea about the statistical significance of point estimates based upon a single history, in the absence of a distribution theory that would guide us (Efron, 1979). The final distribution of out-of-sample statistics is formed by pooling the nine years of distributions for 1995 through 2004. Tables 8 and 9 present calibration and discrimination statistics for the prediction of distress outcome and the bankruptcy processes for the logistic model, respectively, detailed by year. The bottom panel shows in-sample (or estimation / training) results, while the top panel shows out-of-time and sample (or 1-year ahead prediction) results, and the columns present the results by cohort year. The results are in-line with the estimations of the models in which a standard 20% holdout sample was analyzed. This anlysis highlights the high degree of variability in out-of-sample results from year-to-year, as we try and predict ahead in this manner. The weighed proportion correctly classified, or ECM (“expected cost of misclassification” statistic), has a median of 85.4% (66.3%) in-(out-of-sample) for liquidation prediction, and 97.6% (74.1%) in-(out-of-sample) for bankruptcy prediction. The variation in the median over sub-samples or forecast years is mild in-sample, but very high out-of-sample, and is generally wider for prediction of liquidation vs. bankruptcy: a range of [79.00%, 96.5%] ([36.6%, 99.8%]) for liquidation prediction in Table 8, and [79.7%, 87.8%] ([45.3%, 94.6%]) for bankruptcy prediction in Table 8,in-(out-of) sample. As with the ECMs, the AUROCs are significantly higher in-sample as opposed to out-ofsample, median of 74.5% vs. 66.3% (86.4% vs. 75.1%) for liquidation (bankruptcy) prediction in Table 8 (Table 9), as well higher in prediction of bankruptcy as opposed to liquidations, However, resampled results amongst all of the models discussed were closer than the performance statistics either in-sample or out-of-sample as discussed. 27 30 as shown by these numbers. There is also greater consistency over time in-sample as compared to out-of-sample for both prediction problems, as well as compared to the ECM metric both in- and out-of-sample. The p-values of the KS statistic also support that the models have ability to discriminate outcomes, but results are weaker as compared to the ECM and AUROC, especially on an out-of-sample basis. While in-sample p-values are highly significant overall and in each year for liquidation and bankruptcy prediction (medians of 1.3% and 0.73%, respectively), out-of-sample estimated confidence levels are marginal overall (medians of 8.6% and 6.0%, respectively) and in some years not significant (medians exceeding 10% in 1995 and 1996 for both predictions). Further, out-of-sample there are many realizations of p-values greater than 10% for both predictions, in particular years and overall. However, note that we may have less reliance on these tests, as these represent p-values derived from estimates of high quantiles of a test statistic, and such estimation has a high degree of estimation error. This is reflected in the bootstrapped distributions of these p-values, which have high coefficients of variation (on the order of 25-30%) and are highly skewed. 31 7. Conclusions and Directions for Future Research This study represents a comprehensive analysis of bankruptcy resolution. First, motivated by economic theory and models, we perform an exhaustive analysis of fundamental data thought to influence the relative likelihood of liquidation versus resolution, giving rise to a chosen set of financial variables. Second, we estimate a parsimonious empirical model (ordered logistic regression-OLR) that is consistent with theory and having good statistical properties. This exercise is extended by a comparison of this model to alternative econometric models (multiple discriminant analysis-MDA and feedforward neural networks-FNN), both in terms of in-sample fit, as well as out-of-sample classification accuracy. In the latter validation exercise, we extend the literature by considering alternative classification criteria (expected cost of misclassification-ECM, unweighted minimization of misclassification-UMM and deviation from historical average-DHA), which in this context are necessary in order to evaluate model performance. This is made rigorous by the application of resampling methodology, which makes it possible to study an approximate distribution of classification accuracy statistics, thereby comparing model performance across classification accuracy criteria relative to random benchmarks. Finally, we are the first to study one of the premier loss severity datasets (S&P LossStats™) in this context, for a sample of recent defaults. We find evidence that a set of financial variables at the time of default is related to the likelihood of alternative bankruptcy resolutions in a manner consistent with economic theory: a greater proportion of secured debt, greater liquidity or a larger spread on debt or is associated with a greater probability of liquidation; while larger asset size, higher cash-flow, higher leverage, a larger proportion of intangibles to assets, older vintage of debt or filing in certain jurisdictions decreases the likelihood of this outcome. However, results are inconclusive with respect to number of creditor classes, profit margin, and state of the macroeconomy or operation in certain industries. In the preferred OLR model, all coefficient estimates are of the theoretically correct sign, five out 14 of variables are individually statistically significant, and all but four jointly contribute to overall fit in a statistically significant manner. While the OLR model has a pseudo r-squared of only 18.5%, versus 25.7% in the alternative FNN model, the latter model is unsatisfactory in terms of the agreement of signs on coefficients with theory, as well as being several orders of magnitude more computationally intensive. The MDA model is also inferior in-sample, both in terms of explanatory power with a worse fit (r-squared of 13.56%), as well as agreement with theory in terms coefficient estimate signs. We next analyze out-of-sample performance of the models by looking at classification accuracies, both on a split sample basis, as well as in a resampling experiment. The general conclusion is that relative model performance varies across classification criteria. There is also variation across outcomes, in that classification of the liquidation outcome can lead to a different comparison than the reorganization outcome or overall. While, in holdout sample performance, the OLR model seems to be the best, and the FNN the worst, there is not a very sharp differentiation among models. When compared to benchmarks, as measured by approximate 95% binomial confidence bounds in naïve schemes that mimic the three classification criteria, results suggest that the models can generally beat random classification. However, there is variation across models and classification criteria, and results do not appear stable across sub-samples. This motivates a bootstrap exercise, in which the model is repeatedly built and tested on resampled data-sets, and the distributions of the classification accuracy statistics studied. This analysis leads to some sharper conclusions – under the ECM criterion, the MDA model performs best in classifying reorganizations and overall, but worse in classifying liquidations, while under the UMM or DHA criteria this is reversed. The most consistent pattern that emerges is the inferiority of the FNN model in out-of-sample prediction, the only exception being the classification of liquidations under the ECM 32 criterion. These results are confirmed by non-parametric Wilcoxon tests for the differences between the resampled distributions of these statistics, in different models and under different criteria. The main conclusion that comes out of this is that the OLR model seems to best balance fidelity to the data, consistency with hypotheses and out-of-sample performance; in the regard to the latter feature, while there is some variation in performance across criteria and outcomes, we can say that at least the OLR model does not consistently underperform competing models. There are various avenues along which we can proceed in extending this research. First, we can think of additional variables to examine, both financial statement (e.g., offbalance sheet tax assets), economic (e.g., a gauge of macroeconomic conditions) or financial market (e.g., equity price returns, trading prices of debt at default). Second, further variations on candidate econometric models can be considered, such as non- or semi-parametric versions of these models. We could attempt to extend the data-set further back in time or cross-sectionally. Another possibility is to consider the acquisition outcome, in addition to liquidation or reorganization. Finally, we may try to estimate a system of equations to jointly predict various other variables of interest, such as loss given default and time-to-resolution. 33 Appendix: Tables and Figures Table A1: Resolution of Finance Distress, Sample Size by Outcome Resolved out of Court 91 Filed for Bankruptcy 312 Total Sample 403 6 40 46 Liquidated 0 70 70 Total Sample 97 422 519 Emerged Independent Acquired Table A2: Five Possible Paths Following Financial Distress Path Following Default 1. File for bankruptcy and Sample Size emerge 312 independent 2. File for bankruptcy and then acquired 40 3. File for bankruptcy and then liquidated 70 4. Restructure out of court and emerge 91 independent 5. Restructure out of court and then acquired 6 34 Figure A1: Time Line of Events Acquired File for Bankruptcy Emerged independent Liquidated Financial Distress Acquired Resolved out of Court* Emerged independent ---|--------|--------------------|----------------------------------|----------------------------------------| (t-2) (t-2) (t-1) t (t+1) (t+2) (t-1) t (t+1) (t+2) Two years prior to the event of financial distress One year prior to the event of financial distress, firm may or may not exhibit signs of impending distress Event of financial distress, prior to negotiations, for example, default or impending default The year the firm files for bankruptcy or begins out of court negotiations to resolve the financial distress Financial distress is resolved, firm either emerges as an independent entity, is acquired or liquidated * In our sample, we do not have any case where a firm renegotiates out of court and is liquidated. 35 Total Database Compustat Sample Table 1 - Default Outcome and Workout Type by Year (S&P and Moody's Rated Borrowers 1985-2004)1 Year 1985 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Total 1985 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Total Reorganization Liquidation Out-of-Court Bankruptcy Total Percent Percent Percent Percent Percent over Percent over Percent over Percent in over Percent over Count Years in Year Count Years in Year Count Years Year Count Years in Year Count Years 1 0.22% 100.00% 0 0.00% 0.00% 0 0.00% 0.00% 1 0.24% 100.00% 1 0.19% 7 1.56% 100.00% 0 0.00% 0.00% 3 3.09% 42.86% 4 0.95% 57.14% 7 1.35% 19 4.24% 95.00% 1 1.43% 5.00% 5 5.15% 25.00% 15 3.56% 75.00% 20 3.86% 14 3.13% 73.68% 5 7.14% 26.32% 6 6.19% 31.58% 13 3.09% 68.42% 19 3.67% 50 11.16% 96.15% 2 2.86% 3.85% 11 11.34% 21.15% 41 9.74% 78.85% 52 10.04% 46 10.27% 88.46% 6 8.57% 11.54% 15 15.46% 28.85% 37 8.79% 71.15% 52 10.04% 20 4.46% 95.24% 1 1.43% 4.76% 2 2.06% 9.52% 19 4.51% 90.48% 21 4.05% 19 4.24% 100.00% 0 0.00% 0.00% 5 5.15% 26.32% 14 3.33% 73.68% 19 3.67% 14 3.13% 82.35% 3 4.29% 17.65% 4 4.12% 23.53% 13 3.09% 76.47% 17 3.28% 17 3.79% 85.00% 3 4.29% 15.00% 1 1.03% 5.00% 19 4.51% 95.00% 20 3.86% 11 2.46% 68.75% 5 7.14% 31.25% 1 1.03% 6.25% 15 3.56% 93.75% 16 3.09% 10 2.23% 90.91% 1 1.43% 9.09% 0 0.00% 0.00% 11 2.61% 100.00% 11 2.12% 14 3.13% 73.68% 5 7.14% 26.32% 0 0.00% 0.00% 19 4.51% 100.00% 19 3.67% 28 6.25% 68.29% 13 18.57% 31.71% 1 1.03% 2.44% 40 9.50% 97.56% 41 7.92% 36 8.04% 81.82% 8 11.43% 18.18% 2 2.06% 4.55% 42 9.98% 95.45% 44 8.49% 54 12.05% 80.60% 13 18.57% 19.40% 12 12.37% 17.91% 55 13.06% 82.09% 67 12.93% 58 12.95% 95.08% 3 4.29% 4.92% 17 17.53% 27.87% 44 10.45% 72.13% 61 11.78% 28 6.25% 96.55% 1 1.43% 3.45% 10 10.31% 34.48% 19 4.51% 65.52% 29 5.60% 2 0.45% 100.00% 0 0.00% 0.00% 2 2.06% 100.00% 0 0.00% 0.00% 2 0.39% 448 100.00% 86.49% 70 100.00% 13.51% 97 100.00% 18.73% 421 100.00% 81.27% 518 100.00% 1 0.18% 100.00% 0 0.00% 0.00% 0 0.00% 0.00% 1 0.19% 100.00% 1 0.15% 9 1.60% 100.00% 0 0.00% 0.00% 4 3.39% 44.44% 5 0.94% 55.56% 9 1.38% 20 3.55% 95.24% 1 1.15% 4.76% 5 4.24% 23.81% 16 3.01% 76.19% 21 3.23% 19 3.37% 76.00% 6 6.90% 24.00% 8 6.78% 32.00% 17 3.20% 68.00% 25 3.85% 60 10.66% 96.77% 2 2.30% 3.23% 14 11.86% 22.58% 48 9.02% 77.42% 62 9.54% 59 10.48% 89.39% 7 8.05% 10.61% 17 14.41% 25.76% 49 9.21% 74.24% 66 10.15% 25 4.44% 92.59% 2 2.30% 7.41% 4 3.39% 14.81% 23 4.32% 85.19% 27 4.15% 26 4.62% 96.30% 1 1.15% 3.70% 7 5.93% 25.93% 20 3.76% 74.07% 27 4.15% 21 3.73% 84.00% 4 4.60% 16.00% 5 4.24% 20.00% 20 3.76% 80.00% 25 3.85% 27 4.80% 81.82% 6 6.90% 18.18% 2 1.69% 6.06% 31 5.83% 93.94% 33 5.08% 16 2.84% 72.73% 6 6.90% 27.27% 1 0.85% 4.55% 21 3.95% 95.45% 22 3.38% 13 2.31% 86.67% 2 2.30% 13.33% 0 0.00% 0.00% 15 2.82% 100.00% 15 2.31% 17 3.02% 73.91% 6 6.90% 26.09% 0 0.00% 0.00% 23 4.32% 100.00% 23 3.54% 35 6.22% 72.92% 13 14.94% 27.08% 3 2.54% 6.25% 45 8.46% 93.75% 48 7.38% 44 7.82% 78.57% 12 13.79% 21.43% 2 1.69% 3.57% 54 10.15% 96.43% 56 8.62% 66 11.72% 81.48% 15 17.24% 18.52% 13 11.02% 16.05% 68 12.78% 83.95% 81 12.46% 70 12.43% 95.89% 3 3.45% 4.11% 18 15.25% 24.66% 55 10.34% 75.34% 73 11.23% 32 5.68% 96.97% 1 1.15% 3.03% 12 10.17% 36.36% 21 3.95% 63.64% 33 5.08% 3 0.53% 100.00% 0 0.00% 0.00% 3 2.54% 100.00% 0 0.00% 0.00% 3 0.46% 563 100.00% 86.62% 87 100.00% 13.38% 118 100.00% 18.15% 532 100.00% 81.85% 650 100.00% 36 Total Database Compustat Sample Table 2 - Default Outcome and Workout Type by Industry 1 (S&P and Moody's Rated Borrowers 1985-2004) Industry Group Aerospace / Auto / Capital Goods / Equipment Consumer / Service Sector Energy / Natural Resources Financial Institutions Forest / Building Prodects / Homebuilders Healthcare / Chemicals High Technology / Telecommunications Insurance and Real Estate Leisure Time / Media Transportation Utilities Total Aerospace / Auto / Capital Goods / Equipment Consumer / Service Sector Energy / Natural Resources Financial Institutions Forest / Building Prodects / Homebuilders Healthcare / Chemicals High Technology / Telecommunications Insurance and Real Estate Leisure Time / Media Transportation Utilities Total Reorganization Percent Percent Among Within Count Industries Industry Count 42 9.38% 87.50% 6 109 24.33% 81.34% 25 35 7.81% 87.50% 5 14 3.13% 77.78% 4 20 4.46% 95.24% 1 39 8.71% 90.70% 4 80 17.86% 84.21% 15 17 3.79% 94.44% 1 67 14.96% 91.78% 6 17 3.79% 85.00% 3 8 1.79% 100.00% 0 448 100.00% 86.49% 70 51 9.06% 89.47% 6 131 23.27% 81.37% 30 48 8.53% 90.57% 5 22 3.91% 78.57% 6 27 4.80% 93.10% 2 44 7.82% 89.80% 5 87 15.45% 83.65% 17 21 3.73% 95.45% 1 98 17.41% 89.91% 11 21 3.73% 84.00% 4 13 2.31% 100.00% 0 563 100.00% 86.62% 87 Liquidation Percent Percent Among Within Industries Industry Count 8.57% 12.50% 13 35.71% 18.66% 22 7.14% 12.50% 7 5.71% 22.22% 3 1.43% 4.76% 6 5.71% 9.30% 6 21.43% 15.79% 18 1.43% 5.56% 2 8.57% 8.22% 13 4.29% 15.00% 4 0.00% 0.00% 3 100.00% 13.51% 97 6.90% 10.53% 16 34.48% 18.63% 24 5.75% 9.43% 12 6.90% 21.43% 5 2.30% 6.90% 7 5.75% 10.20% 7 19.54% 16.35% 19 1.15% 4.55% 2 12.64% 10.09% 17 4.60% 16.00% 5 0.00% 0.00% 4 100.00% 13.38% 118 Out-of-Court Percent Percent Among Within Industries Industry Count 13.40% 27.08% 35 22.68% 16.42% 112 7.22% 17.50% 33 3.09% 16.67% 15 6.19% 28.57% 15 6.19% 13.95% 37 18.56% 18.95% 77 2.06% 11.11% 16 13.40% 17.81% 60 4.12% 20.00% 16 3.09% 37.50% 5 100.00% 18.73% 421 13.56% 28.07% 41 20.34% 14.91% 137 10.17% 22.64% 41 4.24% 17.86% 23 5.93% 24.14% 22 5.93% 14.29% 42 16.10% 18.27% 85 1.69% 9.09% 20 14.41% 15.60% 92 4.24% 20.00% 20 3.39% 30.77% 9 100.00% 18.15% 532 Bankruptcy Total Percent Percent Percent Among Within Among Industries Industry Count Industries 8.31% 72.92% 48 9.27% 26.60% 83.58% 134 25.87% 7.84% 82.50% 40 7.72% 3.56% 83.33% 18 3.47% 3.56% 71.43% 21 4.05% 8.79% 86.05% 43 8.30% 18.29% 81.05% 95 18.34% 3.80% 88.89% 18 3.47% 14.25% 82.19% 73 14.09% 3.80% 80.00% 20 3.86% 1.19% 62.50% 8 1.54% 100.00% 81.27% 518 100.00% 7.71% 71.93% 57 8.77% 25.75% 85.09% 161 24.77% 7.71% 77.36% 53 8.15% 4.32% 82.14% 28 4.31% 4.14% 75.86% 29 4.46% 7.89% 85.71% 49 7.54% 15.98% 81.73% 104 16.00% 3.76% 90.91% 22 3.38% 17.29% 84.40% 109 16.77% 3.76% 80.00% 25 3.85% 1.69% 69.23% 13 2.00% 100.00% 81.85% 650 100.00% 37 Table 3 - Descriptions and Hypotheses on Key Default Outcome and process Drivers (S&P and Moody's Rated Borrowers 1985-2004)1 Variables2 Hyporthesized Relationship to Liquidation Likelihood Hyporthesized Relationship to Bankruptcy Filing Likelihood Negative Negative Dimension Rationale Leverage 1. Greater leverage implies lower recovery in liquidation, hence an incentive to attempt a reorganization or avoid bankruptcy. 2. Chapter 11 if book value is negative then equity is given a greater say. 3. Higher leverage is a signal that the Book leverage & long term debt ratios, debt to market value fundamental business may be viable in financial distress. of equity ratios. Size / Scale Larger scale of operations implies a better candidate for rehabilitating business model and therefore a successful reorganization. The complexity of larger firms and self-selection may make bankruptcy more likely. Intrinsic Value / Tangibility A greater proportion of intangible assets make a defaulted borrower a more attractive acquisition candidate or makes liquidation more costly thus lowering the chances of liquidation. The bankruptcy process may be more destructive of value with less tangibility, but this may be countered by self-selection. Tobin's Q, book value ratio of intangible to total assets. Liquidity Higher liquidity implies that a firm is in a better position to keep operating through the bankruptcy proceedings and therefore a reorganization is the more likely Interest coverage, free asset, and net working capital to total outcome. Alternatively higher lquidity can lower the costs of liquidation. asset ratios. Either Either Cash Flow Greater cash generating ability indicates better quality of the borrower and ability to restructure and a lower probability of liquidation. Alternatively, agency Free cash flow and cash flow from operations (dollar and problems are greater (Jensen), but this may not be operative in financial distress. ratio to book value of assets). Negative Negative Profitability Might mean better chances of improving business (like size) or liquidation more costly because of franchise value (like intrinsic value). Profit margin, return on equity, retained earnings to total assets, net cash flow to current liabilities. Negative Negative Greater bargaining power among secured creditors makes liquidation or bankruptcy filing more likely. Percent secured debt at time of default. More parties involved in resolving financial distress imply greater difficulties in negotiating a reorganization or negotiating an out-of-court settlement. Number of major creditor classes for defaulted customer. Positive Positive Weighted spread at default or loss-given-default on debt, Altman Z-Score, investment grade indicator, cumulative abnormal equity returns. Positive Positive Time since debt issued, to maturity or between instrument defaults (weighed by outstanding at default) Negative Negative Moody's trailing 12 month speculative grade and allcorporate default rates, S&P 500 equity returns. Either Either Negative Either Dummy variable for Utility ot Technology industries. Negative Negative or Either Negative Negative or Positive Codes: 0 - Unaudited, 1 - Unqualified Opinion, 2 - Qualified Opinion, 3 - No Opinion, 4 - Adverse Opinion Positive Positive Capital Structure Credit Quality / Market Reaction Vintage Macroeconomic Firms with higher initial (or at a suitable horizon) credit quality may have a lower chance of liquidation as this may signal a fundamenmtal capability to successfully undergo a reorganization or avoid bankruptcy. Borrowers that have been around a longer time, or that have had more time to deal with financial distress between default events, may have more franchise value and therefore be either better reorganization or out-of-court settlement candidates. Collateral values might be depressed during recession, implying that claimants are more likely to attempt reorganization or avoid bankruptcy proceedings. Consistent with this is a signaling story: failing in better times is a sign of something fundamentally wrong with the business versus just financial distress. Alternatively, the probability of a new business suceeding might not seem as high in the midst of a recession and parties may be more likely to "cut their losses" & liquidate. Under special legal arrangements liquidation or bankruptcy filing may be a less likely outcome. In certain jurisdictions liquidation may be a less likely outcome. Regulatory / Policy In certain industries liquidation or bankruptcy may be a more or less likely outcome. / Legal Assessment by independent auditiors of the quality of the firm's financial statements and controls.- the less favorable this assessment, the more likely is Auditors Opinion either bankruptcy or liquidation. Book value of total assets, market value of equity, net sales. Negative Dummy variable for pre-packaged bankruptcy type. Dummy variable for filing district (the Southern District of New York & Delaware). Negative Positive Either 1 -Database of 650 S&P’ & Moody's rated firms having extensive loss severity data on 2,732 defaulted instruments from 1985-2003 for which the entire capital structure at default is available. All instruments are detailed by type, seniority, collateral type, position in capital structure, original and defaulted amount, resolution type and instrument price at emergence & settlement 2 - 519 borrowers defaulting from 1985-2003 have some financial statement informatione available on Compustat at the date of first instrument default 38 Profitabilit y Cash Flow Liquidity Tangibilit y Size / Sclae Leverage Groups Table 4 - Summary Statistics and Distributional Tests for Selected Financial Statement Variables by Default Outcome and Workout Type 1 (S&P and Moody's Rated Borrowers 1985-2004) Liquidation Cnt. Variables Leverage Ratio 63 Long Term Debt Ratio 63 Long Term Debt to Market Value Ratio 54 Change in Long Term Debt to Market Value Ratio 52 Long Term Debt to Market Value Ratio - Ind. Adj. 54 Debt to Market Value Ratio - Industry 70 Long Term Debt to Market Value Ratio - Industry 70 Market Value of Equity 54 Book Value Assets 63 Net Sales 62 Change in Market Value of Equity 54 Market Value of Equity - Industry 70 Market Value of Equity - Ind. Adj. 54 Tobin's Q 52 Intangibles Ratio 53 Tobin's Q - Industry 70 Intangibles Ratio - Ind. Adj. 53 Quick Ratio 60 Free Asset Ratio 58 Net Working Capital to Total Assets 61 Quick Ratio - Ind. Adj. 60 Free Asset Ratio - Ind. Adj. 58 Free Cash Flow 61 Cash Flow from Operations to Assets 61 Free Cash Flow - Industry Adj. 61 Cash Flow from Operations to Assets - Ind. Adj. 61 Net Cash Flow to Curent Liabilities 60 Retained Earnings to Total Assets - Industry 70 Return on Equity 62 Price / Earning Ratio - Ind. Adj. 53 Mean 99.74% 42.49% 30.15% 11.06% 18.67% 42.27% 12.01% 1.9606 2.6770 2.5822 -0.2646 234.78 265.47 94.40% 9.07% 101.4% 3.69% 81.83% 19.42% -2.01% -28.8% -2.15% -76.72 -4.46% -93.24 -12.3% -16.4% -2.10% -79.2% 8.47 Std. Dev. 45.68% 30.44% 21.91% 14.17% 23.22% 13.28% 7.29% 0.7775 0.5598 0.7686 0.3779 457.61 1338.00 81.44% 12.51% 56.03% 4.71% 83.48% 27.90% 45.58% 79.33% 26.75% 192.99 20.17% 197.55 22.78% 58.74% 43.81% 499.5% 20.23 Reorganization Cnt. 375 373 275 267 275 448 448 274 375 373 267 448 275 246 323 448 523 334 330 340 334 330 364 348 353 347 322 448 351 275 Mean 107.2% 55.66% 42.22% 15.22% 27.30% 44.42% 14.75% 1.7579 2.6914 2.5747 -0.3992 195.69 39.94 92.12% 18.71% 96.75% 4.25% 80.69% 12.97% -10.12% -32.76% -10.69% 24.62 -0.27% 14.08 -8.35% -1.35% -5.91% -129.2% -4.19 Std. Dev. 67.73% 60.10% 26.14% 17.26% 26.36% 13.58% 8.52% 0.8502 0.5780 0.6395 0.5024 406.69 2337.0 69.22% 20.20% 43.04% 2.79% 69.39% 33.66% 44.69% 74.52% 31.08% 555.88 12.20% 555.97 13.69% 60.34% 100.5% 126.1% 40.92 Tests of Equality Liquidation vs. Reorganization KS PValue 0.1111 0.0410 0.0240 0.2848 0.0292 0.1845 0.0387 0.4796 0.8522 0.5456 0.1980 0.0635 0.5594 0.1289 0.0018 0.2586 0.0069 0.1161 0.5229 0.0659 0.3532 0.0716 0.1001 0.0062 0.0481 0.0103 0.0383 0.4744 0.7745 0.0508 KW PValue 0.2773 0.0492 0.0011 0.1786 0.0611 0.1765 0.0940 0.1676 0.7876 0.4271 0.0378 0.0027 0.5053 0.5423 0.0047 0.7232 0.0109 0.4438 0.2941 0.0741 0.9044 0.0625 0.0549 0.0023 0.0197 0.0343 0.0087 0.3891 0.5743 0.1325 Bankruptcy Cnt. 357 356 280 273 280 421 421 54 63 62 275 421 280 255 303 421 421 320 317 326 320 317 342 336 341 335 313 421 349 279 Mean 106.0% 53.08% 39.83% 15.04% 25.66% 43.74% 14.24% 1.8194 2.7146 2.5913 -0.2646 196.31 43.86 95.28% 16.96% 100.1% 4.18% 78.10% 15.10% -9.34% -37.05% -7.59% -7.4061 -1.04% -18.57 -8.69% -4.27 -2.78% -78.7% -6.86 Out-of-Court Tests of Equality Bankruptcy vs. Out-of-Court Total Std. Std. KS P- KW PStd. Dev. Cnt. Mean Dev. Value Value Cnt. Mean Dev. 48.95% 81 106.6% 48.95% 0.5965 0.7006 438 106.12% 65.03% 59.68% 80 56.75% 42.90% 0.3749 0.8053 436 53.76% 56.95% 26.33% 49 42.58% 23.01% 0.5837 0.4958 329 40.24% 0.11% 17.31% 46 11.56% 13.58% 0.2093 0.2800 319 14.54% 16.85% 26.52% 49 27.14% 23.25% 0.8898 0.6679 329 25.88% 26.03% 13.91% 97 45.82% 11.72% 0.0333 0.0989 518 44.13% 13.54% 8.58% 97 14.98% 7.68% 0.5222 0.3977 518 14.38% 8.41% 0.8033 48 1.6271 1.0281 0.0179 0.0620 328 1.7913 0.8409 0.5644 81 2.5777 0.6099 0.0706 0.0210 438 2.6893 0.5748 0.6726 82 2.5091 0.5931 0.1725 0.1245 435 2.5758 0.6585 0.3779 267 -0.3766 0.4858 0.1980 0.0378 321 -0.3766 0.0378 311.68 97 221.23 704.32 0.0038 0.0028 518 202.48 1688.58 2008.0 49 266.10 872.51 0.8822 0.7935 329 76.96 329.00 74.36% 43 76.15% 47.45% 0.5605 0.2409 298 92.52% 71.36% 19.28% 73 18.99% 20.85% 0.8176 0.5051 376 17.35% 19.58% 47.00% 97 85.49% 32.49% 0.0713 0.0196 518 97.38% 44.98% 5.59% 97 4.14% 5.95% 0.7024 0.5171 376 13.25% 18.44% 65.93% 74 92.80% 91.79% 0.0637 0.2221 394 80.86% 71.60% 31.66% 71 8.73% 37.84% 0.7273 0.5567 388 13.93% 32.91% 46.84% 75 -6.89% 38.28% -0.672 -0.649 401 -8.88% 45.33% 70.97% 74 -11.0% 89.25% -0.0920 -0.0200 394 181.57% 143.8% 28.83% 71 -17.6% 36.58% 0.1618 0.0720 388 11.61% 21.63% 459.60 73 89.98 738.32 0.2268 0.5401 415 9.7242 519.77 14.09% 73 -0.21% 12.03% 0.4233 0.1601 409 -0.90% 13.74% 459.92 73 76.92 738.6 0.4814 0.5238 414 -1.7325 520.17 15.91% 73 -10.1% 12.98% 0.8062 0.7821 408 -8.94% 15.42% 60.71 69 -1.18% 58.54% 0.3231 0.2110 382 -3.72% -60.26% 31.87% 97 -16.7% 209.2% 0.0697 0.0350 518 -5.39% 94.78% 937.1% 72 -331% 196.9% 0.0380 0.2065 421 -121.8% 1180% 28.82 49 6.31 71.11 0.2530 0.1955 328 -4.89 38.35 39 Macro Vintage Credit Quality / Market Cap. Str. Groups Table 5 - Summary Statistics and Distributional Tests for Selected Capital Structure, Instrument and Market Variables by Default Outcome and Workout Type (S&P and Moody's Rated Borrowers 1985-2004) 1 Liquidation Cnt. Variables Number of Creditor Classes 70 Number of Defaulted Instruments 70 Proportion of Secured Debt 70 Proportion of Bank Debt 70 Proportion of Subordinated Debt 70 Altman Z-Score at Default 51 Minimum Credit Rating 47 Number of Downgrades 48 Maximum Downgrade Distance 48 Change in Altman Z-Score 49 Weighted Aveergae Credit Spread 70 Loss Given Default 49 Original Credit Rating 70 Cumulative Abnormal Return 32 Time Since Issue 70 Time-to-Maturity 70 Time Since Issue % Time-to-Maturity 68 Maximum Time Between Instrument Default 70 Average Time Between Instrument Default 70 Time Between First Instrument Default and Filing 70 Moody's All-Corporate Default Rate Lagging 70 Moody's Speculative Default Rate Lagging 70 Moody's All-Corporate Default Rate Coincident 70 Moody's Speculative Default Rate Coincident 70 S&P Return 70 Mean 2.1429 3.8714 45.15% 37.40% 36.14% 0.7422 3.4255 1.3750 3.4583 -1.7228 6.77% 68.92% 2.1571 -37.6% 905.7 1784.6 0.3485 70.80 43.64 20.47 2.69% 6.23% 2.91% 6.00% 0.82% Reorganization Tests of Equality Liquidation vs. Reorganization Bankruptcy Std. Std. KS P- KW PStd. Dev. Cnt. Mean Dev. Value Value Cnt. Mean Dev. 1.0113 448 2.2545 0.8314 0.1637 0.2177 421 2.2328 0.8580 2.8889 448 4.6339 3.7726 0.3470 0.0410 421 4.5558 3.5810 36.45% 448 38.76% 32.48% 0.1290 0.2188 421 40.32% 33.46% 35.24% 448 32.51% 28.11% 0.1249 0.5910 421 33.78% 29.74% 36.18% 448 33.50% 36.77% 0.8342 0.4672 421 33.64% 36.62% 3.0954 243 2.5158 2.5158 0.0010 0.0127 251 0.2542 2.7578 1.3791 309 1.3334 1.3334 1.0000 0.3753 296 3.6757 1.3262 1.8751 314 1.6075 1.6075 0.1646 0.0956 299 1.5819 1.7015 4.0210 317 4.5237 4.5237 0.6597 0.4641 302 3.8940 4.5628 10.661 235 9.9226 9.9226 0.2643 0.2430 245 -0.8449 1.0729 3.82% 448 5.04% 5.04% 0.1229 0.0976 421 7.29% 3.57% 26.17% 319 23.87% 23.87% 0.0388 0.0317 315 65.24% 23.94% 1.8069 448 1.7493 1.7493 1.0000 0.9156 421 2.1924 1.7481 54.6% 168 55.5% 55.5% 0.0022 0.0014 166 -15.0% 59.3% 770.1 448 1076.0 751.4 0.0158 0.0091 421 1044.8 770.4 1478.0 448 1772.4 1115.0 0.1578 0.2391 421 1774.4 1146.3 0.2013 437 0.3937 0.2094 0.0707 0.0643 410 0.3845 0.2056 129.68 448 132.78 216.35 0.0097 0.0037 421 116.30 180.11 93.21 448 81.56 150.81 0.0195 0.0051 421 73.25 136.71 36.06 448 35.91 59.33 0.0326 0.0129 421 31.72 49.57 1.41% 448 3.03% 1.34% 0.2479 0.0574 421 2.91% 1.36% 3.18% 448 7.14% 3.05% 0.1023 0.0285 421 6.85% 3.09% 1.24% 448 2.72% 1.35% 0.0529 0.1973 421 2.78% 1.32% 4.00% 448 5.59% 3.19% 0.0817 0.2798 421 5.71% 4.03% 1.39% 448 0.47% 1.42% 0.0176 0.0254 421 0.56% 1.43% Out-of-Court Cnt. 518 518 518 518 518 43 60 63 63 39 97 53 97 34 97 97 95 97 97 97 97 97 97 97 97 Mean 2.2680 4.4227 36.64% 30.52% 34.80% 0.4243 3.3833 1.5556 3.5079 -0.3191 8.72% 55.82% 2.0412 7.2% 1088.6 1772.8 0.4011 159.57 90.28 42.92 3.30% 7.78% 2.64% 5.36% 0.30% Std. Dev. 0.8602 4.0642 31.36% 26.63% 37.03% 1.8836 1.3912 1.3533 3.9344 3.4419 8.47% 24.60% 1.7907 34.5% 689.1 1168.2 0.2224 298.31 176.21 81.40 1.28% 2.93% 1.40% 4.68% 1.33% Tests of Equality Chapter 11 vs. Out-of-Court KS PValue 1.0000 0.9610 0.7875 0.8388 0.9854 0.6584 0.2338 0.2338 0.9678 0.6022 0.0488 0.0141 0.9116 0.0032 0.5118 0.8536 0.3839 0.7483 0.6896 0.7820 0.0875 0.091 0.4543 0.4530 0.0176 KW PValue Cnt. 0.6998 518 0.4483 518 0.4095 518 0.5615 518 0.8998 518 0.8575 294 0.0248 357 0.0240 362 0.9936 365 0.9306 284 0.0698 518 0.0061 378 0.5412 518 0.0049 200 0.3442 518 0.8217 518 0.5223 505 0.8024 518 0.9815 518 0.7416 518 0.0149 518 0.0094 518 0.3786 518 0.5011 518 0.0254 518 Total Mean 2.2394 4.5309 39.63% 33.17% 33.86% 0.2791 3.6264 1.5774 3.8274 -0.7727 7.56% 63.88% 2.1640 -11.2% 1053.0 1774.6 0.3876 124.40 76.44 33.82 2.98% 7.02% 2.75% 5.64% 0.51% Std. Dev. 0.8577 3.6725 33.08% 29.19% 36.66% 2.6282 1.3399 1.6445 4.4580 1.0437 4.90% 24.23% 1.7554 56.4% 755.4 1169.0 0.2087 207.76 144.89 56.97 1.35% 3.08% 1.33% 4.17% 1.42% 40 Table 6 - Multivariate Logistic Regressions for Default Process Type: Bankruptcy Filing vs. Out-Of-Court Settlement (S&P and Moody's Rated Borrowers 1985-2004) 1 Model 1 Category Leverage Size / Sclae Variable Leverage Ratio (Lagged) Market Value of Equity Intrinsic Value / Tangibility Tobin's Q Liquidity 5.73E-04 Quick Ratio (Industry Adjusted) Cash Flow Free Cash Flow (Time of Default) Free Cash Flow (Lagged) Profitability Return on Equity Capital Structure Credit Quality / Market Contractual / Vintage Macro-economic Legal / Regulatory Altman Z-Score at Default Loss Given Default Cumulative Abnormal Return Time SinceTime IssueBetween % Time-to-Maturity Maximum Instrument Default 2 Diagnostic Statistics Likelihood Ratio - Global McFadden Pseudo R-squared4 Mean Bias5 Hoshmer-Lemeshow6 LCVH Chi-squared7 Area Under ROC Curve8 Kolmogorov Smirnov 9 Spearman Rank Correlation9 Percent Correctly Classified10 Number of Observations Model 4 Model 5 3.94E-05 0.0919 0.0348 0.0480 0.0181 0.0305 0.0135 -0.0208 0.0077 -0.0140 2.37E-04 -9.69E-09 0.3069 -1.79E-05 0.2235 -1.15E-05 0.1030 0.3656 -1.89E-06 0.0865 -6.51E-04 0.1673 -4.86E-04 0.2364 -2.61E-04 0.0515 -1.54E-05 2.63E-03 2.43E-03 7.90E-05 -1.80E-03 1.56E-03 -6.13E-05 0.0348 -9.92E-03 0.0241 0.0427 0.0218 -0.0374 0.1352 -1.30E-03 0.0478 0.0187 0.0132 -0.0159 0.3347 0.0244 0.0188 -9.78E-03 0.0511 1.57E-04 -3.74E-07 0.0327 0.0427 -3.71E-04 0.0371 7.30E-07 0.0495 2.39E-04 0.4869 -6.86E-05 0.4411 0.1308 0.2936 -3.17E-07 0.0958 0.1180 3.28E-03 1.38E-03 7.58E-06 Moody's Speculative Default Rate Lagging -5.40E-03 S&P Return 0.0146 Filing District Prepackaged Bankruptcy Technology Utility Aditors Opinion Model 3 7.53E-04 1.92E-03 -2.49E-05 3.73E-04 Number of Creditor Classes Proportion of Secured Debt Proportion of Subordinated Debt Model 2 Partial Partial Partial Partial Partial Effects1 P-Value Effects P-Value Effects P-Value Effects P-Value Effects P-Value -1.44E-03 0.0246 -8.07E-05 0.0570 -8.64E-03 0.0086 -0.0349 7.43E-03 -0.1000 -1.0000 8.26E-04 1.91E-03 1.03E-05 0.3085 3.23E-03 0.4066 6.80E-03 0.0392 0.2055 0.1840 -3.08E-05 0.1661 7.82E-04 3.39E-03 2.89E-05 0.0191 1.79E-03 0.2921 3.63E-05 0.3542 -7.84E-04 1.96E-03 -6.27E-04 0.0568 2.43E-05 0.4710 2.80E-04 0.3415 -2.75E-06 0.1467 Out-ofInOut-of1 Sample Sample In-Sample Sample Model 6 Partial Effects P-Value -0.0241 0.0184 0.0206 0.0081 3.14E-03 0.2870 0.0268 0.2492 2.16E-03 0.1051 -0.0529 0.0007 0.0012 0.1653 -0.0329 0.0246 0.2101 -2.88E-04 0.4758 0.1621 -0.0129 3.30E-03 -0.1358 0.1486 0.1037 0.2476 -0.2989 0.0184 0.1223 0.4874 -0.1657 0.3939 -0.0486 0.0376 0.0414 3.18E-04 0.2460 0.0277 9.17E-03 0.0198 -0.0165 0.0404 -0.0113 1.00E-03 0.4832 0.0122 -5.34E-04 0.3926 -1.00E-03 3.92E-05 0.0017 0.0040 0.0236 0.1003 0.1804 0.1903 -0.0080 0.0254 0.4913 0.1504 0.4870 0.1701 0.1803 -6.87E-03 0.2036 -0.0157 0.4877 0.4809 0.0395 0.0669 -0.2506 0.3114 InSample Out-ofSample InSample Out-ofSample Out-ofIn-Sample Sample 0.1639 0.0103 0.4107 0.0520 4.66E-06 InSample Out-ofSample 6.58E-12 -2.32E-08 9.86E-08 9.86E-03 8.30E-10 8.26E-05 1.32E-05 1.32E+00 1.25E-05 1.25E+00 8.81E-16 -2.24E-07 0.5194 0.4289 0.6873 0.5193 0.7403 0.5521 0.3867 0.4549 0.3425 0.3225 0.2570 0.1891 -4.76E-06 -4.39E-03 -4.62E-06 -6.85E-03 -2.84E-06 1.46E-05 -1.05E-05 -6.24E-03 -1.26E-08 -4.57E-03 -9.87E-09 8.57E-03 0.9996 0.7758 0.9027 0.2253 0.8980 0.2247 0.2502 1.0000 0.2499 0.1943 1.0000 0.2498 0.5075 0.5000 0.4511 0.1508 0.4465 0.1458 0.1659 0.5340 0.1801 0.1728 0.5000 0.1602 0.7613 0.8532 0.9238 0.7319 0.9116 0.7283 0.6021 0.8649 0.6907 0.6846 0.8002 0.6447 2.92E-07 3.14E-04 2.98E-07 2.53E-04 2.92E-07 3.47E-04 2.92E-07 2.40E-04 4.43E-06 4.39E-03 2.92E-07 3.08E-04 0.5883 0.4673 0.5140 0.3923 0.5628 0.4218 0.4371 0.5120 0.3898 0.3458 0.4673 0.3498 0.8743 0.5532 0.9239 0.7468 0.9483 0.7565 0.6988 0.8323 0.6676 0.4401 0.7450 0.6011 197 116 167 265 142 460 1 - The derivative of the logisitic function evaluated at the median values of the independent variables, an estimate of the change in the modeled probability for a small change in a covariate. 2 - The sample is randomly divided into 80% training and 20% testing data-sets. This is repeated for 100,000 iterations, and the median values of the test statistics (or their p-values) are reported. 3 - The difference in the maximized values of the log-likelihoods, the full model minus the null model having only an intercept, distributed as a chi-squared random variable with degrees of freedom equal to the number of slope coefficients in the full model. 4 - One minus the ratio of the model to the null deviance, where the deviance is equal to one-half the maximized value of the log-likelihood. 5 - The mean difference between predicted probabilities and actual sample frequency of the event modeled: Predicted Avg(P(Bankr.)) - Actual P(Bankr.). 6 - A normalized average deviation between empirical frequencies and average modelled probabilities across deciles of risk, ranked according to modelled probabilities, a measure of model fit or predictive accuracy of the model. 7 - The residual deviance of the model smoothed according to the deviation of the vector of covariates according to a uniform kernel, a measure of model fit or predictive accuracy. 8 - The area under the Receiving Operator Characteristic (ROC) curve, or the plot of event proportions in the population vs. the complement of the risk ranking according to the model, a measure of the discriminatory accuracy of the model. 8 - A test of the equality of the distribution functions of the estimated probabilities of the event vs. the non-event sample, a measure of the discriminatory accuracy of the model. 9 - The Spearman rank correlation between the event indicators and the predicted probabilities, a measure of the discriminatory accuracy of the model. 10 - The proportion of events correctly classified, according to a cutoff model probability that minimizes the Expected Cost of Misclassification (ECM), a measure of the discriminatory accuracy of the 41 Table 6 - Multivariate Logistic Regressions for Default Process Type: Bankruptcy Filing vs. Out-Of-Court Settlement (S&P and Moody's Rated Borrowers 1985-2004) 1 Model 1 Category Leverage Size / Sclae Variable Leverage Ratio (Lagged) Market Value of Equity Intrinsic Value / Tangibility Tobin's Q Liquidity Quick Ratio (Industry Adjusted) Cash Flow Free Cash Flow (Time of Default) Free Cash Flow (Lagged) Profitability Return on Equity Capital Structure Credit Quality / Market Contractual / Vintage Macro-economic Legal / Regulatory Diagnostic Statistics Number of Creditor Classes Proportion of Secured Debt Proportion of Subordinated Debt Altman Z-Score at Default Loss Given Default Cumulative Abnormal Return Time SinceTime Issue % Time-to-Maturity Maximum Between Instrument Default Model 2 Model 3 Model 4 Model 5 Partial Partial Partial Partial Partial Effects1 P-Value Effects P-Value Effects P-Value Effects P-Value Effects P-Value -1.44E-03 0.0246 -8.07E-05 0.0570 -8.64E-03 0.0086 -0.0349 7.43E-03 -0.1000 -1.0000 8.26E-04 1.91E-03 1.03E-05 0.3085 3.23E-03 0.4066 6.80E-03 0.0392 5.73E-04 3.94E-05 0.0919 0.0348 0.0480 0.0181 0.0305 7.53E-04 1.92E-03 -2.49E-05 0.0135 -0.0208 0.0077 -0.0140 2.37E-04 -9.69E-09 0.3069 -1.79E-05 0.2235 -1.15E-05 0.1030 0.3656 -1.89E-06 0.0865 -6.51E-04 0.1673 -4.86E-04 0.2364 -2.61E-04 0.0515 -1.54E-05 2.63E-03 2.43E-03 7.90E-05 -1.80E-03 1.56E-03 -6.13E-05 0.0348 -9.92E-03 0.0241 0.0427 0.0218 -0.0374 0.1352 -1.30E-03 0.0478 0.0187 0.0132 -0.0159 0.3347 0.0244 0.0188 -9.78E-03 0.0511 1.57E-04 -3.74E-07 0.0327 0.0427 -3.71E-04 0.0371 7.30E-07 0.0495 2.39E-04 0.4869 -6.86E-05 0.4411 0.1308 0.2936 -3.17E-07 3.73E-04 0.0958 0.1180 3.28E-03 1.38E-03 7.58E-06 Moody's Speculative Default Rate Lagging -5.40E-03 S&P Return 0.0146 0.2055 0.1840 -3.08E-05 0.1661 -0.2506 0.3114 -0.1358 0.1486 Model 6 Partial Effects P-Value -0.0241 0.0184 0.0206 0.0081 3.14E-03 0.2870 0.0268 0.2492 2.16E-03 0.1639 0.0103 0.4107 0.1051 -0.0529 0.0007 0.0012 0.1653 -0.0329 0.0246 0.2101 -2.88E-04 0.4758 0.1621 -0.0129 3.30E-03 0.1037 0.2476 -0.2989 0.0184 0.1223 0.4874 0.0520 4.66E-06 -0.1657 0.3939 -0.0486 0.0376 Filing District Prepackaged Bankruptcy Technology Utility Aditors Opinion 7.82E-04 3.39E-03 2.89E-05 0.0191 0.0414 3.18E-04 0.2460 3.92E-05 0.1804 0.4913 0.1504 0.4877 1.79E-03 0.2921 3.63E-05 0.3542 0.0277 9.17E-03 0.0198 0.0017 0.1903 0.4870 0.1701 0.4809 -7.84E-04 1.96E-03 -0.0165 0.0404 -0.0113 0.0040 -0.0080 0.1803 -6.87E-03 0.0395 -6.27E-04 0.0568 2.43E-05 0.4710 1.00E-03 0.4832 0.0122 0.0236 0.0254 0.2036 -0.0157 0.0669 2.80E-04 0.3415 -2.75E-06 0.1467 -5.34E-04 0.3926 -1.00E-03 0.1003 Out-ofInOut-ofOut-ofOut-ofOut-ofOut-ofSample Sample1 In-Sample Sample In-Sample Sample In-Sample Sample In-Sample Sample In-Sample Sample Likelihood Ratio - Global2 McFadden Pseudo R-squared4 Mean Bias5 Hoshmer-Lemeshow6 LCVH Chi-squared7 Area Under ROC Curve8 Kolmogorov Smirnov9 Spearman Rank Correlation9 Percent Correctly Classified10 Number of Observations 6.58E-12 3.40E-07 9.86E-08 9.86E-03 8.30E-10 8.33E-05 1.32E-05 1.32E+00 1.25E-05 1.25E+00 8.81E-16 1.72E-07 0.5194 0.4289 0.6873 0.5176 0.7403 0.5630 0.3900 0.4549 0.3445 0.3309 0.2570 0.1937 -4.76E-06 -1.09E-02 -4.62E-06 -6.72E-03 -2.84E-06 -2.89E-04 -1.05E-05 -8.89E-03 -1.26E-08 -8.50E-04 -9.87E-09 -4.19E-03 0.9996 0.7758 0.9026 0.2254 0.8963 0.2245 0.2503 1.0000 0.2499 0.1944 1.0000 0.2505 0.5075 0.5000 0.4582 0.1527 0.4521 0.1474 0.1669 0.5340 0.1806 0.1727 0.5000 0.1663 0.7613 0.8532 0.9238 0.7352 0.9116 0.7289 0.6141 0.8649 0.6921 0.6854 0.8002 0.6424 2.92E-07 2.72E-04 2.98E-07 3.20E-04 2.92E-07 3.40E-04 2.92E-07 3.29E-04 4.43E-06 4.42E-03 2.92E-07 2.75E-04 0.5883 0.4673 0.5140 0.3902 0.5628 0.4227 0.4371 0.5120 0.3804 0.3502 0.4673 0.3486 0.8743 0.5532 0.9239 0.7417 0.9483 0.7610 0.6973 0.8323 0.6660 0.4489 0.7450 0.5947 197 116 167 265 142 460 1 - The derivative of the logisitic function evaluated at the median values of the independent variables, an estimate of the change in the modeled probability for a small change in a covariate. 2 - The sample is randomly divided into 80% training and 20% testing data-sets. This is repeated for 100,000 iterations, and the median values of the test statistics (or their p-values) are reported. 3 - The difference in the maximized values of the log-likelihoods, the full model minus the null model having only an intercept, distributed as a chi-squared random variable with degrees of freedom equal to the number of slope coefficients in the full model. 4 - One minus the ratio of the model to the null deviance, where the deviance is equal to one-half the maximized value of the log-likelihood. 5 - The mean difference between predicted probabilities and actual sample frequency of the event modeled: Predicted Avg(P(Bankr.)) - Actual P(Bankr.). 6 - A normalized average deviation between empirical frequencies and average modelled probabilities across deciles of risk, ranked according to modelled probabilities, a measure of model fit or predictive accuracy of the model. 7 - The residual deviance of the model smoothed according to the deviation of the vector of covariates according to a uniform kernel, a measure of model fit or predictive accuracy. 8 - The area under the Receiving Operator Characteristic (ROC) curve, or the plot of event proportions in the population vs. the complement of the risk ranking according to the model, a measure of the discriminatory accuracy of the model. 8 - A test of the equality of the distribution functions of the estimated probabilities of the event vs. the non-event sample, a measure of the discriminatory accuracy of the model. 9 - The Spearman rank correlation between the event indicators and the predicted probabilities, a measure of the discriminatory accuracy of the model. 10 - The proportion of events correctly classified, according to a cutoff model probability that minimizes the Expected Cost of Misclassification (ECM), a measure of the discriminatory accuracy of the model. 42 1 Out of Sample/Time Training/Estimation Period Out of Sample/Time 1 Year Ahead Prediction Table 8 - Logistic Regression Bootstrapped Model Out-of-Sample and Out-of-Time Model Calibration (Predictive Accuracy) and Discrimination (Classification Accuracy) Analysis for Resolution Outcomes (Liquidation vs. Reorganization) (LossStats™ Database 1985-2004)2 Year Average ECM - Weighted Median Proportions Standard Deviation 5th Percentile Correctly 95th Percentile Classified Area Under Average Receiver Median Operating Standard Deviation Characteristic 5th Percentile 4 95th Percentile Curve Average Median Komogorov- Standard Deviation Smirnov 5th Percentile 95th Percentile Statistic5 Average Median Standard Deviation McFadden 5th Percentile Pseudo R95th Percentile Squared3 Average Median HoshmerLemeshow Chi- Standard Deviation Squared (P- 5th Percentile 95th Percentile Values)4 Average Median Le Cessie-Van Standard Deviation Houwelingen (P- 5th Percentile 95th Percentile Values)5 Period Average ECM - Weighted Median Proportions Standard Deviation 5th Percentile Correctly 95th Percentile Classified Area Under Average Median Receiver Standard Deviation Operating Characteristic 5th Percentile 95th Percentile Curve Average Median Komogorov- Standard Deviation 5th Percentile Smirnov 95th Percentile Statistic Average Median Standard Deviation McFadden 5th Percentile Pseudo R95th Percentile Squared Average Median HoshmerLemeshow Chi- Standard Deviation Squared (P- 5th Percentile 95th Percentile Values) Average Median Le Cessie-Van Standard Deviation Houwelingen (P- 5th Percentile 95th Percentile Values) 1995 0.6706 0.6706 0.5207 0.4473 1.0216 0.6064 0.6500 0.0846 0.2521 0.7944 0.1268 0.1333 0.0310 0.0698 0.1940 0.3374 0.3692 0.0974 0.1249 0.4707 0.1319 0.0875 0.0245 1996 0.6835 0.6353 0.5205 0.3964 0.9332 0.5239 0.5111 0.0817 0.2579 0.7985 0.1135 0.1111 0.0303 0.0556 0.1773 0.3354 0.2940 0.1384 0.1605 0.4933 0.0946 0.0548 0.0218 1997 0.6627 0.7155 0.5164 0.3665 0.9907 0.5938 0.5833 0.1190 0.2587 0.8333 0.0886 0.0941 0.0192 0.0057 0.1077 0.4455 0.4686 0.1497 0.1587 0.6617 0.0279 0.0306 0.0229 1998 1999 0.6838 0.6343 0.6475 0.6881 0.5103 0.5193 0.3958 0.4281 0.8902 0.9282 0.6578 0.6634 0.6667 0.6936 0.0778 0.0933 0.3822 0.5048 0.9008 0.9167 0.0850 0.0692 0.0978 0.0814 0.0232 0.0332 0.0033 0.0018 0.1100 0.0904 0.4548 0.3261 0.4669 0.3477 0.1272 0.0720 0.2476 0.19619 0.6278 0.5267 0.0724 0.0290 0.0683 0.0258 0.0275 0.0123 0.0428 0.0439 0.0158 0.0454 0.00057 0.1907 0.1563 0.1209 0.0879 0.3060 0.2035 0.1060 0.1010 0.5264 1985-94 0.9580 0.8416 0.1044 0.8167 0.8572 0.7033 0.7027 0.0126 0.6877 0.7361 0.0154 0.0121 0.0036 0.0027 0.0780 0.4799 0.4816 0.0545 0.3791 0.5980 0.1469 0.1560 0.0162 0.0057 0.1948 0.4192 0.5101 0.0963 0.2360 0.6210 0.2218 0.2065 0.0861 0.0571 0.3999 1985-95 0.9189 0.8950 0.1056 0.7961 0.9221 0.7071 0.7086 0.0638 0.5803 0.8383 0.0348 0.0303 0.0032 0.0054 0.1004 0.3864 0.3892 0.0814 0.2333 0.5497 0.1230 0.1548 0.0137 0.2093 0.2499 0.0553 0.1063 0.3278 1985-96 0.8873 0.8759 0.1075 0.8084 0.9123 0.7313 0.7397 0.0937 0.6168 0.8500 0.0071 0.0079 0.0027 0.0017 0.0107 0.6358 0.6488 0.1079 0.5069 0.7528 0.1089 0.1991 0.0396 0.006 0.0033 0.1498 0.5191 0.5332 0.0703 0.3818 0.6632 0.1512 0.5360 0.4404 0.0647 0.4099 0.6667 0.1357 2000 0.6534 0.6407 0.5080 0.3656 0.9536 0.6990 0.6875 0.1245 0.5333 0.8750 0.0724 0.0801 0.0252 0.02085 0.0997 0.3235 0.3149 0.0901 0.1919 0.4876 0.0309 0.0412 0.0313 0.0065 0.0999 0.2265 0.3107 0.3070 0.2501 0.2502 0.2576 0.0682 0.0600 0.0674 0.0928 0.1919 0.1145 0.3660 0.4349 0.3850 1985-97 1985-98 1985-99 0.9339 0.8610 0.9061 0.9113 0.8292 0.8681 0.1137 0.1052 0.0997 0.8541 0.7915 0.8197 0.8373 0.9919 0.9295 0.7295 0.6933 0.7419 0.7363 0.7339 0.7403 0.0940 0.0790 0.0534 0.6209 0.5049 0.6540 0.8482 0.8379 0.8293 0.0069 0.0066 0.0069 0.0076 0.0077 0.0074 0.0027 0.0032 0.0027 0.0016 0.0000 0.0024 0.0105 0.0108 0.0103 0.6212 0.4727 0.3671 0.6377 0.5095 0.3587 0.1195 0.0954 0.1004 0.4683 0.2941 0.2122 0.7592 0.6243 0.5477 0.1038 0.0786 0.1144 0.1023 0.0952 0.0750 0.0023 0.0175 0.0290 0.0016 0.0098 1.31E-08 0.0329 0.1158 0.1304 0.5242 0.4147 0.4424 0.5835 0.5417 0.5867 0.0683 0.0750 0.0728 0.3895 0.2651 0.3023 0.6664 0.5700 0.5946 2001 0.6633 0.5946 0.5164 0.4589 0.9753 0.7101 0.7135 0.0924 0.5109 0.8523 0.0847 0.0215 0.0215 0.0344 0.0936 0.3221 0.3144 0.0840 0.2013 0.4827 0.0570 0.0492 0.0309 0.0016 0.1830 2002 0.6510 0.6748 0.5199 0.4859 0.9443 0.7139 0.7100 0.0927 0.6667 0.9250 0.0677 0.0751 0.0280 0.0160 0.0998 0.2560 0.2498 0.0676 0.1558 0.3732 0.0286 0.0460 0.0229 0.0065 0.0712 2003 0.6379 0.6883 0.5158 0.4133 0.9781 0.6537 0.6389 0.1198 0.5089 0.9107 0.0848 0.0889 0.0193 0.0444 0.0919 0.2130 0.2072 0.0605 0.1293 0.3223 0.0323 0.0454 0.0255 0.0054 0.1047 1995-03 0.6607 0.6719 0.5164 0.4235 0.9524 0.6452 0.6630 0.0998 0.3978 0.8708 0.0880 0.0864 0.0263 0.0350 0.1982 0.3285 0.3226 0.1030 0.1665 0.5382 0.0539 0.0385 0.0249 0.0265 0.1998 0.2360 0.2088 0.3597 0.2603 0.2572 0.2593 0.4963 0.2476 0.0615 0.0706 0.0908 0.0756 0.1266 0.1083 0.1781 0.1177 0.3730 0.3915 0.5413 0.4617 1985-00 1985-01 1985-02 1985-03 0.93096 0.9143 0.9367 0.8948 0.8735 0.9450 0.8355 0.8543 0.10489 0.1027 0.0999 0.1054 0.74678 0.8124 0.8702 0.7940 0.95726 0.9449 0.9871 0.9045 0.7414 0.7464 0.7475 0.7329 0.7424 0.7481 0.7474 0.7390 0.0525 0.0429 0.0421 0.0644 0.6517 0.6728 0.6761 0.5763 0.8248 0.8160 0.8185 0.8242 0.0069 0.0072 0.0069 0.0053 0.0076 0.0079 0.0078 0.0117 0.0027 0.0026 0.0028 0.0028 0.0016 0.0018 0.0015 0.0022 0.0104 0.0101 0.0107 0.0280 0.3790 0.3380 0.3024 0.4402 0.3726 0.3316 0.2942 0.3904 0.0965 0.0863 0.0742 0.0923 0.2358 0.2106 0.1905 0.2827 0.5578 0.4875 0.4328 0.6225 0.0884 0.1500 0.1160 0.1128 0.0800 0.0917 0.1133 0.1037 0.0438 0.0153 0.0126 0.0251 0.0087 0.0803 0.0129 0.0232 0.1080 0.1107 0.1182 0.2062 0.4076 0.5419 0.5510 0.4862 0.4415 0.4800 0.5200 0.5123 0.0477 0.0669 0.0201 0.0673 0.3174 0.4125 0.5195 0.3330 0.5117 0.6778 0.5950 0.6462 1 - In each run, observations are sampled randomly with replacement from the training and prediction samples, the model is estimated in the training sample and observations are classified in the prediction period, and this is repeated 100,000 times 2 - 199 observations with variables: long term debt to market value of equity, book value of assets quantile, intangibles to book vaue of assets, interest coverage ratio, free cash flow to book value of assets, net income to net sales, number of major creditor classes, percent secured debt, Altman Z-Score, debt vintage (time since issued), Moody's 12 month trailing speculative grade default rate, industry dummy, filing district dummy, prepackage dummy 3 - .One minus the ratio of the model deviance (sum of squared deviation of liquidation indicators from predicted probabilities normalized by the binomial standard deviation) to the deviance of a model with only an intercept 4 - The sum of squared standardized residuals of the logistic regression model, a measure of fit; large statistics (small p-values) indicate a poor fit (or innaccuate model). 5 - A version of the Pearson chi-squared that non-parametrically smooths the regression residuals according to a unform kernel that measures the distance between covaraites. 43 Out of Sample/Time 1 Year Ahead Prediction Table 9 - Logistic Regression Bootstrapped1 Model Out-of-Sample and Out-of-Time Model Calibration (Predictive Accuracy) and Discrimination (Classification Accuracy) Analysis for Resolution Process Outcomes (Bankruptcy vs. Out-of-Court Settlement) (LossStats™ Database 1985-2004)2 Area Under Receiver Operating Characteristic Curve4 KomogorovSmirnov Statistic5 McFadden Pseudo RSquared3 Pearson ChiSquared (PValues)4 Out of Sample/Time Training/Estimation Period Le Cessie-Van Houwelingen (PValues)5 ECM - Weighted Proportions Correctly Classified Area Under Receiver Operating Characteristic Curve KomogorovSmirnov Statistic McFadden Pseudo RSquared Pearson ChiSquared (PValues) Le Cessie-Van Houwelingen (PValues) Year Average Median Standard Deviation 5th Percentile 95th Percentile Average Median Standard Deviation 5th Percentile 95th Percentile Average Median Standard Deviation 5th Percentile 95th Percentile Average Median Standard Deviation 5th Percentile 95th Percentile Average Median Standard Deviation 5th Percentile 95th Percentile Period Average Median Standard Deviation 5th Percentile 95th Percentile Average Median Standard Deviation 5th Percentile 95th Percentile Average Median Standard Deviation 5th Percentile 95th Percentile Average Median Standard Deviation 5th Percentile 95th Percentile Average Median Standard Deviation 5th Percentile 95th Percentile Average Median Standard Deviation 5th Percentile 95th Percentile 1995 0.6064 0.6500 0.0846 0.2522 0.7932 0.1268 0.1333 0.0310 0.0735 0.1988 0.3374 0.3743 0.0974 0.1249 0.4707 0.1319 0.0875 0.0245 1996 0.5239 0.5111 0.0817 0.2529 0.7913 0.1135 0.1111 0.0303 0.0600 0.1794 0.3354 0.2997 0.1384 0.1605 0.4933 0.0946 0.0548 0.0218 1997 0.5938 0.5833 0.1190 0.2555 0.8333 0.0886 0.0930 0.0192 0.0057 0.1081 0.4455 0.4686 0.1497 0.1587 0.6617 0.0279 0.0062 0.0229 1998 0.6578 0.6667 0.0778 0.3810 0.9008 0.0850 0.0978 0.0232 0.0033 0.1063 0.4548 0.4669 0.1272 0.2476 0.6278 0.0724 0.0683 0.0275 0.0415 0.0475 0.0184 0.0416 0.1907 0.3060 0.2054 0.1060 0.1031 0.5194 1985-94 0.8660 0.9400 0.0284 0.9042 0.8622 0.7092 0.7010 0.0156 0.6808 0.7421 0.0154 0.0121 0.0036 0.0027 0.0780 0.4799 0.4816 0.0545 0.3791 0.5980 0.1469 0.1560 0.0162 0.0057 0.1948 0.4192 0.5101 0.0963 0.2360 0.6210 0.1563 0.2218 0.2032 0.0861 0.0551 0.3952 1985-95 0.8415 0.9561 0.0222 0.8360 0.8928 0.7035 0.7011 0.0590 0.5881 0.8219 0.0348 0.0303 0.0032 0.0054 0.1004 0.3864 0.3892 0.0814 0.2333 0.5497 0.1230 0.1548 0.0137 0.1209 0.1937 0.2499 0.0553 0.0901 0.3073 1985-96 0.8256 0.9027 0.0263 0.9174 0.9072 0.7313 0.7397 0.0937 0.6142 0.8500 0.0071 0.0079 0.0027 0.0017 0.0107 0.6358 0.6488 0.1079 0.5069 0.7528 0.1089 0.1991 0.0396 0.006 0.0033 0.1498 0.5191 0.5332 0.0703 0.3818 0.6632 0.1512 0.5360 0.4404 0.0647 0.4099 0.6667 0.0879 0.2361 0.2503 0.0682 0.1067 0.3783 1985-97 0.8576 0.9608 0.0264 0.9359 0.9387 0.7295 0.7363 0.0940 0.6164 0.8482 0.0069 0.0076 0.0027 0.0016 0.0105 0.6212 0.6377 0.1195 0.4683 0.7592 0.1038 0.1023 0.0023 0.0016 0.0329 0.5242 0.5835 0.0683 0.3895 0.6664 1999 2000 0.6634 0.6990 0.6936 0.6875 0.0933 0.1245 0.5014 0.5333 0.9167 0.8750 0.0692 0.0724 0.0814 0.0801 0.0332 0.0252 0.0014 0.02085 0.0950 0.0997 0.3261 0.3235 0.3477 0.3149 0.0720 0.0901 0.1872 0.1919 0.5267 0.4876 0.0290 0.0309 0.0258 0.0448 0.0123 0.0313 0.0019 0.0012 0.1357 0.0999 0.2732 0.2011 0.2507 0.2514 0.0600 0.0673 0.1606 0.1145 0.4007 0.3845 1985-98 1985-99 0.8220 0.8727 0.9527 0.8981 0.0230 0.0186 0.8222 0.8367 0.9321 0.9004 0.6933 0.7419 0.7339 0.7403 0.0790 0.0534 0.5062 0.6540 0.8379 0.8293 0.0066 0.0069 0.0077 0.0074 0.0032 0.0027 0.0000 0.0024 0.0108 0.0103 0.4727 0.3671 0.5095 0.3587 0.0954 0.1004 0.2941 0.2122 0.6243 0.5477 0.0786 0.1144 0.0952 0.0750 0.0175 0.0290 0.0098 1.31E-08 0.1158 0.1304 0.4147 0.4424 0.5417 0.5867 0.0750 0.0728 0.2651 0.3023 0.5700 0.5946 2001 2002 2003 1995-03 0.7101 0.7139 0.6537 0.6532 0.7135 0.7100 0.6389 0.7145 0.0924 0.0927 0.1198 0.1002 0.5109 0.6667 0.5078 0.4945 0.8523 0.9250 0.9107 0.8866 0.0847 0.0677 0.0848 0.0850 0.0215 0.0751 0.0889 0.0907 0.0215 0.0280 0.0193 0.0263 0.0344 0.0160 0.0444 0.0363 0.0972 0.0998 0.0919 0.1966 0.3221 0.2560 0.2130 0.3362 0.3144 0.2498 0.2072 0.3204 0.0840 0.0676 0.0605 0.1028 0.2013 0.1558 0.1293 0.1665 0.4827 0.3732 0.3223 0.5340 0.0570 0.0286 0.0323 0.0564 0.0492 0.0460 0.0454 0.0484 0.0309 0.0229 0.0255 0.0249 0.0043 0.0038 0.0072 0.0263 0.1830 0.0712 0.1047 0.2061 0.3072 0.3480 0.3597 0.2734 0.2587 0.2568 0.4963 0.2501 0.0624 0.0754 0.0908 0.0765 0.1248 0.0986 0.1781 0.1132 0.3747 0.4009 0.5413 0.4559 1985-00 1985-01 1985-02 1985-03 0.85599 0.8632 0.8312 0.8954 0.8832 0.9608 0.9595 0.9756 0.01897 0.0183 0.0307 0.0236 0.82748 0.8501 0.9065 0.8672 0.93167 0.8819 0.9362 0.9394 0.7414 0.7464 0.7475 0.7315 0.7424 0.7481 0.7474 0.8636 0.0525 0.0429 0.0421 0.0643 0.6517 0.6728 0.6761 0.6636 0.8248 0.8160 0.8185 0.8987 0.0069 0.0072 0.0069 0.0053 0.0076 0.0079 0.0078 0.0117 0.0027 0.0026 0.0028 0.0028 0.0016 0.0018 0.0015 0.0022 0.0104 0.0101 0.0107 0.0280 0.3790 0.3380 0.3024 0.4402 0.3726 0.3316 0.2942 0.3904 0.0965 0.0863 0.0742 0.0923 0.2358 0.2106 0.1905 0.2827 0.5578 0.4875 0.4328 0.6225 0.0884 0.1500 0.1160 0.1128 0.0800 0.0917 0.1133 0.1037 0.0438 0.0153 0.0126 0.0251 0.0087 0.0803 0.0129 0.0232 0.1080 0.1107 0.1182 0.2062 0.4076 0.5419 0.5510 0.4862 0.4415 0.4800 0.5200 0.5123 0.0477 0.0669 0.0201 0.0673 0.3174 0.4125 0.5195 0.3330 0.5117 0.6778 0.5950 0.6462 1 - In each run, observations are sampled randomly with replacement from the training and prediction samples, the model is estimated in the training sample and observations arelong classified in the prediction period, and this is repeated 20,000quantile, times intangibles to book vaue of 2 - 199 observations with variables: term debt to market value of equity, book value of assets assets, interest coverage ratio, free cash flow to book value of assets, net income to net sales, number of major creditor classes, percent secured debt, Altman Z-Score, debt vintage (time since issued), Moody's 12 month trailing speculative grade default rate, industry dummy, 3 - .One minus the ratio of the model deviance (sum of squared deviation of liquidation indicators from predicted probabilities normalized by the binomial standard deviation) to the deviance of a model with only an intercept 4 - The sum of squared standardized residuals of the logistic regression model, a measure of fit; large statistics (small p-values) indicate a poor fit (or innaccuate model). 5 - A version of the Pearson chi-squared that non-parametrically smooths the regression residuals according to a unform kernel that measures the distance between covaraites. 44 Table 10 - Bootstrapped1 Out-of-Sample and Out-of-Time Classification and Predictive Accuracy Model Comparison Analysis 2 (S&P and Moody's Rated Borrowers 1985-2004) Liquidation vs. Reorganization In-Sample / Time Training / Estimation Period Out-of-Sample / Time 1 Year Ahead Prediction Test Statistic ECM - Weighted Proportions Correctly 3 Classified Area Under Receiver Operating 4 Characteristic Curve Komogorov-Smirnov 5 Statistic McFadden Pseudo RSquared6 Hoshmer-Lemeshow Chi-Squared (PValues)7 Le Cessie-Van Houwelingen (PValues)8 ECM - Weighted Proportions Correctly Classified Area Under Receiver Operating Characteristic Curve4 Komogorov-Smirnov Statistic5 McFadden Pseudo RSquared3 Hoshmer-Lemeshow Chi-Squared (PValues)4 Le Cessie-Van Houwelingen (PValues)5 Model Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Median 5th Percentile 95th Percentile Logistic Local Regression Regression 0.6719 0.5639 0.4235 0.3070 0.9524 0.8690 0.6630 0.4671 0.3978 0.2512 0.8708 0.7685 0.0864 0.1445 0.0350 0.0742 0.1982 0.3003 0.3154 0.2198 0.1659 0.1111 0.5303 0.4335 0.0547 0.0267 0.0257 0.0128 0.2020 0.1003 0.2471 0.1279 0.1173 0.0586 0.4592 0.2307 0.8543 0.9121 0.7940 0.8237 0.9045 0.9501 0.7438 0.8183 0.5646 0.6084 0.8421 0.8983 0.0148 0.0010 0.0018 5.75E-05 0.0279 0.0180 0.3865 0.5894 0.2839 0.4192 0.6284 0.7499 0.1045 0.2082 0.0217 0.0435 0.1958 0.3919 0.5066 0.6164 0.3318 0.5447 0.6453 0.8065 Bankruptcy vs. Out-Of-Court Neural Logistic Local Nertwork Regression Regression 0.5090 0.7405 0.6823 0.2488 0.5259 0.4396 0.8263 0.9681 0.8905 0.3591 0.7145 0.5966 0.2028 0.4945 0.3474 0.7047 0.8866 0.7904 0.1732 0.0488 0.0733 0.1115 0.0150 0.0225 0.4582 0.1019 0.1319 0.1839 0.4697 0.3040 0.0929 0.2423 0.1638 0.3877 0.7932 0.5292 0.0172 0.1128 0.0752 0.0091 0.0773 0.0516 0.0666 0.3012 0.2312 0.0400 0.3227 0.2761 0.0177 0.1680 0.1400 0.0668 0.5489 0.4580 0.9496 0.9092 0.9503 0.8464 0.8672 0.8973 0.9923 0.9394 0.9662 0.8729 0.8636 0.9192 0.6374 0.6636 0.7277 0.9470 0.8987 0.9201 1.05E-04 9.43E-04 7.15E-05 -2.08E-05 1.46E-04 1.40E-05 1.83E-03 2.65E-03 1.77E-03 0.7027 0.7666 0.8443 0.5008 0.5624 0.6805 0.8253 0.9413 0.9415 0.3119 0.2159 0.3228 0.0648 0.0652 0.1305 0.6182 0.2978 0.4467 0.5995 0.6635 0.7970 0.6163 0.4930 0.5916 0.8876 0.7761 0.9318 Neural Nertwork 0.5828 0.3212 0.7918 0.4527 0.1517 0.6399 0.0881 0.0290 0.1484 0.2495 0.1425 0.4463 0.0630 0.0405 0.2086 0.2506 0.1273 0.4362 0.9756 0.9202 0.9826 0.9512 0.7673 0.9416 6.79E-06 1.49E-06 1.19E-04 0.8879 0.7427 0.9438 0.4193 0.1957 0.5808 0.8773 0.6508 0.9783 1 - In each run, observations are sampled randomly with replacement from the training and prediction samples, the model is estimated in the training sample and observations are classified in the prediction period, and this is repeated 100,000 times 2 - 199 observations with variables: long term debt to market value of equity, book value of assets quantile, intangibles to book vaue of assets, interest coverage ratio, free cash flow to book value of assets, net income to net sales, number of major creditor classes, percent secured debt, Altman Z-Score, debt vintage (time since issued), Moody's 12 month trailing speculative grade default rate, industry dummy, filing district dummy, prepackage dummy 3 - . The proportion of events correctly classified, according to a cutoff model probability that minimizes the Expected Cost of Misclassification (ECM), a measure of the discriminatory accuracy of the model. 4 - The area under the Receiving Operator Characteristic (ROC) curve, or the plot of event proportions in the population vs. the complement of the risk ranking according to the model, a measure of the discriminatory accuracy of the model. 5 - A test of the equality of the distribution functions of the estimated probabilities of the event vs. the non-event sample, a measure of the discriminatory accuracy of the model. 6 - One minus the ratio of the model to the null deviance, where the deviance is equal to one-half the maximized value of the loglikelihood. 7 - A normalized average deviation between empirical frequencies and average modelled probabilities across deciles of risk, ranked according to modelled probabilities, a measure of model fit or predictive accuracy of the model. 8 - The residual deviance of the model smoothed according to the deviation of the vector of covariates according to a uniform kernel, a measure of model fit or predictive accuracy. 45 Fig.1 - Densities of Liquidation Proportions Correctly Classified 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network 3.0 Probability Density 2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 % Correctly Classified Fig.2 - Densities of Bankruptcy Proportions Correctly Classified 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network 3.0 Probability Density 2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 % Correctly Classified 46 Fig.3 - Densities of AUROCs for Liquidation Prediction 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network 3.0 Probability Density 2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 AUROC Fig.4 - Densities of AUROCs for Bankruptcy Prediction 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network 4 Probability Density 3 2 1 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 AUROC 47 Fig.5 - Densities of KS P-Values for Liquidation Prediction 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network 8 Probability Density 6 4 2 0 0.0 0.1 0.2 0.3 0.4 0.5 KS Fig.6 - Densities of KS P-Values for Bankruptcy Prediction 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network 20 Probability Density 15 10 5 0 0.00 0.05 0.10 0.15 0.20 0.25 KS 48 Fig.8 - Densities of McFadden Pseudo R-Squareds for Bankruptcy Prediction 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network Probability Density 4 3 2 1 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 McFadden Pseudo R-Squared 49 Fig.9 - Densities of Hoshmer-Lemeshow P-Values for Liquidation Prediction 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network 4 3 2 Probability Density 1 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Hoshmer-Lemeshow P-Values Fig.10 - Densities of Hoshmer-Lemeshow P-Values for Bankruptcy Prediction 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network 4 3 2 Probability Density 1 0 0.0 0.2 0.4 0.6 0.8 Hoshmer-Lemeshow P-Values 1.0 1.2 50 Fig.11 - Densities of LCVH P-Values for Liquidation Prediction 100,000 Repetitions Out-of-Sample and Out-of-Time 1995-2004 Logistic Regression Local Regression Neural Network 4 3 2 Probability Density 1 0 0.0 0.1 0.2 0.3 0.4 0.5 Le Cessie-Van Houlwelingen P-Values 0.6 0.7 51 References Akhigbe, A. and J. 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