Download Table A1: Resolution of Finance Distress, Sample

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 Xi , 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 | Xi , 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 minF(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
 


1Y
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. Madura, 1996, Intra-industry effects of voluntary corporate liquidations,
Journal of Business Finance & Accounting 23, 915-30.
Altman, E.I., 1968, Financial ratios, discriminant analysis and the prediction of corporate
bankruptcy, Journal of Finance, 23, 589-609.
, 1986, Handbook of Corporate Finance (John Wiley and Sons, New York).
Baird, D. G., 1993, Revisiting auctions in chapter 11, Journal of Law and Economics 36, 633669.
Barniv, R., Agarwal, A. and R. Leach, 2002, Predicting bankruptcy resolution, Journal of
Business Finance & Accounting 29, 497-520.
Bradley, M. and M. Rosenzweig, 1992, The untenable case for chapter 11, The Yale Law
Journal 101, 1043-1095.
Bris, Arturo, Welch, Ivo and Zhu, Ning, 2004, The costs of bankruptcy, Yale ICF Working
Paper No. 04-13; AFA 2005 Philadelphia Meetings.
Bryan, D. M., S. L. Tiras and C. M. Wheatley, 2001, The interaction of solvency with liquidity
and its association with bankruptcy emergence, Journal of Business Finance and
Accounting 29, 935-965.
Bulow, J.I. and J.B. Shoven, 1978, The bankruptcy decision, Bell Journal of Economics 9,
437-56.
Casey, C., McGee, V. and C. Stickney, 1986, Discriminating between liquidated and
reorganized firms in bankruptcy, The Accounting Review 6, 249-62.
Clark, K. and E. Ofek, 1994, Mergers as a means of restructuring distressed firms: An
empirical investigation, Journal of Financial and Quantitative Analysis 29, 541-565.
Davidson, A.C. and D.V. Hinckley, 1997, Bootstrap Methods and their Application
(Cambridge University Press, Cambridge).
Dhumale, R. , 1998, Earnings retention as specification mechanism in logistic regression
models: a test of the free cash theory.” Journal of Business Finance & Accounting, vol. 10
(Spring): 167-79.
Davison, A.C. and D.V. Hinkley. 1997. Bootstrap Methods and their Application,
Cambridge University Press, Cambridge.
Easterbrook, F. H., 1990. Is corporate bankruptcy efficient, Journal of Financial Economics
27, 411-417.
Efron, B., 1979, Bootstrap methods: another look at the jackknife, American Statistician 7,
1-23.
Efron, B and R, Tibshirani, 1986, Bootstrap methods for standard errors, confidence
intervals, and other Measures of statistical accuracy, Statistical Science 1, 54-75.
52
Fisher, T.C.G. and J. Martel, 2003, The firm’s reorganization decision: empirical evidence
from Canada, Unpublished Working Paper.
Frydman, H., Altman, E .I. and D. Kao, 1985, Introducing recursive partitioning for financial
classification: the case of financial distress, Journal of Finance 40, 269-91.
Hong, S. C., 1984, The outcome of bankruptcy: Model and empirical Test, (University of
California, Berkeley, CA).
Hotchkiss, E. S., 1993, The liquidation/reorganization choice of firms entering chapter 11,
(New York University, NY).
,1995, Postbankruptcy performance and management turnover, Journal of
Finance 50, 3-21.
Hsieh, S.J. 1993, A note on the optimal cutoff point in bankruptcy prediction models,
Journal of Business Finance & Accounting 20, 457-64.
Jensen, M. C., 1991, Corporate control and the politics of finance, Journal of Applied
Corporate Finance 4, 13-33.
Kahl, M., 2001, Financial distress as a selection mechanism: Evidence from the United
States, University of California, Unpublished working paper.
, 2002, Economic distress, financial distress, and dynamic liquidation, Journal of
Finance 57, 135-168.
Keisman , D. and K, van de Castle, 2000, Suddenly structure mattered: insights into
recoveries of defaulted debt, Corporate Ratings – Commentary, Standard and Poors.
Kim, M. and M. Kim, 1999, A note on the determinants of outcomes of bankruptcy
petitions: evidence from Korea, Journal of Business, Finance & Accounting 26, 997-1011.
Klein, M. I., 1979, The bankruptcy reform act of 1978, American Bankruptcy Law Journal 53,
1-33.
Lachenbruch, P.A, 1967, An almost unbiased method for obtaining confidence intervals
for the probability of misclassification in discriminant analysis, Biometrics 23, 639-645.
Lehavy, R, 2002, Reporting discretion and the choice of fresh start values in companies
emerging from Chapter 11 bankruptcy, Review of Accounting Accounting Studies 7, 5373.
Lennox, C.S. , 1999, The accuracy and incremental information content of audit reports in
predicting bankruptcy, Journal of Business Finance & Accounting 26 , 757-78.
LoPucki, L.M., 1983, The debtor in full control-system failure under Chapter 11 of the
bankruptcy code, American Bankruptcy Law Journal, 99-126.
Maddala, G.S. , 1983, Limited Dependent and Qualitative Variables in Finance (
Cambridge University Press, Cambridge).
53
, 1991, The perspective on the use of limited-dependent and qualitative
variables models in accounting research, The Accounting Review 66: 788-807.
Miller, M. H. and F. Modigliani, 1963, Corporate income taxes and the cost of capital,
American Economic Review 53, 433-443.
Modigliani, F. and M. H. Miller, 1958, The cost of capital, corporation finance, and the
theory of investment, American Economic Review 48, 261-297.
Morse, D. and W. Shaw, 1988, Investing in bankrupt firms, Journal of Finance 43, 1193-206.
Platt H. D. and M. B. Platt, 2002, A re-examination of the effectiveness of the bankruptcy
process, Journal of Business Finance and Accounting 29, 1209-1237.
Pratt, H.D., Kane, G.D. and J.G. Pedersen, 1994, Bankruptcy discrimination with real
variables, Journal of Business Finance & Accounting 21, 491-510.
Ohlson, J.A., 1980, Financial ratios and the probabilistic prediction of bankruptcy, Journal
of Accounting Research 18, 109-31.
Schleifer, A. and R. Vishny, 1992, Liquidation values and debt capacity: a market
equilibrium approach, Journal of Finance, 47, 1343-1366.
Stromberg, P., 2000, Conflicts of interest and market illiquidity in bankruptcy auctions:
Theory and tests, Journal of Finance 55, 2641-2692.
Rogueries, D. and R. Toffler, 1996, Neural networks and empirical research in accounting,
Accounting and Business Research 26, 347-55.
Venables, W.N. and B.D. Ripley, 1999, Modern Applied Statistics with S-Plus, 3rd Edition
(Springer-Verlag, New York).
Ward, T.J. and B.P. Foster, 1997, A note on selecting a response measure for financial
distress, Journal of Business Finance & Accounting 24, 869-78.
White, M.J. 1981, The economics of bankruptcy: liquidation and reorganization, Journal
of Finance 38, 477-87.
, 1983, Bankruptcy costs and the new bankruptcy code, Journal of Finance 38,
477-488.
, 1989, The corporate bankruptcy decision, Journal of Economic Perspectives
3, 129-151.
, 1990, Bankruptcy Liquidation and Reorganization. In D. Logue, ed., Handbook
of Modern Finance, 2nd edition (Warren, Gorham & Lamont, MA) Chapter 37.
Zmijewski, M.E., 1984, Methodological issues related to the estimation of financial distress
in prediction models, Journal of Accounting Research 18, 261-97.
54