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: March 2006
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 (either bankruptcy or default), either liquidation or reorganization, for a sample of
200 defaulted firms in the S&P LossStats™ Database for which there is an indication for
the type of resolution and financial statement data at the time of default. Various
qualitative dependent variable models are estimated and compared: ordered logistic
regression (OLR), multiple discriminant analysis(MDA) 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 this outcome – number of classes of debt, proportion of secured
debt in the capital structure, credit quality, asset size, leverage, intangibles as a
proportion of assets, free cash flow to assets, interest coverage ratio, profitability,
macroeconomic state, industry and an indicator for pre-packaged bankruptcy.
Estimation results reveal the OLR model to achieve best balance between in-sample fit,
consistency with financial theory and out-of-sample classification accuracy. In the
preferred OLR model, a stepwise analysis shows that with the exception of only 4 of these
(classes of debt, profit margin, industry and macro state), all these variables both
contribute significantly to joint explanation of liquidation likelihood and have 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)
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.
Classification accuracy is assessed according to alternative categorization criteria
(expected cost of misclassification, minimization of total misclassification and deviation
from historical averages) and through comparison to naïve random benchmarks. While
in- and out-of-sample accuracy exhibits wide variation across models and classification
criteria, the OLR and MDA models are found to perform comparably, while the FNN
model is found to consistently underperform. While most models fail to accurately
predict the liquidation outcome, overall they perform favorably relative to random
criteria. The statistical significance of these results is rigorously analyzed and confirmed
through a resampling procedure, yielding estimated sampling distributions of the
classification accuracy statistics, confirming these observations.
2
Introduction
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
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
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 pre-packaged 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.

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% r-squared and classification accuracy of 5081%).

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.
4

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 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
5
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.
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 SarbanesOxley 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.
6
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 pre-filing 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 auctionlike 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.
While, Kahl (2002) finds that correctly separating efficient firms from inefficient
firms is extremely difficult and the continuation of inefficient firms is necessary in
7
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.
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).
8
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 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.
9
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).
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) and non-linear
models (multi-perceptron neural networks-MNN and local regression modelsLOESS). 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%
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.
10
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.
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:

exp βTr Xi +  ri
Pr(Yi = r | Xi ) = F  β 2 ,.., β R , Xi  =
 exp 
R
1+
βTj Xi

+  ji

i = 1,..N;r = 2,.., R
(1)
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

i = 1,..N
(2)
j=2
Where Pr(.) denotes probability, F(.) is a cumulative distribution function,
T
βr  βr1 ,..,βr k  is a vector of regression coefficients for the rth resolution type, and
Xi   Xi1 ,..,Xik  is a vector of explanatory variables for the ith observation.
T
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:
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.
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 


11
 Pr(Yi = r | Xi )  T
log 
  β r Xi +  ri
 Pr(Yi =1| Xi ) 
i = 1,..N;r = 2,..,R
(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)
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 )
(5)
i=1 r=1
The second model that we implement in the linear qualitative dependent
variable class is multiple discriminant analysis (MDA). In the binary dependent
variable case, MDA reduces to ordinary least squares regression of the indicator
dependent variable on the explanatory variables:


Pr(Yi  1| Xi )  F β T Xi  β T Xi  ε i
(6)
As discussed in Maddala (1983), model (3) should be viewed as only
approximate, in that the normality assumption on the error term εi is violated. This
is included primarily to benchmark the results of the more complex models, and
since it has been used extensively in the earlier literature. Finally, 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


(7)
Where φ  x   1  exp  x   is taken to be the logistic function, φ 0 . is the
1
activation function 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.
9
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).
12
Measuring model performance in this context is the analysis of classification
accuracy, which centers upon the choice of a cutoff probability for optimal
classifying an observation. We follow the approach of choosing a cutoff point
that minimizes some measure of misclassification (Altman, 1968), both within and
out-of-sample.10 In the formulation of the first objective function considered, we
minimize an expected cost of misclassification (ECM) function (Frydman et al,
1985):
ECM 
K
P C
r
q|r
r 1
n r c 
Nr
(8)
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). 11
Therefore, for K = 2 , Cr|l = 3 and Cl|r = 1 (5) becomes:
ECM 0  Pr
nr c
Nr
 3Pl
nl c
(9)
Nl
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).12 Second, we assume that the relative costs of
misclassification, as well as the likelihoods, between liquidation and
reorganization are equal (Cq|r = 1 and Pr = 1/2 for all r ). This gives rise to the
simplified criterion of minimizing the total proportion of resolutions misclassified:
UMM =
nr c
Nr
+
nl c
Nl
(10)
The Lachenbruch (1967) “U-technique” can be thought of as a hybrid of in- and out-ofsample 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 insample prediction, in which each observation is classified with the models as built on the
full sample (Barniv et al, 2003).
11
This is based upon analysis of cumulative abnormal returns (CARs) for equity prices of
defaulted firms through the resolution period.
12
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).
10
13
Where UMM denotes un-weighted minimization of misclassification. The choice
of (5) may be justified by the context under which this study was initially
commissioned – from a risk management perspective, it can be argued that it is
best to agnostic about the relative costs of misclassification, as opposed to
distressed debt investment context. Finally, we considered a criterion that
minimizes the distance between the proportions correctly classified and the long
run historical averages, giving rise to the deviation from historical average (DHA)
criterion:
 n c
  n c

DHA  1  r
 Pr   1  l
 Pl 
Nr
Nl

 

2
2
(11)
Where 1 – ni(c)/Ni and Pi are the proportions correctly classified and prior
probabilities, respectively, for resolution types i = liquidation, reorganization.
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*  argmin  c | Pr , Pl , N r , N l , βˆ Θ
c

  ECM, UMM, DHA
(12)
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 sub-sample, 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 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 theory13 (Efron,
1979; Efron et al, 1986; and Davison et al, 1997).
In the terminology of classical statistical inference, under the null hypothesis of
liquidation, reorganizations (liquidations) incorrectly (correctly) classified are false
positives (negatives).
13
14
Table 1 - Bankruptcy Outcome by Year
(LossStats™ Database 1995-2003)
Reorganization
Year
1985
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Total
Liquidation
Total
Percent
Percent
Count Total
Count Total
Count
1 100.00%
0
0.00%
1
8
88.89%
1
11.11%
9
20
95.24%
1
4.76%
21
19
79.17%
5
20.83%
24
56
96.55%
2
3.45%
58
60
89.55%
7
10.45%
67
26
96.30%
1
3.70%
27
25
96.15%
1
3.85%
26
18
81.82%
4
18.18%
22
27
84.38%
5
15.63%
32
14
70.00%
6
30.00%
20
11
84.62%
2
15.38%
13
17
73.91%
6
26.09%
23
34
72.34%
13
27.66%
47
42
80.77%
10
19.23%
52
52
85.25%
9
14.75%
61
43
97.73%
1
2.27%
44
12
92.31%
1
7.69%
13
485
86.61%
75
13.39%
560
Table 2 - Frequency of Default Outcome Types by Industry (LossStats™ Database 19952003)
Industry
AEROSPACE/DEFENSE
AIRLINES
AUTOMOTIVE
BUILDING MATERIALS
CHEMICALS
COMPUTERS & ELECTRONICS
CONSTRUCTION
ENTERTAINMENT AND LEISURE
FINANCIAL, INSURANCE, SECURITIES & LEASING
FOOD AND BEVERAGE
GAMING AND HOTELS
HEALTHCARE
MACHINERY
MANUFACTURING
MEDIA
METALS & MINING
OIL & GAS
REAL ESTATE
RETAIL FOOD & DRUG
RETAILING
STEEL
TELECOMMUNICATIONS
TEXTILE & APPAREL MFG.
UTILITIES
OTHER
Grand Total
Percent of
Percent
Total
Total
Cases
Liquidated Industry
Borrowers Borrowers Liquidated in Industry Dummy
5
0.89%
0
0.00%
1
8
1.43%
3
37.50%
18
3.21%
3
16.67%
10
1.79%
1
10.00%
14
2.50%
2
14.29%
38
6.79%
7
18.42%
5
0.89%
0
0.00%
1
17
3.04%
1
5.88%
26
4.64%
7
26.92%
18
3.21%
2
11.11%
22
3.93%
1
4.55%
28
5.00%
3
10.71%
11
1.96%
0
0.00%
1
4
0.71%
0
0.00%
1
24
4.29%
3
12.50%
7
1.25%
0
0.00%
1
33
5.89%
4
12.12%
21
3.75%
0
0.00%
23
4.11%
4
17.39%
73
13.04%
16
21.92%
10
1.79%
0
0.00%
1
46
8.21%
6
13.04%
29
5.18%
5
17.24%
12
2.14%
0
0.00%
1
52
9.29%
7
13.46%
560 100.00%
75
13.39%
7
15
Data – The LossStats™ Database and Summary Statistics
The S&P LossStats™ Database is probably 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, 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. 200 borrowers defaulting from 1985-2003 are selected, for which
financial statements are available on Compustat at the time of 1st instrument
default.
Table 1 summarizes resolution outcomes by year. Over 18 years, 13.4% (86.6%) of
resolutions are liquidation (reorganization), although there is wide variation
across time (e.g., a range of 0-30% for liquidation percentages). 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 an
increase during the 1998-2000 period, which precedes a downturn in the
economic cycle. Table 2 presents a breakdown of the database by industry
and resolution type within each industry. The data is rather thin at the industry
level to make very precise conclusions. The borrowers are rather evenly spread
out among industries, which supports the presumption that this sample is
representative of the broader universe of large companies having publicly
traded debt. It appears that there are almost no liquidations in industries that we
would expect for this to be the case: Aerospace / Defense, Construction,
Machinery, Manufacturing, Metals & Mining, Steel and Utilities. These form the
basis of the “special” industry indicator, the 7th explanatory variable.
In order to explain resolution of financial distress, 14 variables were chosen, on
the basis of univariate and multivariate analyses. This set is optimal in the sense
of balancing performance across models with theoretical considerations.14 The
dimensions that they capture, the empirical proxies used and hypothesized
relation to the resolution type are listed in Table 2.1. Among the financial
statement variables, those hypothesized to reduce the probability of liquidation
include asset size (log book value of assets), leverage (total book value of debt
to assets), intangibles ration (book value intangibles to assets), cash flow (free
cash flow to total assets) and profitability (profit margin). Liquidity (interest
coverage ratio) is though to have either a positive or negative influence. The
capital structure variables, percent secured debt and number of major creditor
classes at default, are thought to be positively related to the probability of
liquidation. The vintage of debt, measured by the outstanding weighted
average time to maturity, is hypothesized to be negatively related to the
probability of liquidation. The macroeconomic state, as measured by the
14
Other variables considered included sales, free cash flow, working capital, short-term debt, net income as
well as alternative transformations and ratios of these and the chosen variables.
16
1
Table 2.1 - Descriptions and Hypotheses on Key Default Outcome Drivers (LossStats™ Database )
Dimension
Size / Scale
Leverage
Intrinsic Value
Rationale
Larger scale of operations implies a better candidate for rehabilitating
business model and therefore a successful reorganization.
Greater leverage implies lower recovery in liquidation, hence an incentive
to attempt a reorganization. Also, under Chapter 11 if book value is
negative then equity is given a greater say.
A greater proportion of intangible assets makes a defaulted borrower a
more attractive acquisition candidate or makes liquidation more costly
thus lowering the chances of liquidation.
Variable2
Logarithm (base 10) of the book value of
total assets
Leverage ratio (book value of total debt to
the book value total assets)
Cash Flow
Profitability
Might mean better chances of improving business (like size) or
liquidation more costly because of franchise value (like intrinsic value).
Capital Structure
Credit Quality
Vintage
Macroeconomic
Negative
Negative
Ratio of the book value of intangible assets
to the book value of assets
Negative
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 outcome. Alternatively higher lquidity can lower the costs of Interest coverage ratio (EBITDA / Interest
liquidation.
Expense)
Greater cash generating ability indicates better quality of the borrower
and ability to restructure and a lower probability of liquidation.
Alternatively, agency problems are greater (Jensen), but this may not be
operative in financial distress.
Free Cash Flow / Book Value of Assets
Liquidity
Hyporthesized
Relationship to
Liquidation
Likelihood
Either
Negative
Profit margin (Net Income / Sales)
Negative
Percent secured debt at time of default
Number of major creditor classes for
defaulted customer
Positive
Spread at default weighed by principal at
default
Positive
Borrowers that have been around a longer time may have more
franchise value and therfore be better reorganization candidates
Collateral values might be depressed during recessions implying that
claimants are more likely to attempt reorganization. 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.
Time since debt issued (weighed by
outstanding at default)
Negative
Under special legal arrangements liquidation may be a less likely
outcome.
Dummy variable for pre-packaged
bankruptcy type
Dummy variable for filing district (the
Southern District of New York & Delaware)
Dummy variable for industries in which there
are constraints to liquidation
Negative
Greater bargaining power among secured creditors makes liquidation
more likely.
More types of creditors imply greater difficulties in negotiating a
reorganization
Firms with lower 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.
In certain jurisdictions liquidation may be a less likely outcome.
Regulatory / Policy
considerations In certain industries liquidation may be a less likely outcome.
Moody's trailing 12 month speculative grade
default rate.
Either
1 - S&P’s LossStats™ has extensive loss severity data on 2,102 defaulted instruments from 1985-2003 for 560 borrowers having some public debt
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 - 200 borrowers defaulting from 1985-2003 are selected, for which financial statements are available on Compustat at the date of first instrument default
Moody’s trailing 12 month speculative default rate, may have either effect.
Borrowers with lower credit quality prior to default, as measured by the
outstanding weighted spread at debt prior to default, are thought to be better
candidates for liquidation. Prepackaged bankruptcies are believed to be less
likely to result in liquidation. In certain legal jurisdictions, liquidation is less likely.
Finally, there are certain industries in which liquidation would be less frequent.
Alternative variables that capture many or all of these dimensions were
considered in preliminary analyses, based upon previous studies of financial
distress (Atman, 1968; Ohlson, 1980; and Frydman et al, 1985) as well as
bankruptcy resolution (Barniv et al, 2002 and Fisher et al, 2003). Coefficient
estimates and classification accuracies were examined in both univariate and
multivariate regressions (results available upon request). It was determined that
17
Table 3 - Summary and Two-Sample Equality of Mean Statistics: Financial Statement and Capital Structure
1
Variables (LossStats™ Database 1995-2003)
Liquidation
Reorganization
Overall1
Equality of Means Test
Standard
Standard
Standard Wilcoxon
Count Average Deviation Count Average Deviation Count Average Deviation Statistic* P-Value
Asset Size2
2.6386
0.5740
2.6867
0.5792
2.6829
0.5781 0.6200 0.2678
Leverage Ratio3
1.0850
1.6072
1.2264
0.6827
1.1125
0.6281 3.0076 0.0014
Intangibles Ratio4
7.88% 18.56%
18.56% 20.21%
17.17% 19.03% 3.4417 0.0003
Interest Coverage Ratio5
-1.0739
7.2770
-1.6649
7.7459
-1.5888
7.6815 0.5310 0.2979
Free Cash Flow / Assets6
-24.67
58.84
-1.7774
117.06
-4.8453
111.27 1.4064 0.0802
Profit Margin7
-123.08
908.13
-2.7982
40.64
-18.36
328.79 2.5247 0.0060
Classes of Debt8
2.2522
1.0113
2.1429
0.8308
2.2375
0.8571 1.6251 0.0524
Percent Secured9
0.4595
0.3705
0.4156
0.3354
0.4215
0.3403 1.0031 0.0581
Spread10
7.6783
5.0353
6.7658
3.8210
7.5550
4.8957 1.4494 0.0739
Vintage11
905.68
770.10
1078.92
753.67
1055.51
757.48 1.7798 0.0379
Macroeconomic12
0.0624
0.0319
0.0714
0.0310
0.0703
0.0312 2.2306 0.0131
37
163
200
1 - Only available if there are financials at date of 1st instrument default in Compustat (out of 560 total names) and filed for bankruptcy
2 - The logarithm (base 10) of the book value of assets
3 - Book value of total debt to book value total assets
4 - Book value of intangible assets to book value of total assets
5 - EBITDA / Interest Expense where EBITDA = Net Income + Interest Expense + Depreciation / Amortization
6 - Free Cash Flow = Operating Income before Depreciation - Income Taxes - Interest Expense - Common & Preferred Dividends
7 - Net Income / Net Sales
8 - Number of major creditor classes for defaulted customer in LossStats database
9 - Secured debt as a proportion of total debt at default
10 - Spread on debt weighted by amount outstanding at default (in percentage points)
11 - Time since issue on debt weighted by amount outstanding at default (in days)
12 - Moody's trailing 12 month speculative grade default rate
* Non-parametric 2 sample test of equality of population location parameters
this set of variables best balanced the considerations of statistical significance
and theoretical justification, providing for a parsimonious representation of the
set of factors influencing bankruptcy outcome.
Table 3 presents detailed summary statistics and diagnostic tests on the 11
continuous variables, in liquidation and reorganization sub-samples. 37 out of
the 200 or 18.5% of the observations are liquidations, a slightly higher frequency
than the 13.4% in the broader sample. The differences in sample mean
between the liquidation and reorganization subsamples are in line with the
hypotheses across all variables: in the case of liquidations, higher mean
leverage, number of classes of debt, percent secured and spread at default;
while for reorganizations, higher mean Log(Assets), Intangibles/Assets, Free Cash
Flow / Assets, Profit Margin and Vintage. Lower interest coverage ratio or worse
economic state are not contrary to hypotheses. Non-parametric Wilcoxon Rank
Sum tests can reject the hypothesis that the means are equal in all cases except
Log(Assets) and interest coverage ratio. A comparison of the quantiles (not
shown) characterizing these distributions for liquidation vs. reorganization support
these conclusions, showing the distributions shifted in the directions predicted by
our hypotheses, with the differences most pronounced for EBITDA and
Intangibles/Assets. Univariate logistic regressions (not reported) confirm these
findings, with all signs in line with theory and estimated slope coefficients
significant.
18
Table 4 - Ordered Logistic Regression of Liquidation Indicator
on Financial Statement, Capital Structure and Industry
1
Variables (LossStats™ Database 1995-2003)
Variables
Intercept
2
Asset Size
3
Leverage Ratio
4
Intangibles Ratio
5
Interest Coverage Ratio
6
Free Cash Flow / Assets
7
Profit Margin
8
Classes of Debt
9
Percent Secured
10
Spread
11
Vintage
12
Macroeconomic
13
Prepack
14
Filing District
15
Industry
Goodness-of-Fit Statistics
Standard
Error
Estimate
-0.3596
-0.5773
-1.6995
-3.6429
0.0829
-0.0076
-0.0012
0.0004
1.3893
0.3082
-0.9876
2.2948
-0.5031
0.3040
-0.0303
Log-
T - Statistic P-Value
1.5407
0.4834
0.8550
1.7498
0.0413
0.0050
0.0088
0.2758
0.7324
0.1412
1.0480
7.2752
0.3482
0.2266
0.3748
Residual
16
17
-0.2334
0.8157
-1.1942
0.2339
-1.9877
0.0483
-2.0819
0.0387
2.0069
0.0462
-1.5283
0.1281
-0.1355
0.8924
0.0014
0.9988
1.8967
0.0594
2.1829
0.0303
-0.9423
0.3472
0.3154
0.7528
-1.4448
0.1502
1.3417
0.1813
-0.0808
0.9357
McFadden
Pseudo R- Likelihood
18
19
Liklihood
Deviance Squared
Ratio
-77.9723 155.9446
0.1859 35.6119
1 - 200 observations (out of 560 total names in database) for which complete
financial statement information is available at 1st instrument non-accrual date
16 - The null deviance in a model with only an intercept
17 - Minus 2 times the log-likelihood (residual sum of squares in a linear
model)
18
- Generalization of the r-squared concept equal to qualitative dependent variable
settings: r^2 = 1 - (residual deviance) / (null deviance) where residual deviance =
normalized total variation in predicted probabilities from liquidation indicators and null
deviance = residual deviance in model with only an intercept as an explanatory
variable
19 - Test of change in overall goodness-of-fit in moving from more general to
restricted model: X^2(n) = -2*(logl_1-logl_0) where logl_1 (logl_0) denotes the
2
maximized log-likelihood value of the restricted (more general) model & X (n) a chisquared distribution with n degrees of freedom (= number of restrictions). In this
context logl_0 is the likelihood in a model with only an intercept (or minus 1/2 time the
null deviance).
Estimation Results
In this section we discuss the results of estimating the ordered logistic regression
(OLR), multiple discriminant analysis (MDA) and feed-forward neural network
(FNN) econometric models. Table 4 presents the estimation results for the OLR
model. A stepwise procedure is implemented, which starts with the most general
model, successively drops the least significant coefficient estimates, each time
measuring the significance of the change in the r-squared. We measure model
19
Table 4.1 - Ordered Logistic Regression of Liquidation Indicator on
Financial Statement and Capital Structure Variables - Stepwise
Regression Analysis
(LossStats™ Database 1995-2003)1
Variable Eliminated
McFadden
Pseudo R- Residual LogLikelihood
Squared2 Deviance3 Likelihood Ratio4
P-Value
All (only intercept)
0.0000
191.5565
-95.7783
0.0000
N/A
None (Unrestricted Model)
Classes of Debt
Profit Margin
Industry
Macroeconomic
0.1859
0.1853
0.1841
0.1819
0.1795
155.9446
156.0611
156.2909
156.7124
157.1721
-77.9723
78.0305
78.1455
78.3562
78.5861
35.6119
0.1165
0.2299
0.4214
0.4597
0.0012
0.7329
0.6316
0.5162
0.4977
1 - 200 observations (out of 560 total names in database) for which complete financial statement
information is available at 1st instrument non-accrual date
2 - Generalization of the r-squared concept equal to qualitative dependent variable settings: r^2 =
1 - (residual deviance) / (null deviance) where residual deviance = normalized total variation in
predicted probabilities from liquidation indicators and null deviance = residual deviance in model
with only an intercept as an explanatory variable
3 - Minus 2 times the log-likelihood (residual sum of squares in a linear model)
4 - Test of change in overall goodness-of-fit in moving from more general to restricted model:
X^2(n) = -2*(logl_1-logl_0) where logl_1 (logl_0) denotes the maximized log-likelihood value of
the restricted (more general) model & X2(n) a chi-squared distribution with n degrees of freedom
(= number of restrictions)
in-sample fit with the McFadden Pseudo R-Squared statistic, which is the
analogue to the r-squared of ordinary least squares regression, that is commonly
used in a generalized linear setting (Maddala, 1983). This is a generalization of
the
r-squared concept to qualitative dependent variable settings, defined as 1 –
(residual deviance) / (null deviance), where residual deviance is the normalized
total variation in predicted probabilities from indicator dependent variables,
while the null deviance is the residual deviance in a model with only an intercept
as an explanatory variable. The significance in the change (reduction) in the
pseudo r-squared is measured by the Likelihood Ratio (LR) statistic, defined as
minus twice the change in the log-likelihood from the more to less general
(restricted) model, which under the null-hypothesis that the restrictions are valid
has a chi-squared distribution equal to the number of coefficient set equal to
zero. This is a test of the hypothesis that the restricted set of variables has overall
explanatory power equivalent to the expanded set of variables.
Table 4 contains the estimation results for the OLR model. The regression as a
whole is significant – a likelihood ratio 35.6 (p-value .001 for a chi-squared with 14
degrees of freedom) and an r-squared of 18.5%. All signs are consistent with
hypotheses, except the dummy for filing district. Only 5 out of 14 coefficients are
significant at the 10% level or better. However, a stepwise analysis in Table 4.1
shows that we can drop profit margin, Classes of Debt, Macro and Industry
without harming overall fit (other signs and p-values basically unchanged).
20
Table 5 compares the estimation results for the three classes of models under
consideration, ordered logistic regression (OLR), multiple discriminant analysis
(MDA) and feed-forward neural networks (FNN). A stepwise procedure applied
in the MDA estimation resulted in the same favored model, the restricted model
that retains all variables except profit margin, Classes of Debt, Macro and
Industry.
An FNN architecture of one hidden layer and 2 input units was decided upon
based upon fit to the data, smoothness and stability of convergence. FNN results
in better in-sample fit, classification accuracy and accurate parameter
estimates than OLR, which in turn is better than MDA. Signs of coefficients are
most consistent with theory in OLR and least so in the case of FNN. In-sample
classification accuracy is best in FNN and worst in MDA, but this difference does
not appear material. FNN several orders of magnitude more computationally
intensive, with this comparison less favorable in terms of CPU time (re-running to
checking stability of convergence). Judging from the signs on the weights, the
FNN results reject non-linearities / non-monotonicities.
21
1
2
Table 6 - Comparison of Classification Accuracy: Ordered Logistic Regression , Multiple Discriminant Analysis and
3
Feedforward Neural Network Models (LossStats™ Database 1995-2003)
Minimizing
(Optimal)
Cutoff
Percentage8
Model Classification Criterion
OLR1
Expected Cost of
Misclassification (ECM)4
Unweighted Minimization of
Misclassification (UMM)5
Deviation from Historical
Average (DHA)6
MDA2
Expected Cost of
Misclassification (ECM)
Unweighted Minimization of
Misclassification (UMM)
Deviation from Historical
Average (DHA)
FNN3
Expected Cost of
Misclassification (ECM)
Unweighted Minimization of
Misclassification (UMM)
Deviation from Historical
Average (DHA)
Full Sample7
Sub-Sample7
Holdout Sample
Full Sample
Sub-Sample
Holdout Sample
Full Sample
Sub-Sample
Holdout Sample
Full Sample
Sub-Sample
Holdout Sample
Full Sample
Sub-Sample
Holdout Sample
Full Sample
Sub-Sample
Holdout Sample
Full Sample
Sub-Sample
Holdout Sample
Full Sample
Sub-Sample
Holdout Sample
Full Sample
Sub-Sample
Holdout Sample
0.2770
0.4390
0.1980
0.2040
0.3080
0.3060
0.2590
0.3930
0.1500
0.2100
0.2770
0.3130
0.2500
0.2420
0.2030
0.1840
0.2500
0.2420
Minimized
Value of
Criterion
0.3319
0.3618
0.4556
0.6955
0.5645
1.3097
0.0790
0.0672
0.1383
0.3489
0.3619
0.4020
0.7091
0.5993
0.9921
0.0833
0.0821
0.1774
0.4020
0.4020
0.4020
0.6864
0.8112
0.9688
0.1895
0.1895
0.1895
Optimal
Proportion of
Liquidations
Correctly
Classified
0.3409
0.5909
0.0000
0.5909
0.8000
0.0000
0.1591
0.2000
0.0000
0.3182
0.8864
0.0000
0.8864
0.8400
0.1053
0.1591
0.2000
0.0000
0.0000
0.7045
0.0000
0.7055
0.6000
0.4737
0.0000
0.0000
0.0000
Optimal
Proportionof
Reorganizations
Correctly
Classified
0.9227
0.7136
0.9381
0.7136
0.6355
0.6903
0.9409
0.8785
0.8319
0.9136
0.4045
1.0000
0.4045
0.5607
0.9735
0.9455
0.9252
0.9823
1.0000
0.6091
1.0000
0.6091
0.5888
0.5575
1.0000
1.0000
1.0000
Optimal
Proportion
Overall
Correctly
Classified
0.8258
0.6904
0.8030
0.6932
0.6667
0.5909
0.8106
0.7500
0.7121
0.8144
0.4958
0.8561
0.4848
0.6136
0.9027
0.8144
0.7879
0.8409
0.8333
0.6272
0.8561
0.6250
0.5909
0.5455
0.8333
0.8106
0.8561
4 - ECM = 3PLLI(c) + PRRI(c) where PL / PR = 0.134 / 0.866 are the prior probabilities (historical means) of liquidation / reorganization, L I(c) / RI(c) =
proportions of liquidations / reorganizations misclassified as a function of the cutoff c; EMC measures of the expected cost of misclassification
5 - UMM = LI(c) + RI(c) where LI(c) / RI(c) = proportion of liquidations / reorganizations misclassified as a function of the cutoff c; UMC measures of total
classification accuracy, unweighted by prior probabilities or relative costs
6 - DHA = ([%LC(c) - PL]^2 + [%RC(c) - PR]^2)^.5 where PL / PR = 0.134 / 0.866 are the prior probabilities (historical means) of liquidation / reorganization;
%LC(c) / %RC(c) are the proportions of liquidations / reorganizations correctly classified as a function of the cutoff c; DHAC is the deviation in prediction
accuracies from the historical frequencies
7 - The 264 observations are arbitrarily partitioned such that the 1st 132 in the database form the estimation sample and the remaining 132 form the
holdout sample. The cutoff used in the holdout sample is the optimal cutoff determined in the estimation sub-sample.
8 - The classification cutoff value which results in the lowest criterion (EMC, UMC or DHAC); this value is such that if predicted probability is greater (less
than), classify as liquidation (reorganization)
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 the significance of intrinsic value and asset size,
respectively. However, we are in line with Lenn and Poulson (1989), but at
variance with Jensen (1991), regarding cash flow. Finally, we inconsistent on
profitability, but consistent n overall firm quality, with Kahl (2002); consistent with
Matsunga et al (1991) and Bryan et al (2001) regarding the interest coverage
ratio.
Model Validation Results: Within and Out-of-Sample Classification
Accuracy
Table 6 compares classification accuracy statistics, proportions of each outcome
and overall outcomes correctly classified, across econometric models (OLR,
MDA and NN), as well as across classification criteria (ECM, UMC and DHA).
22
Table 6.1: Proportions Correctly Classified Under Naïve
Randomization Rules - Expected Values and Approximate
Binomial Confidence Bounds
Criterion
Lower
Random
Expected
ECM
Upper
Lower
Random
Expected
UMM
Upper
Lower
Random
Expected
DHA
Upper
Lower
Always
Expected
Reorg
Upper
Liquidation
Reorganization
0.21%
49.32%
4.25%
59.15%
8.28%
68.98%
1.70%
33.39%
6.70%
43.30%
11.70%
53.21%
-0.86%
66.33%
1.80%
75.00%
4.45%
83.66%
0.00%
79.79%
0.00%
86.60%
0.00%
93.41%
Overall
53.76%
63.40%
73.03%
40.00%
50.00%
60.00%
68.35%
76.79%
85.23%
79.79%
86.60%
93.41%
Within sample, for a given model an optimal cutoff is determined under one of
the three classification criteria, observations are classified, and statistics tallied
using the entire sample. The out-of-sample analysis is on a simple split sample
basis: models are estimated and optimal cutoffs determined for a sub-sample,
and then a holdout sample is classified. For simplicity, we randomly split half the
264 observations into a training sub-sample, and then use the remaining half as a
holdout sample. In order to view these results in context, we may compare each
of these criteria to naïve randomization schemes, in which only information
about prior probabilities and relative costs of misclassification from outside the
regression sample are utilized. In the case of the ECM criterion, such a naive
version entails setting the probability of reorganization to approximately 2.15
times that of liquidation, which is equivalent to randomly classifying a resolution
as a liquidation 31.7% of the time and as a reorganization the other 68.3% of the
time. It can be shown that this produces expected correct classification rates of
4.25%, 59.15% and 63.4% for liquidation, reorganization and overall,
respectively.15 For the UMM criterion, we would randomly classify a resolution as
liquidation or reorganization 50% of the time – this would result in expected
correct classification rates of 6.7%, 43.3% and 50.0% for liquidation, reorganization
and overall, respectively. A random scheme that seeks to mimic the DHA
criterion, with no information other than the long run historical averages, classifies
as a liquidation outcome with 13.4% frequency and as a reorganization 86.6% of
the time. The corresponding expected correct classification rates are 1.80%,
75.0% and 76.8% for liquidation, reorganization and overall, respectively. Finally,
This is derived from an odds ratio of (1/3)*(0.866/0.134) = PR/PL, where PR (PL) is the
probability of classifying as a reorganization (liquidation) in any particular case. The term
(1/3) accounts for the fact that it is 3 times more costly to misclassify a liquidation as
compared to a reorganization, and the second term (.866/.134) is the ratio of the prior
probabilities P0(R)/P0(L). Solving this with the constraint PL + PR = 1 yields PL = 0.317 and PR
= 0.683. The expected proportions correctly classified are derived by taking the
expectation of these quantities with respect to prior measure (multiplying these “trial”
probabilities by the prior probabilities): P0(L)*PL = 0.134*0.317 = 0.0425, P0(R)*PR =
0.866*0.683 = 0.5915 and the sum 0.0425 + 0.5915 = 0.6340 for liquidation, reorganization
and overall, respectively. Similar calculations apply to the naïve versions of the UMM and
DHA.
15
23
we may consider a scheme, which always classifies a resolution, types as
reorganization, which will be correct an expected 86.6% of the time. Of course,
if any of these were done repeatedly there would be some variation around the
expected proportions correctly classified in either outcome or overall, so that we
hope that our models exceed these by a substantial margin. Table 6.1 shows the
expected proportions correctly predicted, and approximate binomial
confidence bounds for these, under these naïve randomization rules.
The main observation with respect to the within sample classification accuracy is
that there is wide variation in performance relative to benchmarks across both
models and criteria. The second observation is that the results differ significantly
in the sub-sample, which has a direct bearing on the uneven out-of-sample
performance of the models. The only clear pattern that emerges from the insample analysis is that the OLR model seems to most consistently outperform its
benchmarks across all criteria and outcome types. Also, the UMM criterion
seems to give rise to most consistent results across models. Under the ECM
criterion, It appears to be the case that the models can beat the naïve rule, at
least in-sample: the overall percent correctly classified is 82.6%, 81.4% and 83.3%
in the OLR, MDA and FNN models, respectively, all well in excess of the naïve
random benchmark upper bound of 73.0%. The proportion of reorganizations
correctly classified is also in well in excess of the 70.0% benchmark across all
models: 92.3%, 91.8% and 100% in the OLR, MDA and FNN models, respectively.
This almost also holds for the classification of liquidation under the ECM criterion,
as we see that 2 out of the 3 the models far outperform with respect to the 8.2%
random benchmark, 34.1% and 31.8% in the OLR and MDA models, respectively.
However, the FNN model breaks down, classifying none of the liquidations
correctly. Results differ in the sub-sample: the OLR model now classifies a higher
proportion of liquidations (59.1%) and lower proportion of reorganization (71.4%).
While these beat the 69.0% and 8.3% upper bounds on the benchmarks for
reorganization and liquidation, respectively, the overall proportion classified is
borderline (69.04% vs. a 73.0% benchmark). The change in MDA model results in
the sub-sample is similar: 88.6%, 10.0% and 48.5% of liquidations, reorganization
and overall correctly classified, with the latter two failing to exceed upper
bounds on benchmarks. The change in FNN in the sub-sample is qualitatively
similar to the case of the MDA model under the ECM criterion.
The in-sample comparisons differ slightly under the UMM criterion. In-sample, for
both the broader and sub-samples, the OLR model exceeds upper bounds on
benchmarks for both resolutions as well as overall. The MDA does this well for the
sub-sample, but in the full sample fails for reorganizations and overall. The FNN
model beats benchmarks for the individual resolutions under UMM, but fails to do
so overall, for both full and sub-samples. Under the UMM criterion, the OLR results
differ qualitatively in the sub-sample in that a higher (lower) proportion of
liquidations (reorganization) are classified correctly, while the broader and subsample results are close for both MDA and FNN models. Under the DHA
criterion, the in-sample results tell yet anther story. For both the OLR and the
MDA models, while the proportions correctly classified of individual outcomes
comfortably exceed upper bounds on random benchmarks, the overall
prediction rates fall slightly short of this, in both the full sample and in the sub-
24
1
Table 7 - Out-Of-Sample Bootstrap Classification Accuracy Analysis: Ordered Logistic Regression,
Multiple Discriminant Analysis and Feedforward Neural Network Models (LossStats™ Database 19952
2003)
Overall
Reorganization
Liquidation
Distributional Statistics on
Resampled Percent Correctly
Classified
Mean
Standard Deviation
5th Percentile
25th Percentile
Median
75th Perecentile
95th Perecentile
Skewness
Kurtosis
Kolmogorov-Smirnov Test6
Mean
Standard Deviation
5th Percentile
25th Percentile
Median
75th Perecentile
95th Perecentile
Skewness
Kurtosis
Kolmogorov-Smirnov Test
Mean
Standard Deviation
5th Percentile
25th Percentile
Median
75th Perecentile
95th Perecentile
Skewness
Kurtosis
Kolmogorov-Smirnov Test
OLR
3
ECM
0.1689
0.1035
0.0158
0.0909
0.1647
0.2314
0.3489
0.3759
-0.4609
MDA
4
5
UMM
DHA
0.1880
0.0169
0.1605
0.0339
0.0000
0.0000
0.0426
0.0000
0.1613
0.0000
0.3199
0.0252
0.4538
0.0833
0.5927
2.8364
-0.4067 10.1977
ECM
0.0162
0.0419
0.0000
0.0000
0.0000
0.0000
0.1002
4.0724
20.4490
UMM
0.4873
0.3484
0.0000
0.1371
0.5756
0.7968
0.9493
-0.1043
-1.5497
FNN
DHA
0.1384
0.0937
0.0000
0.0811
0.1299
0.1860
0.3186
0.8029
0.4538
ECM
0.3648
0.1373
0.0588
0.3017
0.3821
0.4377
0.5871
-0.4598
0.4616
UMM
0.6365
0.3988
0.0000
0.3333
0.7249
1.0000
1.0000
-0.5085
-1.3310
DHA
0.1483
0.1905
0.0000
0.0000
0.0000
0.3158
0.4802
0.8841
-0.6410
0.0663 0.1206*** 0.3912*** 0.4105*** 0.1340*** 0.1047*** 0.0914** 0.2989*** 0.3119***
0.8266
0.8171
0.9833
0.9844
0.5113
0.8667
0.6418
0.3603
0.8408
0.0974
0.1467
0.0225
0.0368
0.3432
0.0780
0.1161
0.3927
0.1923
0.6749
0.5275
0.9304
0.9296
0.0641
0.7415
0.4950
0.0000
0.5063
0.7608
0.7210
0.9732
0.9896
0.1667
0.8308
0.5817
0.0000
0.6492
0.8256
0.8411
0.9934
1.0000
0.4886
0.8703
0.6271
0.3298
1.0000
0.9025
0.9481
1.0000
1.0000
0.8438
0.9086
0.6748
0.6093
1.0000
0.9869
1.0000
1.0000
1.0000
1.0000
0.9872
0.9487
1.0000
1.0000
-0.0526 -0.5511 -1.5914 -3.6082
0.1140 -1.4138
1.1397
0.5160 -0.6361
-0.7870 -0.5590
1.8307 14.0779 -1.5358
6.2489
2.2392 -1.2644 -1.2698
0.0554 0.1061*** 0.2291*** 0.3359*** 0.1358*** 0.0935** 0.2989*** 0.3005*** 0.3261***
0.7196
0.7163
0.8375
0.8253
0.5070
0.7469
0.5968
0.4022
0.7314
0.0694
0.1027
0.0374
0.0298
0.2302
0.0576
0.0800
0.2699
0.1337
0.6021
0.5152
0.7763
0.7839
0.2044
0.6627
0.4924
0.1169
0.5076
0.6752
0.6506
0.8125
0.8068
0.2727
0.7159
0.5521
0.1515
0.6061
0.7273
0.7273
0.8428
0.8295
0.4943
0.7538
0.5890
0.3788
0.7841
0.7699
0.7936
0.8674
0.8447
0.7169
0.7841
0.6222
0.5814
0.8485
0.8261
0.8674
0.8902
0.8674
0.8373
0.8223
0.7807
0.8561
0.8750
-0.2334 -0.4239 -0.4318 -1.1324
0.1014 -1.6180
1.0435
0.4767 -0.4905
-0.2053 -0.4981 -0.0888
2.5422 -1.4989
7.1952
2.1524 -1.2466 -1.2717
0.0772
0.0655
0.0766 0.0966** 0.1440*** 0.0855* 0.3119*** 0.2105*** 0.1740***
1 - In each run, 2 independent random samples with replacement are made from the dataset. The model is built in one of these and tested on the other. This
is repeated 1000 times and statistics on the percents correctly classified are noted. The optimal classification cutoff value, such that if the predicted probability
is greater (less than) classify as liquidation (reorganization), is determined in the training sample to achieve the lowest criterion (ECM, UMM, or DHA)
2 - 264 observations (out of 560 total names in database) for which financial statement information is available at the date of 1st instrument default date
3 - Expected Cost of Misclassification Criterion = P(L)XC LIX%LI(c) + P(R)XCRIX%RI(c) where P(L) = 0.134 / P(R) = 0.866 are the respective prior probabilities
(historical means) of liquidation / reorganization (based upon 560 names in LossStats database); %LI(c) / %RI(c) are the proportions of liquidations /
reorganizations incorrectly classified as a function of the cutoff c; C LI / CRI are the relative costs of incorrectly classifying liquidations / reorganizations; ECM is
the expected cost of misclassification
4 - Unweighted Minimization of Misclassification Criterion = Proportion of Liquidations Misclassified + Proportion of Liquidations Misclassified; measure of total
classification accuracy, unweighted by prior probabilities or relative costs
5 - Deviation from Historical Average Criterion = ([%LC(c) - P(L)]^2 + [%RC(c) - P(R)]^2)^.5 where P(L) = 0.134 / P(R) = 0.866 are the respective prior
probabilities (historical means) of liquidation / reorganization (based upon 560 names in LossStats database); %LC(c) / %RC(c) are the proportions of
liquidations / reorganizations correctly classified as a function of the cutoff c; DHA is the expected deviation in prediction accuracies from the historical
frequencies
6 - Test of null-hypothesis of normality. ***,** and * indicates statistical significance (normality is rejected) at the 10%, 5% and 1% levels, respectively
sample. On the other hand, the FNN model breaks down, failing to correctly
classify a single liquidation correctly but correctly classifying all of the
reorganizations, while falling short of beating the benchmark in overall
classification accuracy, in both full and sub-samples.
The main conclusion that falls out of the analysis of out-of-sample performance is
the inability of models to correctly classify liquidation outcomes, across all
classification criteria. This highlights the inherent difficulty faced in trying to
25
predict a relatively uncommon event in a finite sample. Under the ECM and
DHA criteria, all models fail to predict a single liquidation correctly out-of sample.
Trivially, the models can closely match or beat the upper bounds on the
benchmarks for classifying reorganization (the OLR model under DHA is
borderline at 83.2%). For overall classification out-of-sample, all models beat
benchmark upper limits under ECM, while under DHA the OLR model fails to do
so (71.2%) and the other 2 are borderline (84.1% and 85.6% for MDA and FNN,
respectively). The only apparent exception to the inability to classify liquidations
is under the UMM criterion: the MDA and FNN models perform well in comparison
with benchmarks, with prediction rates of 10.5% and 47.4%, respectively, as
compared with random UMM upper bounds of 11.7%. The MDA model far
outperforms in classifying reorganizations and overall, 97.4% and 90.3%, while the
FNN model exceeds the upper bound for reorganizations at a rate of 55.8%, as
compared with UMM upper bounds of 53.2% and 60.0%, for reorganizations and
overall, respectively. 16
Table 7 presents distributional statistics, sample moments and quantiles, for the
bootstrapped proportions correctly predicted for each model and classification
criterion. These results offer evidence that the econometric models significantly
exceed the performance of the naïve benchmarks across the respective
classification criteria. However, as with the split sample classification accuracy
exercise, we see that there is quite a bit of variation in the degree of
outperformance, across models and classification criteria. Across most
classification criteria, for overall and classification of reorganization, the OLR
models most consistently outperforms the naïve random benchmarks, in the
sense that upper bounds on these correspond to low sample quantiles.
However, results are mixed for the classification of liquidation outcomes. In
overall classification accuracy, the OLR model outperforms the random
benchmarks by the largest margin under the UMM criterion, and the MDA model
does so under the ECM criterion, while the FNN model performs worse than the
other two models across all criteria. The upper bound on the approximate 95%
confidence interval for the naïve version of the UMM criterion is 60.0%, and this is
at the 18th percentile of the resampled distribution of overall percent correctly
predicted, for the OLR model under UMM (i.e., in 82% of the resampled
observations, OLR beat the upper bound on this benchmark). For the ECM and
DHA criteria, the respective naïve criteria upper bounds are 73.0% and 85.2%,
which are close to the medians of the resampled distributions of 72.7% and 84.3%
(i.e., in 50% of resamples the OLR model exceeded the upper 95th confidence
bounds for the random versions of these criteria). In the MDA model, under the
ECM criterion, 75% of the bootstrapped percents overall correctly predicted
exceed the 73% upper bound on the naïve version of ECM. However, MDA does
not do as well as OLR under the UMM or DHA criteria, the benchmark upper
bounds corresponding to the 60th and 97th percentiles of the resampled
distributions of this statistic. Finally, in overall classification accuracy the
Note that the ECM tends to produce a higher optimal cutoff, as it is heavily influenced
by the greater likelihood of the reorganization outcome, while UMM tends to produce a
lower cutoff, while the DHA is somewhere in between.
16
26
bootstrap experiment reveals the FNN model to be universally inferior to the
other two: the random benchmark upper bounds correspond to the 88th, 62nd
and 75th percentiles of the resampled distributions under ECM, UMM and DHA,
respectively. However, none of the models are capable of beating the 93.4%
upper bound on the rule that always classifies resolution types as reorganization,
although it can be argued that this may be an inappropriate classification
criterion for which to measure model performance. Figures 1 and 2 compare
bootstrapped distributions of percents overall correctly classified, for different
models under the ECM criterion, and for the OLR model under different
classification criteria, respectively.
Turning to the classification of reorganizations, we see that the OLR model
generally performs best, while the FNN model globally performs the worst, across
all classification criteria. The 95% upper confidence limits on the random
schemes – 69.0%, 53.2% and 83.7% for ECM, UMM and DHA, respectively –
correspond to approximately the 6th, 5th and 4th percentiles of the resampled
distributions of reorganizations correctly classified by the OLR model. While the
MDA model performs slightly better under the ECM criterion, as the 69.0% upper
bound is approximately the 4th percentile of the resampled distribution, it
performs worse under the UMM and DHA criteria, in that the upper bounds on
the random versions of these correspond to approximately the 50th and 25th
percentiles, respectively. The results are least impressive for the FNN model, as
the random upper bounds on the ECM, UMM and DHA criteria correspond to
sample quantiles of approximately the 75th, 69th and 39th percentiles, far worse
than either the OLR or MDA model. Finally, we observe that the results for the
classification of liquidations are rather different from those for either the
classification of reorganizations or overall, and the preferred models vary across
classification criteria. Now the OLR model is not the best across classification
criteria. In the case of ECM and UMM, the OLR and FNN models are now
comparable in performance, with FNN slightly better - the respective random
classification upper bounds of 8.3% and 11.7% correspond to approximately the
23rd (18th) and 35th (21st) percentiles for OLR (FNN). The MDA model performs
most poorly under the ECM criterion, as the 8.3% cutoff is approximately the 91st
percentile of the resampled proportion of liquidations correctly classified.
However, MDA performs the best under the UMM and DHA criteria, as the upper
bounds of 11.7% and 4.5% are approximately the 8th and 14th percentiles of the
resampled distributions, respectively. Figures 3 and 4 compare bootstrapped
distributions of proportions of liquidations correctly classified, for different models
under the ECM criterion, as well as for the OLR model under different
classification criteria, respectively.
Table 8 presents pairwise Wilcoxon statistics, which non-parametrically test the
equality of distributions, an alternative way to look at the differences in the
bootstrapped classification accuracy statistics. The results support the
observations that different models give rise to different distributions of
classification accuracy statistics across different classification accuracy criteria,
and are generally in line with the comparisons to naïve benchmarks made
above. The statistically significant and negative Wilcoxon statistic of -10.47 and -
27
Figure 1 – Comparison of Overall Proportions Correctly Classified for the OLR,
MDA and FNN Models under the ECM Classification Criterion
0 1 2 3 4 5 6
% Overall Correctly Predicted Out-Of-Sample Bootstrap-Logistic(ECM Criterion)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Ov erall.v ec .glm.1
0
5
10
15
% Overall Correctly Predicted Out-Of-Sample Bootstrap-Discriminant(ECM Criterion)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Ov erall.v ec .LM.1
0 1 2 3 4 5 6
% Overall Correctly Predicted Out-Of-Sample Bootstrap-Neural Net(ECM Criterion)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Ov erall.v ec .N N .1
Figure 2 – Comparison of Overall Proportions Correctly Classified in the OLR
Models under the ECM, UMM and FNN Classification Criteria
0 1 2 3 4 5 6
% Overall Correctly Predicted Out-Of-Sample Bootstrap-Logistic(Expected Cost Misclassification)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Ov erall.v ec .glm.1
0
1
2
3
% Overall Correctly Predicted Out-Of-Sample Bootstrap-Logistic(Minimize Misclassification)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Ov erall.v ec .glm.2
0
2
4
6
8 10
% Overall Correctly Predicted Out-Of-Sample Bootstrap-Logistic(Historical Calibration)
0.0
0.2
0.4
0.6
Perc .C orr.Ov erall.v ec .glm.3
0.8
1.0
28
Figure 3 – Comparison of Proportions of Liquidations Correctly Classified for the
OLR, DMA and FNN Models under the ECM Classification Criterion
0
1
2
3
% Liquidation Correctly Predicted Out-Of-Sample Bootstrap-Logistic (ECM Criterion)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Liqu.v ec .glm.1
0
5
10
15
% Liquidation Correctly Predicted Out-Of-Sample Bootstrap-Discriminant (ECM Criterion)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Liqu.v ec .LM.1
0
1
2
3
% Liquidation Correctly Predicted Out-Of-Sample Bootstrap-Neural Net (ECM Criterion)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Liqu.v ec .N N .1
Figure 4 – Comparison of Proportions of Liquidations Correctly Classified in the
OLR Models under the ECM, UMM and FNN Classification Criteria
0
1
2
3
% Liquidation Correctly Predicted Out-Of-Sample Bootstrap-Logistic(Expected Cost Misclassification)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Liqu.v ec .glm.1
0
1
2
3
% Liquidation Correctly Predicted Out-Of-Sample Bootstrap-Logistic(Minimize Misclassification)
0.0
0.2
0.4
0.6
0.8
1.0
Perc .C orr.Liqu.v ec .glm.2
10
20
30
% Liquidation Correctly Predicted Out-Of-Sample Bootstrap-Logistic(Historical Calibration)
0
29
0.0
0.2
0.4
0.6
Perc .C orr.Liqu.v ec .glm.3
0.8
1.0
10.89 confirms that the under the ECM criterion, the distribution of proportions
correctly classified overall and of reorganization outcomes is shifted to the right
in the MDA model, as compared to the OLR model (i.e., better performance of
the MDA model). However, in considering only the liquidation outcome, the
distribution is shifted to the left in MDA relative to the OLR model (i.e., better
performance of the OLR model). However, under both the UMM and DHA
criteria the test results are reversed, with the MDA model performing worse in
classifying both overall and the reorganization outcome (statistically significant
Wilcoxon statistics of 6.11 and 10.43 under UMM and DHA for overall,
respectively), and better in classifying liquidation outcomes (statistically
significant Wilcoxon statistics of -5.62 and -10.44 under UMM and DHA for
liquidation, respectively). These tests present evidence that the FNN model
generally performs worse in classification accuracy overall and of reorganization
outcomes, but better in classifying liquidation outcomes, relative to OLR or MDA:
under ECM and DHA this is true across the board; while under UMM this is true
only in the comparison of FNN and OLR, as the Wilcox statistics are not
statistically significant in the comparison to the MDA model under this criterion.
The results for the comparison of the FNN model to the other two are slightly
different from the analysis of quantiles relative to random schemes, as the MDA
model did better than either FNN or OLR under the UMM and DHA criteria.
Finally, the comparison of the distributions of classification accuracy statistics
given different models, given in the bottom panel of Table 8, are largely
consistent with the results of the top panel as well as the analysis of quantiles in
Table 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 averageDHA), 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.
30
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 rsquared 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 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
31
statement (e.g., off-balance 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.
32
Appendix
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
33
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.
34
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