IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 12, NO. 4, JULY 2001 929
Bankruptcy Prediction for Credit Risk Using Neural
Networks: A Survey and New Results
Amir F. Atiya, Senior Member, IEEE
Abstract—The prediction of corporate bankruptcies is an
important and widely studied topic since it can have signifi-
cant impact on bank lending decisions and profitability. This
work presents two contributions. First we review the topic of
bankruptcy prediction, with emphasis on neural-network (NN)
models. Second, we develop an NN bankruptcy prediction model.
Inspired by one of the traditional credit risk models developed
by Merton, we propose novel indicators for the NN system. We
show that the use of these indicators in addition to traditional
financial ratio indicators provides a significant improvement in
the (out-of-sample) prediction accuracy (from 81.46% to 85.5%
for a three-year-ahead forecast).
Index Terms—Asset-based model, bankruptcy prediction, cor-
porate distress, corporate failure prediction, credit risk, default
prediction, financial ratios, financial statement data, multilayer
networks.
I. INTRODUCTION
B
ANKRUPTCY prediction has long been an important and
widely studied topic. The main impact of such research is
in bank lending. Banks need to predict the possibility of default
of a potential counterparty before they extend a loan. This can
lead to sounder lending decisions, and therefore result in sig-
nificant savings. In this study we focus only on the corporate
bankruptcy prediction problem. For the consumer bankruptcy
prediction problem, there is likewise an extensive amount of re-
search, but the reader is referred to [19], [40], and [52] for a
review of this topic.
To get an idea about the potential impact of the bankruptcy
prediction problem, we note that the volume of outstanding debt
to corporations in the United States is about $5 trillion. An
improvement in default prediction accuracy of just a few per-
centage points can lead to savings of tens of billions of dol-
lars. In addition to avoiding potentially troubled obligors, the
research can also benefit in other ways. It can help in estimating
a fair value of the interest rate of a loan (that reflects the cred-
itworthiness of the counterparty). It can help in accurately as-
sessing the credit risk of bank loan portfolios. The credit risk
problem is essentially the computation of the loss level, which
is defined as the level for which there is a probability of 1% that
the loss incurred in the portfolio will exceed that level in a par-
ticular time period. Credit risk has been the subject of much re-
search activity, especially after realizing its practical necessity
after a number of high profile bank failures in Asia. As a re-
Manuscript received February 13, 2001; revised March 16, 2001 and March
25, 2001.
The author is with the California Institute of Technology, Pasadena, CA
91125 USA (e-mail: amir@caltech.edu).
Publisher Item Identifier S 1045-9227(01)05006-8.
sult, the regulators are acknowledging the need and are urging
the banks to utilize cutting edge technology to assess the credit
risk in their portfolios. Measuring the credit risk accurately also
allows banks to engineer future lending transactions, so as to
achieve targeted return/risk characteristics. The other benefit
of the prediction of bankruptcies is for accounting firms. If an
accounting firm audits a potentially troubled firm, and misses
giving a warning signal (say a “going concern” opinion), then it
faces costly lawsuits.
The traditional approach for banks for credit risk assessment
is to produce an internal rating, which takes into account var-
ious quantitative as well as subjective factors, such as leverage,
earnings, reputation, etc., through a scoring system [48]. The
problem with this approach is of course the subjective aspect
of the prediction, which makes it difficult to make consistent
estimates. Some banks, especially smaller ones, use the ratings
issued by the standard credit rating agencies, such as Moody’s
and Standard & Poor’s. The problem with these ratings is that
they tend to be reactive rather than predictive (for the agencies
to change a rating of a debt, they usually wait until they have
a considerably high confidence/evidence to support their deci-
sion). There is a need, therefore, to develop fairly accurate quan-
titative prediction models that can serve as very early warning
signals for counterparty defaults.
There are two main approaches to loan default/bankruptcy
prediction. The first approach, the structural approach, is based
on modeling the underlying dynamics of interest rates and firm
characteristics and deriving the default probability based on
these dynamics. The second approach is the empirical or the
statistical approach. Instead of modeling the relationship of
default with the characteristics of a firm, this relationship is
learned from the data. The focus of this article is on the empir-
ical approach, especially the use of NNs. In the next section
we give a review on this approach. To give a flavor about the
structural approach, it is also very briefly reviewed in the next
section. Section III presents some results of simulations that
we have performed, where we introduce novel inputs that lead
to considerable improvement in prediction accuracy. Section
IV is the summary and conclusion of this paper.
II. A R
EVIEW OF BANKRUPTCY PREDICTION MODELS
A. Early Empirical Approaches
The pioneers of the empirical approach are Beaver [7],
Altman [2], and Ohlson [34]. Beaver was one of the first re-
searchers to study the prediction of bankruptcy using financial
statement data. However, his analysis is very simple in that
it is based on studying one financial ratio at a time and on
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930 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 12, NO. 4, JULY 2001
developing a cutoff threshold for each ratio. The approaches by
Altman and Ohlson are essentially linear models that classify
between healthy/bankrupt firms using financial ratios as inputs.
Altman uses the classical multivariate discriminant analysis
technique (MDA). It is based on applying the Bayes classifi-
cation procedure, under the assumption that the two classes
have Gaussian distributions with equal covariance matrices.
The covariance matrix and the class means are estimated from
the training set. Altman used the following financial ratios as
inputs:
1) working capital/total assets;
2) retained earnings/total assets;
3) earnings before interest and taxes/total assets;
4) market capitalization/total debt;
5) sales/total assets.
These particular financial ratios have been widely used as in-
puts, even for NNs and other nonlinear models. They are de-
scribed in more detail in the next subsection.
Ohlson introduced the logistic regression approach (LR) to
the bankruptcy prediction problem. It is essentially a linear
model with a sigmoid function
at the
output (it is thus similar to a single-neuron network). Because
the output is in between 0 and 1, the model has a nice proba-
bilistic interpretation. Ohlson used a novel set of financial ratios
as inputs. Both the MDA model and the LR model have been
widely used in practice and in many academic studies. They
have been standard benchmarks for the loan default prediction
problem.
B. Neural-Network (NN) Approaches
Research studies on using NNs for bankruptcy prediction
started in 1990, and are still active now. There are a number of
reasons why a nonlinear approach would be superior to a linear
approach. It can be argued that there are saturation effects in
the relationships between the financial ratios and the prediction
of default. For example, if the earnings/total assets changes
say by an amount of 0.2, from
0.1 to 0.1, it would have a far
larger effect (on the prediction of default) than it would if that
ratio changes from say 1.0 to 1.2. One can also argue that there
are multiplicative factors as well. For example, the potential for
default for a firm with negative cash flow gets more amplified if
it has large liabilities. The reason is that highly leveraged firms
have a harder time borrowing money to finance their deficits.
As will be seen from the review below, NNs have generally
outperformed the other existing methods. Currently, several
of the major commercial loan default prediction products are
based on NNs. For example, Moody’s Public Firm Risk Model
[32] is based on NNs as the main technology. Many banks have
also developed and are using proprietary NN default prediction
models.
The following is a review of the NN bankruptcy prediction
studies. There has been also a number of other review papers.
For example, Vellido et al. [52] survey the use of NNs in busi-
ness applications. This survey includes a section on bankruptcy
prediction. Also, the survey of Wong et al. [56] on NNs in busi-
ness applications includes some references on the bankruptcy
prediction problem. Dimitras et al. [15] provide a survey on
the classical empirical approaches. Zhang et al. [58] include in
their paper a nice review of existing work on NN bankruptcy
prediction. The majority of the NN approaches to default pre-
diction use multilayer networks. Since this is the dominant ap-
proach, henceforth when we mention NNs we mean multilayer
networks.
One of the first studies to apply NNs to the bankruptcy pre-
diction problem was the work by Odom and Sharda [33]. Odom
and Sharda used Altman’s financial ratios (described above) as
inputs to the NN, and applied their method, as well as MDA as
a comparison, to a number of bankrupt and solvent US firms,
where the data used for the bankrupt firms are from the last fi-
nancial statement before declaring bankruptcy. They considered
128 firms, and performed severalexperimentswhere they varied
the proportion of bankrupt/healthy firms in the training set. The
NN achieved a Type I correct classificationaccuracyinthe range
of 77.8% to 81.5% (depending on the training setup), and a Type
II accuracy in the range of 78.6% to 85.7%. The corresponding
results for MDA were in the range of 59.3% to 70.4% for Type I
acuracy, and in the range of 78.6% to 85.7% for Type II acuracy.
Let us now discuss why the particular indicators of [33]
(which are the same as Altman’s indicators) have been chosen.
Most other studies use indicators similar in nature, and the
analysis presented will somewhat apply to these studies as well.
A company’s total assets consists of current assets and long
term assets. The total assets gives some indication of the size
of the firm. Therefore it is frequently used as a normalizing
factor (like in indicators 1,2,3,5 of Altman’s indicators). The
current assets can or will typically be turned into money
fairly fast. The firm’s liabilities consists of current liabilities
and long term debt. The current liabilities include short term
loans (less than one year due), accounts payable, taxes due,
etc. The working capital is current assets minus the current
liabilities. It is an indication of the ability of the firm to pay
its short term obligations. If it is too negative, the company
might default on some payments. The firm’s total assets is
financed by a) the total liabilities and b) the shareholders’
equity [therefore the name “balance sheet,” since the total
assets have to exactly equal the sum of the two items in a) and
b)]. The shareholders’ equity consists of the capital raised in
share offerings and the retained earnings. The retained earnings
means the accumulation of the firm’s earnings since the firm’s
inception. The shareholders’ equity is also called the book
value of the firm. Even though it is based on the historical costs
(plus adjustments through depreciation/amortization) of the
firm’s assets and liabilities, rather than market values, it has
been a very useful indicator in assessing the financial health
of a firm. Retained earnings is a related and similarly useful
indicator. The firm’s earnings is also an important indicator.
Highly negative earnings indicate that the firm is losing its
competitiveness, and that geopardizes its survival. Another
related, widely used indicator is the cash flow. It is less prone
than earnings to management manipulation. In addition, it
measures directly the ability of the firm to generate cash to
retire debt. The rationale behind Altman’s fourth indicator is
the following. The firm can issue and sell new shares in the
market to repay its debt. A large market capitalization (relative
to the total debt) indicates a high capacity to perform that.
ATIYA: BANKRUPTCY PREDICTION FOR CREDIT RISK USING NEURAL NETWORKS 931
Finally, the firm’s sales is an indication of the health of its
business. However, this indicator is probably the least effective
among the five Altman indicators, because sales to total assets
can vary a lot from industry to industry.
Tam and Kiang [46], [47] considered the problem of bank
failure prediction. They compared between several methods:
MDA, LR, K-nearest neighbor (KNN), ID3 (a decision tree clas-
sification algorithm), single-layer network, and multilayer net-
work. For the case of one-year-ahead, the multilayer network
was the best, while for the case of two-year-ahead, LR was the
best. When they used a leave-one-out procedure instead of a
hold-out sample, the multilayer network was the clear winner
(for both forecast horizons). KNN and ID3 were almost always
inferior to the other methods.
Salchenberger et al. [41] considered the problem of pre-
dicting thrift failures. They compared NN with LR. The NN
significantly outperformed the LR. For example for 18-months
ahead prediction the LR achieves 83.3–85.4% accuracy (de-
pending on some threshold), whereas the NN achieves 91.7%.
Coats and Fant [12] compared between NN and MDA. They
obtained a classification accuracy in the range of 81.9% to
95.0% for the NN (depending on the horizon: from three-years
ahead to less than a year-ahead), and in the range of 83.7% to
87.9% for the MDA (also depending on the horizon).
Kerling and Poddig [23] compared NN with MDA for a data-
base of French firms for a three-year-ahead forecast. The NN
achieved a prediction accuracy in the range of 85.3–87.7% com-
pared to 85.7% for MDA. Kerling tested several cross-validation
procedures and early-stopping procedures in a follow-through
study [22].
Altman et al. [3] applied NN and MDA to a large database
of 1000 Italian firms for one-year ahead prediction. The com-
parison yielded no decisive winner, though MDA was slightly
better.
Boritz and Kennedy [9] (see also [10]) compared between a
number of techniques, including different NN training proce-
dures, LR and MDA, using the indicators chosen by Altman,
and those chosen by Ohlman. The results of the comparison are
inconclusive.
Fernandez and Olmeda [17] compared NN with MDA, LR,
MARS and C4.5 (two well known methods that are based on the
CART decision tree algorithm) on Spanish banks (no horizon
is specified). The NN obtained 82.4% accuracy compared with
61.8–79.4% for the competing techniques.
Alici [1] used principal component analysis and self-orga-
nizing maps for the input selection phase, together with a skele-
tonization step for the NN. He achieved an accuracy in the range
of 69.5% to 73.7% (dependinding on some parameter variation),
compared with 65.6% for MDA and 66.0% for LR for a data-
base of UK firms (no horizon is mentioned).
Leshno and Spector [27] used a novel NN architectures
containing cross-terms and cosine terms, and achieved pre-
diction accuracy for the two-years-ahead case in the range of
74.2–76.4% (depending on the order of the network), compared
with 72% for the linear perceptron network.
Lee et al. [25] propose hybrid models. Specifically, they
tested combinations of the models MDA, ID3, self-organizing
maps, and NN. They applied their study to the problem of
default prediction of Korean firms.
Back et al. [4] propose the use of genetic algorithms for input
selection, to be used in conjunction with multilayer networks.
They applied their method to data covering the periods one to
three years before the bankruptcy, where it obtains significant
improvement over MDA and LR.
Kiviluoto [24] use self-organizing maps on an extensive data-
base of Finnish firms (horizon is not specified), and show that it
obtains comparable results to MDA and learning vector quanti-
zation (in the range from 81% to 86%). Kaski et al. (this issue
[60]) developed a novel self-organizing map procedure based
on the Fisher metric, and applied it also to a number of Finnish
firms.
Zhang et al. [58] compared between NN and LR, and
employed a five-fold cross-validation procedure, on a sample
of manufacturing firms (horizion is not specified). They used
Altman’s five financial ratios plus the ratio current assets/cur-
rent liabilities as inputs to the NN. The NN significantly
outperformed LR with accuracy of 88.2% versus 78.6%.
Piramuthu et al. [37] developed a technique to construct sym-
bolic features, to be inputed to a multilayer network. They ap-
plied their technique to a collection of Belgian firms (no fore-
cast horizon is mentioned), where they obtained an accuracy of
82.9% versus 76.1% for the nontransformed input case. They
applied it also to a problem of one- and two-year ahead default
prediction for US banks. They get superior results, and signif-
icantly outperform the nontransformed input case. Piramuthu
[36] applies a similar input selection technique in conjunction
with decision tree classifiers.
Martinelli et al. [29] compared between two decision tree al-
gorithms, C4.5 and CN2, and NN on a database of Brazilian
firms. C4.5 outperform the other methods.
Yang et al. [57] used probabilistic NNs (PNNs) [45], which
essentially implement the Bayes classification rule. They
tested it on firms in the oil sector. The results were mixed:
PNN tied with the multilayer networks, but with a particular
preprocessing step MDA was the best.
McKee and Greenstein [30] developed a method based on
decision trees and applied it to a number of US firms for one
year ahead forecast. Their method obtains better results than NN
and MDA for Type II error, but worse results for Type I error.
Fan and Palaniswami [59] propose the use of support
vector machines (SVMs) for predicting bankruptcies among
Australian firms, and compared it with NN, MDA and learning
vector quantization (LVQ). SVM obtained the best results
(70.35%–70.90% accuracy depending on the number of inputs
used), followed by NN (66.11%–68.33%), followed by LVQ
(62.50%–63.33%), followed by MDA (59.79%–63.68%).
These reviewed papers are just a sample of what has been
done on the topic of NN default prediction. There are many
other studies (e.g., [5], [6], [11], [13], [16], [18], [21], [26], [35],
[38], [39], [42], [43], [44], [49], [50], [51], [53]), but for space
considerations they are not reviewed here.
C. A Brief Review of the Structural Approach
One of the earlier and commonly used methods is the asset-
based approach by Merton [31] (developed further by Longstaff
932 IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 12, NO. 4, JULY 2001
and Schwartz [28]). This model views a firm’s equity as an op-
tion on the firm (held by the shareholders) to either repay the
debt of the firm when it is due, or abandon the firm without
paying the obligations. The probability of default can be de-
rived by modeling the market value of the firm as a geometric
Brownian motion. What makes that model successful is its re-
liance on the equity market as an indicator, since it can be ar-
gued that the market capitalization of the firm (together with the
firm’s liabilities) reflect the solvency of the firm. This model
has been successfully developed into a successful commercial
product by KMV Corporation.
Another approach, by Jarrow and Turnbull [20], models de-
fault as a point process, where the time-varying hazard func-
tion for each credit class is estimated from the credit spreads.
The CreditRisk+ product, developed by Credit Suisse Financial
Products, is also based on the same concept of modeling default
as a Poisson process.
Wilson [54], [55] proposed a discrete-time dynamical model,
whereby the default probabilities are a function of macro-eco-
nomic variables. J.P. Morgan’s CreditMetrics product [14] is
based on modeling changes in the credit quality ratings. By
modeling the “rating migrations,” one can obtain an estimate
for the probability of default. Several other models have been
proposed. For a more detailed review of structural credit risk
models refer to Crouhy
et al. [14].
D. Challenges for the NN Prediction Models
In spite of the success of NN models, there are a number of
open issues that should desirably be addressed by the research
community. Even though a prediction of the default event is by
itself very useful, an estimate of the default probabilty is very
desirable. For portfolio credit risk estimation, this is essential
in order to compute the loss level. (As described in the intro-
duction section, the loss level is the level for which there is a
probability of 1% that the loss incurred in the portfolio will ex-
ceed that level in a particular time period.) Also, typically banks
have several prediction systems in place. They make a lending
decision based on the combination of these predictions. Having
a probability of default rather than a (binary) prediction of de-
fault is valuable for them. Even though there are some objective
function measures that achieve that, such as cross-entropy error
function [8], our experience with this objective function has not
been very favorable.
The other open issue is to consider macroeconomic indicators
as inputs to the NN. The prevailing economic conditions (as
well as the current interest rates) can have a significant effect
on the probability of bankruptcy. There are very few studies
that consider these factors in conjunction with NN models. This
should therefore be a recommended study.
III. T
HE DEVELOPED BANKRUPTCY PREDICTION MODEL
In this work we introduce a novel set of indicators that can
be used in addition to the financial ratios and lead to significant
improvement in prediction accuracy. These indicators are ex-
tracted from the stock price of the firm. (We are inspired here by
Merton’s asset-based model, described in Section II-C, which
is based on information extracted from the equity markets.) It
is well known that the equity markets are very-early predictors
of shortfalls (or improvements) in the performance of a firm. A
problem faced by a firm will typically be reflected in the stock
price well before it shows up in its balance sheet and income
statement. As such, indicators obtained from the stock price can
be beneficial especially in long horizon default forecast. Ex-
amples of indicators tested are: volatility, change in volatility,
change in price, absolute price, price-cashflow ratio, etc. We de-
scribe the developed model below.
To test the comparative advantage of stock-price-based indi-
cators, we have developed two systems: one system based on fi-
nancial ratios alone (financial ratio system), and another based
on financial ratios and price-based indicators (financial ratio
and equity-based system). We will not compare here with linear
models such as MDA and LR, because that is not the objective
of the paper, and because there are so many previous studies
that have performed such a comparison (see Section II-C). The
NN is designed to predict default three-years-ahead, so it gives
a fairly long-horizon forecast. Each developed system consists
of two stages: the input selection stage, and the NN application
stage. We have considered a pool of about 120 candidate inputs
(financial statement data, ratios, stock price data, and transfor-
mations of these). Using an initial prescreening procedure based
on individual indicator prediction accuracy and correlation ma-
trix, and then a subsequent cross-validation procedure to narrow
down the choice, we select the best five or six inputs from this
pool of indicators. For the financial ratio system the chosen in-
dicators were:
1) book value/total assets BV/TA;
2) cashflow/total assets CF/TA;
3) rate of change of cashflow per share ROC(CF);
4) gross operating income/total assets GOI/TA;
5) return on assets ROA.
For the financial ratio and equity-based system the chosen indi-
cators are:
1) book value/total assets BV/TA;
2) cashflow/total assets CF/TA;
3) price/cashflow ratio P/CF;
4) rate of change of stock price ROC(P);
5) rate of change of cashflow per share ROC(CF);
6) stock price volatility VOL.
To test the system, we have collected historical data from de-
faultedand from solvent US firms.The defaulted firmdata cover
the period spanning 1 month to 36 months before the bank-
ruptcy event. (median time-to-default is 13 months). Note that
we have selected the solvent firms randomly (from among all
solvent firms), so the choice covers the whole spectrum from
healthy to border-line firms in order to avoid any selection bias.
We have considered 716 solvent firms and 195 defaulted firms.
We have performed the prediction for the defaulted firms at two
or three instants before default. The number of data points then
became 1160 (444 defaulted and 716 solvent). We note that
the size of the data set is quite large compared to the majority
of bankruptcy prediction studies. To our knowledge, only the
work by Altman et al.[3] uses a comparable size data set (1000
firms). The in-sample set consists of 491 data points, while the
ATIYA: BANKRUPTCY PREDICTION FOR CREDIT RISK USING NEURAL NETWORKS 933
TABLE I
R
ESULTS FOR THE NEURAL NETWORK DEFAULT PREDICTION MODEL:FINANCIAL
RATIO MODEL
TABLE II
R
ESULTS FOR THE NEURAL NETWORK
DEFAULT PREDICTION MODEL:FINANCIAL RATIO AND EQUITY-BASED MODEL
out-of-sample set consists of 669 data points. In case of mul-
tiple prediction instants for one firm, the firm’s data are either
all in the in-sample set or all in the out-of-sample set in order
to avoid bias. Note that we maintained a fixed ratio of number
of defaulted data points/number of solvent data points for both
in-sample and out-of-sample set (about 62%). The in-sample
data-set is used for the design of the input selection stage and
the NN design, while the out-of-sample set is reserved for the
final test of the system. Using the repeated random partitioning
procedure for the in-sample set into training set and validation
set, and repeated training and validation for the different parti-
tions, we determined optimal valuesof the different network and
learning parameters and performed the input selection. Based
on this tuning approach we selected a network of size 2 hidden
nodes. Since training a network till death for highly noisy ap-
plications can introduce some overfitting, we have used early
stopping. The best number of iterations is determined with the
help of the validation set to be 100.
Tables I and II show the results for both systems, along with
a break-down according to time till default. For the financial
ratio system we obtained a prediction accuracy of 84.52% for
the in-sample set, and 81.46% for the out-of-sample set. For
the financial ratio and equity-based system we obtained a pre-
diction accuracy of 89.41% for the in-sample set, and 85.50%
for the out-of-sample set. One can see that it outperforms by a
full 4 percentage points the financial ratio system, indicating the
value of indicators extracted from the equity markets. Note also
that its edge gets better for long horizon forecasts. It can clas-
sify significantly better data points that correspond to a large
time before default (for example more than 18 months). An ex-
planation of this observation is that financial statement data tend
to be lagging, since all the figures are reported by its book value.
Also, the stock market is highly predictive. It reflects qualitative
factors such as business conditions and insider information that
trickle through the market.
Table III showsthe correlation matrix for all 8 indicators used.
Of particular interest is the uniformly negative correlation of the
volatility indicator (VOL) with the other indicators. This makes
it a particularly useful indicator as part of the group, since it
might add discriminating powernot there in the other indicators.
IV. S
UMMARY AND CONCLUSION
In this article we reviewed the problem of bankruptcy predic-
tion using NNs. From the many studies existing in the literature,
it can be seen that NNs are generallymore superior to other tech-
niques. Once this is established, the logical next step for the re-
search community is to improve further the performance of NNs
for this application, perhaps through better training methods,
better architecture selection, or better inputs. It is this latter im-
provement aspect that we have addressed in the second half of