Predicting Bankruptcy through Financial Statement AnalysisApplication of Altman Z-score Model and Logistic Regression Modeling to Analyze Publicly Held Banks in Bangladesh to Predict Bankruptcy

31st May,

2011

Prepared for:Mohammad SaifNoman KhanAssistant Professor,Institute of Business Administration,University of Dhaka.

Prepared by:Group 8Omaer Ahmad, ZR-09KawsarAhmad, ZR-50RafaatWasik Ahmed, ZR-53NasimUlHaque, ZR-54Rashed Al Ahmed Tarique, ZR- 61BBA 16th Batch,Institute of Business Administration,University of Dhaka.

Term Paper

Financial Markets and Instruments

Predicting Bankruptcy through Financial

Statement Analysis

- Application of Altman Z-score Model and Logistic

Regression Modellingto Analyze Publicly Held

Banks in Bangladesh to Predict Bankruptcy

Team Leader: Rashed Al Ahmad Tarique

Contact:

e-mail: rtarique@gmail.com

Mobile: 01671507262

Mohammad SaifNoman Khan

Assistant Professor,

Institute of Business Administration,

University of Dhaka.

Dear Sir,

We, Group 8, present to you our term paper for the course Financial Markets and Institutions.

The title of our paper is “Predicting Bankruptcy through Financial Statement Analysis”. Along

with this paper we provide you with a number of articles, spreadsheets and other documents to

support our work.

In this paper, we have studied models widely used over the world to predict bankruptcy in

different sectors and have applied them to locally enlisted scheduled banks. This paper only

derives its ideas from other researchers and hence is an original analysis. No works have been

copied for its production. As we have not worked on the topic on any other course, this paper is

exclusively for the purposes of this course. We will not, therefore, use any of its content without

written permission from you.

We have tried our best to abide by your guidelines in the preparation of this paper. For further

inquiry about it, please feel free to contact us.

Yours Sincerely,

Omaer Ahmad, ZR-09 Kawsar Ahmad, ZR-50

RafaatWasik Ahmed, ZR-53 NasimUlHaque, ZR-54

Rashed Al Ahmad Tarique, ZR-61

BBA 16th Batch,

Institute of Business Administration,

University of Dhaka

31st May, 2011.

ContentsExecutive Summary.......................................................................................................................4

Introduction....................................................................................................................................5

Literature Review...........................................................................................................................6

Financial Ratios as Predictors Failure.......................................................................................6

Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy...............6

Step-Wise Multiple Discriminate Analysis..................................................................................7

On the Pricing of Corporate Debt: The Risk Structure of Interest Rates...................................7

Option-Based Bankruptcy Prediction.........................................................................................8

Bankruptcy Prediction for Credit Risk Using Neural Networks..................................................9

Bankruptcy Prediction of Turkish Commercial Banks Using Financial Ratios...........................9

Limitations & Scope.....................................................................................................................10

Methodology................................................................................................................................11

Altman z-score test..................................................................................................................11

Logistic Regression Model (Logit model).................................................................................13

Results.........................................................................................................................................15

Recommendations.......................................................................................................................20

Bibliography.................................................................................................................................20

Table 1: Banks for the study........................................................................................................11

Table 2: Ratios for the Logistic Regression Model......................................................................13

Table 3: Summarized z-scores for Banks....................................................................................15

Table 4:Summarized Bank Logit Score.......................................................................................18

Executive Summary

Banks are an integral part of everyday lives of people. Their importance is only increasing with

every passing day. They are among the fastest growing corporations in the country. Hence, it is

vital that such an arm of society does not come down and bring down with it the savings and

livelihoods of a large chunk of the population.

This report attempts to look at a number of tools which have been developed around the world

in various spheres of industry. These include William H. Beaver’s t-tests, Edward Altman’s z-

score, Fulman’s step-wise multiple discriminate analysis, Robert C. Merton’s Merton model,

Andreas Charitou and Lenos Trigeorgis’s Options based bankruptcy prediction model, Amir F.

Atiya’s Neural Network based bankruptcy prediction model and finally logistic regression model

by Birsen Eygi Erdogan. These bankruptcy prediction tools were developed as pre-warning

systems to identify problematic organizations and provide a method to warn stakeholders at

least a couple of years before to wake up and get their act together.

We used annual report data from the enlisted banks on Dhaka Stock Exchange and used ratio

analysis to get the variables that allowed us to run a couple of tests on them. These were the

Altman z-score model and the Logistics Regression Model. These allowed us to identify

corporations under threat.

Of the banks analyzed First Security Islami Bank and Uttara Bank Limited were found to have

problems that they need to address urgently. Another major finding of the report was that when

these models were being developed in the western world, they encountered fewer instances of

bankruptcy probability that here. This points out the excellent job that the Bangladesh Bank has

been doing.

Introduction

Around the world, globalization of the marketplace is taking place. This has resulted from a

deregulation of the markets. Banks now-a-days can delve into many spheres of business. Many

industry experts reckon that this was one of the major reasons behind the financial crisis that

rocked the world and from which we are still struggling to recover from. Numerous firms went

bankrupt, taking with them many peoples’ entire life’s savings.

Banks have become tied to every walk of life. It provides a liquidity to customers through a wide

variety of services. It provides credit to entrepreneurs and home-buyers. It provides a means for

building up a store of wealth for people through savings instruments for when they retire. So

when a bank goes down, not only is the equity holder, the actual owner of the bank, affected,

but everyone around them. Hence, it is crucial that early warning systems be in place so that

these vital organs of society be able to offer their services in continuum.

The regulatory body on banking in Bangladesh is Bangladesh Bank, the central bank. It has

received plaudits from various corners of the globe for its role in effectively managing the banks

in Bangladesh and not allowing them to fail. It has been vigilant in thinking on its feet and

changing with the times and implementing new and effective measures whenever the need

hasrisen for a change in regulations governing the banks to safeguard the money of the

customers.

The regulations set up by the central bank have been crucial to building the confidence of the

general public in the banking system. The strict guidelines set by the Bank have allowed the

banks to maintain their health and build themselves up. As a result, the banking industry is one

of the fastest growing in the country.

The purpose of this report is to test the fortitude of the banks towards staving off bankruptcy.

We will look at a number of tools used to identify signs of possible bankruptcy on the horizon.

We will apply these tools to analyze publicly available data on the banks and identify

weaknesses or cracks, if any, in the banking sector. Finally we will attempt to come up with

recommendations to plug the holes.

Literature Review

The study of bankruptcy extends to at least 1932.Paul J. FitzPatrick published a paper in The

Certified Public Accountant on the topic.He used data for 20 matched pairs of firms and

discussed accounting ratios as indicators of bankruptcy. This formed the basis for a much more

thorough paper by William Beaver in 1968.

Financial Ratios as Predictors Failure

William H. Beaver’s paper named “Financial Ratios as Predictors Failure”(Beaver 1966), was

the first truly credible paper on the topic. Financial ratios as a means of identifying the position

and health of a firm and its credit worthiness had already been in practice by 1966.He aimed to

identify the efficacy of these ratios as predictors of financial distress. For his study, he took

paired sample of both failed and firms still in business to comparemeansusing t-tests.He then

performed a dichotomousclassification test of likelihood ratios using the ratio of cash flow to

total debt. He gleaned from the study “Althoughratio analysis may provide useful information, it

be used with discretion :(1) Not all ratios predict equally well. The cash-power throughoutflowto

total-debt ratio has excellentdiscriminatory power in the five-yearperiod. However, the

predictivepower of the liquid assetratios is much weaker. (2) The ratios do not predict failed and

non-failed firms can be correctlyclassified to a greaterextentthan can failed firms.”

Financial Ratios, Discriminant Analysis and the Prediction of Corporate

Bankruptcy

Following Beaver’s work, Edward I. Altman from the Stern Business School of New York

University wrote a paper on assessing the analytical quality of ratio analysis. Titled “Financial

Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy” (Altman Sep.,1968).

Due to the relatively unsophisticated manner of traditional ratio analysis, it had lost its shine in

academic spheres.In order to assess whether financial ratios were still up to the job, he

combined a set of financial ratios in a discriminant analysis approach to the problem of

corporate bankruptcy prediction. The theory is that “ratios, if analyzed within a multivariate

framework, will take on greater statistical significance than the common technique of

sequential ratio comparisons.” The discriminant-ratio model proved to be extremely accurate

in predicting bankruptcy correctly in “94 per cent of the initial sample with 95 per cent of

all firms in the bankrupt and non-bankrupt groups assigned to their actual group

classification.” Furthermore, the discriminant function was accurate in several secondary

samples introduced to test the reliability of the model. The model's findings were that

bankruptcy can be accurately predicted up to two years prior to actual failure with the

accuracy diminishing rapidly after the second year. A limitation of the study was that the

firms examined were all publicly held manufacturing corporations for which comprehensive

financial data were obtainable, including market price quotations. Several practical and

theoretical applications of the model were suggested. Among them were business credit

evaluation, internal control procedures, and investment guidelines.

Step-Wise Multiple Discriminate Analysis

John G. Fulmer (Fulmer 1984) and his team used step-wise multiple discriminate analysis to

evaluate 40 financial ratios applied to a sample of 60 companies -30 failed and 30 successful.

This model was different as it focused on small firms. The average asset size of these firms was

$455,000.Fulmer reported a 98% accuracy rate in classifying the test companies one year prior

to failure and an 81% accuracy rate more than one year prior to bankruptcy.

Another paper that looked into the topic was by James A. Ohlson (A.Ohlson, 1980). The major

findings of the study can be summarized briefly. First, he identified four basic factors as being

statistically significant in affecting the probability of failure (within one year). These are: (i) the

size of the company; (ii) a measure(s) of the financial structure; (iii) a measure(s) of

performance; (iv) a measure(s) of current liquidity. He conducted the study due to concern that,

if one employs predictors derived from statements which were released after the date of

bankruptcy, then the evidence indicates that it will be easier to "predict" bankruptcy. However,

even if one allows for this factor, for the sample of firms used in this study, the prediction error-

rate is larger in comparison to the rate reported in the original Altman [1968] study.He

expressed that the previous models were relatively simple to apply and may be of use in

practical applications. He stated that a potential disadvantage was that the model does not

utilize any market transactions (price) data of the firms.

On the Pricing of Corporate Debt: The Risk Structure of Interest Rates

The Merton model is a model proposed by Robert C. Merton in 1974 for assessing the credit

risk of a company by characterizing the company's equity as a call option on its assets. Put-call

parity is then used to price the value of a put and this is treated as an analogous representation

of the firm's credit risk. (Merton May 1974) The model takes three company specific inputs: the

equity spot price, the equity volatility (which is transformed into asset volatility), and the

debt/share. The model also takes two inputs which should be calibrated to market quoted CDS

spreads: the default barrier, and the volatility of the default barrier. These inputs are used to

specify a diffusion process for the asset value. The entity is deemed to have defaulted when the

asset value drops below the barrier. The barrier itself is stochastic, which has the effect of

incorporating jump-to-default risk into the model. The Merton model evolves asset value

movements through a diffusion process and a fundamental purpose of the default barrier

volatility is to provide a jump-like process which can capture short term default probabilities.

Option-Based Bankruptcy Prediction

More recent approaches towards predicting bankruptcy include option valuation models for

bankruptcy prediction. Some of the pioneers of this technique are Andreas Charitou and Lenos

Trigeorgis. (Option-Based Bankruptcy Prediction, June 2000) Their study builds on and extends

option-pricing theory to explain financial distressbased on a sample of 420 distressed U.S. firms

for the period 1986-2001. Their results indicatethat the primary option variables, such as firm

volatility, play an important role in explainingdistress up to five years prior to bankruptcy filing.

When the model is extended to accountfor the probability of default on interest and debt

repayments due at intermediate times priorto debt maturity (due to voluntary equityholder

default or due to cash flow problems), anoption-motivated transformation of the cash flow

coverage is shown to have incrementalexplanatory power, while the primary option variables

remain statistically significant. The significant primary option variables include the face value of

debtowed at maturity (lnB), the current market value of the firm’s assets (lnV), and the standard

deviation (σ) of firm value changes (returns). The distance to default (d2d) and theprobability of

default at maturity (-d2) were also found to be significant predictor variables. Despite the

probability of intermediatedefault on due interest and debt repayments, the above primary

option variables maintaintheir sign and significance. The latter results indicate that the extended

option variablesbased on cash flow coverage have incremental explanatory power beyond the

primary optionvariables.

The latest models for bankruptcy prediction depend on neural network modeling. Artificial neural

networks are composed of interconnecting artificial neurons (programming constructs that mimic

the properties of biological neurons). Good performance (e.g. as measured by good predictive

ability, low generalization error), or performance mimicking animal or human error patterns, can

then be used as one source of evidence towards supporting the hypothesis that the abstraction

really captured something important from the point of view of information processing in the

brain. Another incentive for these abstractions is to reduce the amount of computation required

to simulate artificial neural networks, so as to allow one to experiment with larger networks and

train them on larger data sets.Mathematically, a neuron's network function   is defined as a

composition of other functions  , which can further be defined as a composition of other

functions. This can be conveniently represented as a network structure, with arrows depicting

the dependencies between variables. What has attracted the most interest in neural networks is

the possibility of learning. Given a specific task to solve, and a class of functions,  , learning

means using a set of observationsto find   which solves the task in some optimal sense.

Bankruptcy Prediction for Credit Risk Using Neural Networks

Amir F. Atiya (Bankruptcy Prediction for Credit Risk Using Neural Networks: A Survey and New

Results, JULY 2001) developed a model for predicting bankruptcy using Neural Networks. In the

article he reviewed the problem of bankruptcy prediction using NNs.He found NNs generally

superior to other techniques. Once that was established, the logical next step for the research

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

improvement aspect that he addressed in the second half ofthis paper. He proposed novel

inputs extracted from the equity markets. His results showed new indicators which improve the

prediction considerably, especially for long horizon forecast. This can be explained by the

tendency ofthe equity markets to be highly predictive, not only of the healthof a firm, but also of

the health of the economy, which in turnaffects the creditworthiness of the firm.

Bankruptcy Prediction of Turkish Commercial Banks Using Financial Ratios

In his paper “Bankruptcy Prediction of Turkish Commercial Banks Using Financial Ratios”,

(Erdogan 2008) Birsen Eygi Erdogan uses data compiled from the years 1997 and 1999.

Logistic Regression was used to form a prediction model with financial ratios. 42 commercial

banks were included in this research. It was observed that 80% of failed banks could be

predicted two years a priori, and Logistic Regression can be used as a part of an “early warning”

system. In this research, in order to determine the statistically significant ratios many suggested

methods were used, such as Single Logistic Regression, Multivariate Variable Selection

Procedure, All Possible Regression, Forward and Backward Elimination methods. 20 financial

ratios were examined for each year for the 1997 -1999 periods. After using Factor Analysis, the

forward logistic regression and backward elimination methods were applied, and different

combinations of the ratios were tested. The selection of the final ratios was based on the

statistical significance (at 10% level) of the estimated parameters and the model classification

results.

Logistic Regression is a method coming from statistics whose objective is to obtain a functional

relationship between a transformation from a qualitative variable called logit and predictor

variables which can be either quantitative or qualitative. Where B(X) is a classification model,

the Logistic Regression model is described by the following formula:

Prob(X) = 1/(1+e(−B(X))

It is used to classify new individuals starting from rules in the following way:

“If Prob(x) < c then individual is classified as 0, otherwise it is classified as 1”.

“c” is the cut-off point. The cut-off point or level of probability that is used to categorize a bank

as “failed” is usually chosen as 0.5 in literature. In this research bankrupt banks were classified

as “0” and successful banks were classified as “1”. Cut off point was chosen as 0.5. Those

under 0.5 were classified as “0” and above 0.5 as “1”. In some studies it is noted that classifying

a “failed” bank as a “non-failed” bank can have more severe consequences than classifying a

“non-failed” bank as a “failed” bank.

It was observed that from predictions made by the study, 18 banks were predicted to fail over

the coming two years. Of these all were predicted successfully.

Limitations & Scope

In this report, we will analyze bankruptcy probability only among the enlisted banks on Dhaka

Stock Exchange. Information only available from the financial statements of these companies

would be used to find out the ratios used for the report. Therefore, only the methods that use

financial ratios to predict bankruptcy of firms.

The lack of cases of bank failure in the country (due to vigilance of the central bank) means the

sample for testing these models is very low. Therefore, this study will only apply the established

tools used elsewhere and not test them.

Methodology

The report will use the annual reports of the enlisted banks on Dhaka Stock Exchange. We will

apply the Altman z-score test and the Logistic Regression model. The banks that were

considered were:

Table 1: Banks for the study

ABBANK EBL JAMUNABANK PREMIERBAN SHAHJABANK

ALARABANK EXIMBANK MERCANBANK PRIMEBANK STANDBANKL

BANKASIA FIRSTSBANK MTBL PUBALIBANK TRUSTBANK

BRACBANK ISLAMIBANK NBL RUPALIBANK UCBL

CITYBANK ICBIBANK NCCBANK SOUTHEASTB UTTARABANK

DHAKABANK IFIC ONEBANKLTD SIBL

Altman z-score test

The Multi Discriminant Analysis narrows down multiple variables into a single dimension. This

single dimension is the z-score. The z-score model is defined as:

Z=V1X1+V2X2+…+VnXn

Where V1, V2.. are the discriminant coefficients and X1,X2 … are the actual values of the

financial ratios.

Of the 22 variables initially selected, five were identified to have the greatest significance in

predicting bankruptcy. These variables were:

X1= (Working Capital/Total Assets)

X2= (Retained Earnings/Total Assets)

X3= (EBT/Total Assets)

X4= (MV of Equity/Total Liabilities)

X5= (Interest Income/Total Assets)

Using MDA for the banking sector, the values obtained for the discriminants were:

V1=1.2

V2=1.4

V3=3.3

V4=0.6

V5=1.0

Using the spreadsheets titled “Altman z-score” we find the relevant z-scores for the banks

analyzed by using the following equation:

Z= 1.2*X1+1.4* X2+3.3* X3+0.6*X4+1.0* X5

According to Altman, the z-score boundaries that we should look for are:

Z≥3 The company will continue to thrive

1.8≥Z≥2.7 The company is in a grey area. The firm should be kept under strict management

scrutiny

Z≤1.8 The company is highly likely to go bankrupt in the next three years.

Logistic Regression Model (Logit model)

The ratios that were considered in the study included:

Table 2: Ratios for the Logistic Regression Model

The ratios that were found to be statistically significant are:

C2 = (Shareholders’ Equity + Total Income)/ (Deposits + Non-deposit

Funds)

C12 = Net Income (Loss)/ Average Total Assets

C14 = Net Income (Loss)/ Average Share-in Capital

C16 = Interest Income/ Interest Expenses

C17 = Non-Interest Income/ Non-Interest Expenses

C19 = Provision for Loan Losses/ Total Loans

Using these ratios, the following equation was developed using the logit analysis:

XB = -13,20738+ 626098xC2-2,169955xC12+ 9,429545E-02xC14+ 5,528393E-

02xC16+2,361215E-02xC17-1,704793xC19

Where XB refers to the expectation of bankruptcy and the coefficients are obtained through logit

analysis.

Results

The ratings found from the Altman z-score analysis for the banks are:

Table 3: Summarized z-scores for Banks

Bank(in Alphabetical Order)Z-

scorePrediction

ABBANK 3.0 Will survive

ALARABANK 2.5Needs careful

management

BANKASIA 4.3 Will survive

BRACBANK 4.2 Will survive

CITYBANK 4.9 Will survive

DHAKABANK 4.9 Will survive

EBL 5.6 Will survive

EXIMBANK 4.7 Will survive

FIRSTSBANK 2.3Needs careful

management

ISLAMIBANK 3.7 Will survive

ICBIBANK 7.8 Will survive

IFIC 5.6 Will survive

JAMUNABANK 3.6 Will survive

MERCANBANK 4.2 Will survive

MTBL 4.2 Will survive

NBL 7.7 Will survive

NCCBANK 7.2 Will survive

ONEBANKLTD 4.8 Will survive

PREMIERBAN 3.5 Will survive

PRIMEBANK 6.2 Will survive

PUBALIBANK 5.6 Will survive

RUPALIBANK 2.5Needs careful

management

SOUTHEASTB 4.8 Will survive

SIBL 3.7 Will survive

SHAHJABANK 5.2 Will survive

STANDBANKL 4.6 Will survive

TRUSTBANK 4.5 Will survive

UCBL 3.7 Will survive

UTTARABANK 1.8Needs careful

management

It can be observed that none of the banks in the study are predicted to run into financial distress

in the upcoming two years. However, Uttara Bank is on the brink and First Security Islami Bank

is following suit. This can be stated with an error of 5%.

The following table shows condensed results of the logistical regression analysis run on the

banks:

Table 4:Summarized Bank Logit Score

XB Prob(Y=1)Success

C=0.8

ABBANK 2.60350284 0.93109 1

ALARABANK 1.914949135 0.87157 1

BANKASIA 2.481710771 0.92285 1

BRACBANK 2.368667275 0.91441 1

CITYBANK 2.344648753 0.91251 1

DHAKABANK 2.287322983 0.90782 1

EBL 1.925777817 0.87278 1

EXIMBANK 1.649473182 0.83882 1

FIRSTSBANK -0.129509725 0.46767 0

ISLAMIBANK 1.905841949 0.87055 1

ICBIBANK 3.32887004 0.96541 1

IFIC 2.590530777 0.93025 1

JAMUNABANK 1.81528443 0.86000 1

MERCANBANK 1.948493876 0.87528 1

MTBL 1.743904699 0.85118 1

NBL 2.940085608 0.94979 1

NCCBANK 2.206194565 0.90080 1

ONEBANKLTD 2.3020672 0.90905 1

PREMIERBAN 2.977622628 0.95155 1

PRIMEBANK 3.880745967 0.97978 1

PUBALIBANK 1.083317134 0.74712 0

RUPALIBANK 1.499605496 0.81752 1

SOUTHEASTB 2.132822901 0.89405 1

SIBL 1.452824034 0.81043 1

SHAHJABANK 2.869738662 0.94633 1

STANDBANKL 2.015806192 0.88245 1

TRUSTBANK 2.39490092 0.91644 1

UCBL 2.427403216 0.91889 1

UTTARABANK 1.228150789 0.77349 0

From the above table the only bank found likely to fail in the next two years is First Security

Islami Bank if we use a cut-off point of 0.8, as prescribed for developing economies.

If we combine the findings of the two analysis we arrive at a number of conclusions. First, when

utilizing models developed in developed economies we observe that the probability of failure

among local banks are very low. This clearly refers to the great job done by the Central Bank in

managing the private banking sector in Banlgadesh. The second conclusion that can be derived

from the results is that a couple of banks – First Security Islami Bank and Uttara Bank - have

performed sorrily on both counts. Careful management of the firm’s asset quality, gapping

strategies, cash management and provisions made for bad loans, cost cutting in non-interest

earning fields will be needed to nurse these banking businesses.

Recommendations

Further study with data available outside the financial statements needs to be undertaken. All

the models described need to undergo tests. A more rigorous study needs to be undertaken to

find the validity of these models in predicting failures in the sector. This will help in the ultimate

goal which is to develop a thorough holistic model that will avert danger in the sector.

Bibliography

A.Ohlson, James. "Financial Ratios and the Probabilistic Prediction of Bankruptcy." Journal of

Accounting Research, Vol. 18, No. 1, (Spring, 1980: 109-131.

Altman, Edward I. "Financial Ratios, Discriminant Analysis and the Prediction of Corporate

Bankruptcy." The Journal of Finance, Vol.23, No.4. , Sep.,1968: 589-609.

"Bankruptcy Prediction for Credit Risk Using Neural Networks: A Survey and New Results."

IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 12, NO. 4, JULY 2001: 929-936.

Beaver, William H. "Financial Ratios as Predictors of Failure." Journal of Accounting Research,

1966: 71-111.

Erdogan, Birsen Eygi. "Bankruptcy Prediction of Turkish Commercial Banks Using Financial

Ratios." Applied Mathematical Sciences,Vol.2,no.60,2973-2982, 2008.

Fulmer, John G. Jr., Moon, James E., Gavin, Thomas A., Erwin, Michael J. "A Bankruptcy

Classification Model For Small Firms." Journal of Commercial Bank Lending, 1984: 25-37.

Merton, Robert C. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates." The

Journal of Finance, Vol. 29, No. 2, May 1974: 449-470.

Trigeorgis, Andreas Charitou and Lenos. "Option-Based Bankruptcy Prediction." European

Financial Management Journal, June 2000.