Bankruptcy studies

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Bankruptcy studies empirical works on prediction and financial markets
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Empirical works on prediction and financial markets
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v, 158 leaves : ill. ; 28 cm.
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Bi, Keqian, 1941-
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Bankruptcy -- Forecasting   ( lcsh )
Money market -- Mathematical models   ( lcsh )
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bibliography   ( marcgt )
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Thesis:
Thesis (Ph. D.)--University of Florida, 1989.
Bibliography:
Includes bibliographical references (leaves 155-157).
Statement of Responsibility:
by Keqian Bi.
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Typescript.
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Vita.

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oclc - 21387281
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BANKRUPTCY STUDIES: EMPIRICAL WORKS ON
PREDICTION AND FINANCIAL MARKETS







By

KEQIAN BI


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1989










ACKNOWLEDGEMENTS

I am greatly indebted to the members of my dissertation

supervisory committee: Dr. Roy L. Crum and Dr. Haim Levy,

committee cochairmen, and Dr. David Denslow. Their support,

advice, and guidance have made this dissertation a reality and

have greatly enhanced my academic experience at the University

of Florida.

I would also like to thank my family for their unwavering

support, without which this dissertation would have been

impossible. Even as I write now, I think of my kind, loving

parents, Professors Zhongjie Bi and Shaoxiang Huang, who,

though half a world away, have wished so much for my success

in this Ph.D. program. I want to share it today with many

people, but with them most of all.

Finally, I want to dedicate my dissertation to a new

future for my homeland, China. The lessons and memories of

May and June 1989 will be remembered forever.












TABLE OF CONTENTS


ACKNOWLEDGEMENTS . .

ABSTRACTS. ..... . .

CHAPTERS


1 OVERVIEW AND OUTLINE. ... . 1
Topic Overview. . . 1
Dissertation Outline. .. . .. 5
Note. . . 7

2 LITERATURE REVIEW ... . .. 8
Summary of Current Literature . 8
Significance of this Dissertation .. 14

3 METHODOLOGY TO STUDY FINANCIAL MARKETS
AND BANKRUPTCY . .. 17
Note . . 22

4 RESULTS ON FINANCIAL MARKETS AND BANKRUPTCY 27
Notes . . .. 35

5 EMPIRICAL MODEL OF BANKRUPTCY .. 48
Variable Definitions. . ... 51
Hypotheses. ..... . .. 57

6 METHODOLOGY TO TEST EMPIRICAL MODEL .. 62
The Logist Analysis Methodology .. 62
Logist versus Discriminant Analysis .. .64
Sample Design . .. .. 67


7 RESULTS OF EMPIRICAL MODELS OF BANKRUPTCY

8 SUMMARY AND CONCLUSIONS ..
Research Summary. . .
Future Research . .

APPENDIX . .. ..

REFERENCES .. . .

BIOGRAPHICAL SKETCH. . .


. 74

. 99
. 99
. 102

. 104

. 154

. 157


iii


o o







Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

BANKRUPTCY STUDIES: EMPIRICAL WORKS ON
PREDICTION AND FINANCIAL MARKETS

By

Keqian Bi

August 1989


Chairman: Roy L. Crum
Cochairman: Haim Levy
Major Department: Finance, Insurance, and Real Estate

This dissertation studied two areas not covered by

current bankruptcy research. First, the question whether

financial markets could assess bankruptcy risk beforehand was

addressed. Second, the problems of long-term bankruptcy

prediction models were discussed, and a new model with

reasonably accurate long- as well as short-term predictive

powers was developed.

On the subject of financial markets, this dissertation

looked at whether the market could assess bankruptcy risk

ahead of time. The risk premia of corporate bonds of bankrupt

companies were used to investigate whether there was any rise

in risk premia as companies approached bankruptcy. Then, an

event study was done to determine whether bond downgrades

affected the performance of a later-bankrupt company's stock's

daily rates of return.





It was found that risk premia did increase as companies

approached bankruptcy, and that the risk premia of companies

which were later liquidated rose more than the risk premia of

companies which later re-organized. The event-study showed

that the daily rates of returns of stocks of companies which

later went bankrupt did fall significantly during the first

downgrade, unlike those of companies which did not.

On the subject of bankruptcy prediction, this

dissertation looked at whether an accurate, long-term

bankruptcy model could be developed using variables which

assess a company's fundamental characteristics as well as its

current financial position. A model based on the following

eight variables was developed: return on assets, fixed charge

coverage, balance ratio, market-to-book ratio, relatedness

ratio, net rate of management stock acquisitions, relative

sales growth, and capital intensity. It had achieved high

classification success and predictive accuracy, and, unlike

those of past models, its predictive powers did not decrease

over time.

Finally, work was done on the use of logist analysis in

bankruptcy predictions. It was shown that any non-random,

state-based sample selection technique would distort the

probabilities generated by logist models. A formula was

derived to remedy this problem by providing an adjustment

scheme whereby the resulting probabilities could be made to

work for a general population.













CHAPTER 1
OVERVIEW AND OUTLINE



Topic Overview



Bankruptcy is one of the most important topics in modern

finance. It plays a strong, visible role in all dimensions

of financial economics, such as the efficient market theory,

portfolio theory, capital asset pricing theory, option pricing

theory, and agency theory. Thus, understanding bankruptcy is

important to financial research in both theory and practice.

In theory, if we thoroughly understood the dynamics and causes

of bankruptcy, we should be able to make the risk of

bankruptcy a parameter in market valuations of debt and

equity. Assuming that investors are naturally risk averse,

such formulas can determine how the probability of bankruptcy

affects the average investor's utility. In practice,

researchers have tried to develop predictive models of

bankruptcy that can alert interested parties to the impending

dangers of bankruptcy before it is too late to take corrective

actions. Because practically any group involved with a

company would be interested in the risk of bankruptcy it





2

faces, potentially widespread demand for such a model has

inspired much research in this area. To date, several

approaches have been taken to develop predictive models; they

are discussed in the Literature Review section.

While substantial work has been done on various aspects

of bankruptcy, including empirical forecasting and prediction,

we believe that past works have left a few areas unexplored.

First, many successful predictive models of bankruptcy have

been developed, but most of these models base their assessment

of a company's bankruptcy risk primarily on its current

financial position. They rely heavily on such accounting data

as retained earnings and capitalization ratios. Some of these

predictive models have grown quite complex. Because they use

mostly current financial data, however, their predictive power

is limited to a relatively short period before bankruptcy,

usually one year. When they are used to predict bankruptcy

further into the future than one year, their accuracy falls

significantly.

Second, no one, to date, has studied whether the market

can somehow predict bankruptcy. Modern finance considers

financial markets to be efficient, but no research has yet

been done on whether this efficiency extends to the evaluation

of companies' bankruptcy risk. After all, if the market were

truly efficient, then it should include the risk of bankruptcy

as one of the determinants of the value of a company's

securities. Hence, the market's assessment of a company's






3

securities' risk should include as a component the company's

chances of bankruptcy.

In this dissertation, we address both of these areas that

present bankruptcy research has largely overlooked. First,

we explore the market's ability to "sense" coming bankruptcy

by looking at the risk premia of corporate bonds. We first

examine whether such risk premia rise as the event of

bankruptcy approaches. Then, we investigate what role the

bond rating agencies, Standard & Poor's and Moody's, play in

the market assessment of a company's overall risk in general

and bankruptcy risk in particular. In other words, if the

market actually does include bankruptcy risk in its overall

assessment of a company's risk, then how do S&P's and Moody's

ratings affect this market assessment? Do they provide new

information to the market and, therefore, serve as a crucial

link in the process, or does the market itself already reflect

all of the information these rating agencies provide?

To answer this question we have to study two problems.

First, assuming that the first consistent downgrade of a

corporate bond provides the most relevant information, we

determine whether S&P's and Moody's downgrades precede or

follow increases in the bond's risk premium.1 Second, with

the same assumption, we explore what impact, if any, the first

bond downgrade has on the performance of the company's stock.

Arguably, if nothing happens to the stock's return or the bond

risk premium after a bond downgrade, then we can infer that





4

the market has already absorbed all the information S&P's and

Moody's provide in the rating change. In that case, we can

say that S&P's and Moody's provided no new information in the

market's assessment of a company's bankruptcy risk. If,

however, the market reacts strongly after a bond downgrade and

the bond's risk premium rises or the stock return changes

significantly with the downgrade, then we can say that S&P's

and Moody's do provide new information to the market in its

assessment of bankruptcy risk. In that case, we can further

conclude that bond downgrades are good indicators of increased

bankruptcy risk and correspondingly higher risk premia.

To study bond risk premia and bankruptcy, we first

compile the yield-to-maturity of bonds of companies that went

bankrupt and subtract from them the yield to maturity of

government bonds. Then, to assess the impact of bond rating

downgrades, we use the methodology known as "event study,"

which is described in greater detail later in Chapter 3.

The second area that has largely been overlooked in

bankruptcy research is the "nearsightedness" problem of

current predictive models of bankruptcy. We attempt to

overcome this shortcoming by building an empirical model that

includes new sets of variables with a long-term orientation.

We believe that as one tries to predict bankruptcy farther

ahead in time, a company's current financial position becomes

less significant, while other, currently unexplored factors

play increasingly larger roles. For example, a company's






5

current return on assets (ROA) may be critical to whether it

is solvent or bankrupt within the next few years, but its

long-term financial health would probably depend less on

current profit levels than on the fundamental characteristics

of the company that predetermine future ROA. Hence, to make

accurate long-term bankruptcy forecasts, we must examine not

only a company's current financial position, but also its more

fundamental operating characteristics, such as its lines of

business, degree of diversification, management efficiency,

and growth.

We adopt this approach to develop an empirical model of

bankruptcy that can forecast the extent of bankruptcy risk.

In addition to a group of four variables designed to assess

a company's current financial position, we adopt variables

that describe a company's management ownership position, its

degree of diversification, the lines of business in which it

operates and their relationship, and its growth relative to

the rest of the industry. We expect that a model based on

this broader specification of variables will have high long-

term as well as short-term predictive powers.


Dissertation Outline


In the following chapters, we present the research design

and findings of our dissertation. Chapter 2 examines current

literature on both bankruptcy prediction and the effects of

bond rating changes, which, as stated earlier, are used to





6

study financial markets' signals about bankruptcy. Chapter

3 discusses the techniques and methodologies we employ to

study the financial market's ability to sense impending

bankruptcy. Then Chapter 4 identifies the data sources for

our work on financial markets and bankruptcy and presents the

results we obtained in the market-oriented part of the

dissertation. Chapter 5 discusses in depth the rationale for

and the variables used in our empirical model of bankruptcy.

Attention is focused on why each variable was chosen, what

values each variable should have, and what we expect our model

to tell us about the role each of our variables should play

in assessing bankruptcy risk. In Chapter 6 the methodology

we used to build our empirical model is described. This is

logist analysis, and we will discuss the advantages it has

over the more traditional discriminant analysis. Chapter 7

gives the results we obtained from tests of our empirical

model. Finally, Chapter 8 summarizes our research, presents

the conclusions we reach, and points out possibilities for

future research.












Note

1. "Consistent" means a bond downgrade after which there were
no upgrades until the company filed for Chapter 11. In other
words, this downgrade is the first of a series of downgrades
which eventually lead to bankruptcy, uninterrupted by any
upgrades of the same bond.














CHAPTER 2
LITERATURE REVIEW


Summary of Current Literature



Market Efficiency Studies of Bond Rating Changes



Katz (1974), in one of the earliest works on bond rating

changes, developed an event-oriented methodology for testing

the efficiency of the bond market. He looked for "unusual

behavior" in a bond's yield to maturity twelve months prior

to and five months after a rating change. His data consisted

of electric utilities bonds from 1966 to 1972. Katz derived

a quadratic regression equation of yield to maturity at any

given time, t, based on maturity, total float, and coupon

rate. Then, he compared his expected yields with the actual

yields and the changes in the actual yields with premium

differentials of two rating classes. He concluded that no

anticipation exists prior to a public announcement of a rating

change. After the rating change, there was a lag of six to

ten weeks before yield-to-maturity fully adjusted to the new

rating class.




9

Weinstein (1977) tried to determine if bond rating

changes contained new information by studying the bonds'

prices during the time period surrounding rating change

announcements. His sample consisted of utilities and

industrial bonds from July 1962 to July 1974. Weinstein

started with portfolios which, for every month, contained all

bonds with a given rating. He then constructed a series of

risk-adjusted returns for each bond by subtracting the return

on the appropriate rating class portfolio from the return on

the given bond. He selected the bonds that had a rating

change and looked at if those bonds had abnormal returns

during periods of rating changes. Weinstein concluded that

bond rating changes caused no significant price change during

or after the announcement, and that adjustments in the market

were made 18 to six months before the event. Hence, his study

suggested that rating changes provided no new information.

Pinches and Singleton (1978) studied the effects of bond

rating changes on the market returns of stocks during the

period from January 1950 to September 1972. For each stock,

they derived a market return based on its beta and measured

the actual return against the expected return for a period of

thirty months before to twelve months after a rating change.

Their study calculated disturbance terms (residuals) of stock

returns during the period. Pinches and Singleton concluded

that all changes attributable to companies' financial

situations were fully anticipated 15 to 18 months ahead of





10

time, while all changes attributable to company-specific

events were anticipated six months ahead of time. Thus,

although there were abnormally high and low returns

corresponding to upgrades and downgrades, respectively, before

a rating change, there were normal returns after the rating

change. Again, a study concluded that bond rating downgrades

provided no new information to the market.

Finally, Griffin and Sanvincente (1982) used three

different methodologies to study the effects of rating changes

on common stock prices. Their study contained 180 rating

changes from 1960 to 1975. First, they used a portfolio

method similar to that of Weinstein (1977). Then they

employed a one-factor and a two-factor model, basing their

expected stock prices on betas, as had Pinches and Singleton

(1978). They found that although rating upgrades had no

effect on stock prices, downgrades did have significant

effects. Because of the inconclusive nature of their results,

further research in this area was necessary.

The methodology employed in this dissertation differs

from previous works in several important ways. First,

previous authors used yield-to-maturity, an absolute value,

as their indicator of return. It is our position that

absolute yield-to-maturity, in this application, is not an

accurate measure of return. Instead, we suggest using a

relative value, the risk premium, which is defined as the

difference between a bond's yield-to-maturity and the yield-






11

to-maturity of a risk-free security. Second, we construct our

samples not by industry but by the nature of the event. In

other words, we defined the event as the filing of Chapter 11

under the Federal Bankruptcy Act. As far as we know, this is

the first study of bond rating changes to be based on data of

companies from all industries.




Theoretical Models of Bankruptcy


Wilcox (1971) is one of the earliest and most primitive

theoretical models of bankruptcy. It assumes that a company

starts with a positive amount of capital, K, which changes

randomly over time. Positive changes in K indicate positive

cash flow and increases in the company's assets, while

negative changes in K indicate financial losses which require

the company to liquidate assets. When a company's K is

sufficiently negative, it becomes bankrupt. Expressions for

the expected probability of bankruptcy, as well as time to

bankruptcy, are mathematically derived, just as they would be

for the gamblers' game.

Scott (1976) and (1977) attempted to improve on this

simple model. Scott's early models assumed that a company has

a potentially infinite life and can meet losses by selling

debt or equity in an efficient market without incurring

flotation costs. They further assumed that the secondary

market for real assets is imperfect and that a firm begins






12

with an optimal level of assets. Therefore, it would much

rather sell securities and debt than liquidate assets to cover

its losses. Scott then showed that a company would remain

solvent as long as stockholder wealth, measured by market

value, remained positive.

Scott (1981) developed a revised version of the earlier

model. In this newer model, Scott assumed that a company may

have imperfect access to external capital, so it might incur

flotation costs when it sells securities, or there may be a

tax system which favors internally-financed corporate

investments. Further, systematic imperfections in the market

valuation of securities can hinder corporate access to

external capital. This model, however, also assumed that the

company has no debt and can issue only equity. Thus,

according to this model, a company will go bankrupt when the

market value of its securities is less than the amount of

investment needed at times of negative income. Therefore,

bankruptcy is not the result of a conflict of the benefits and

costs of debt, but rather the product of investment managers'

mistakes.



Empirical Works on Bankruptcy



Beaver's 1966 paper was the first empirical work that

tried to build a predictive model of bankruptcy. He looked

at 30 accounting ratios which could be used to predict






13

bankruptcy, and for each ratio he derived a cut-off point for

bankruptcy. He concluded that three ratios were the best

predictors of financial failure: Cash Flow/Total Assets, Net

Income/Total Debt, and Cash Flow/Total Debt.

Altman, Haldeman, and Narayanan (1977), a follow-up of

Altman (1969), used the more complex multi-variate

discriminant analysis approach to build a predictive model.

Their work included all industrial failures from 1969 to 1975

with at least $20 million in assets, which made a sample of

53 bankrupt firms, and Altman et al. found a matching sample

of 58 non-bankrupt firms. The samples were matched by

industry, year of bankruptcy, and size of assets. Their model

included seven variables: return on assets (ROA), stability

of earnings, debt service (times-interest-earned or TIE),

cumulative profitability, current assets/liabilities ratio,

capitalization, and size. After using various statistical

techniques, Altman et al. derived a value ZETA as the cut-off

for bankruptcy. This model, commonly known as the ZETA model,

is highly accurate, especially when bankruptcies are near.

Today, it is the leading model for predicting bankruptcy, and

because many financial institutions use it, it has become an

industry standard.

Ohlson (1980) took another approach to bankruptcy

prediction by using logist analysis to build his model. His

sample included 105 failed firms, but he did not find a

matching sample by asset size. Hence, among his nine





14

variables, size became the most significant one. Since his

model had error rates of 17.4% for non-bankrupt (type I error)

and 12.4% for bankrupt firms (type II error) even just one

year before bankruptcy, it has remained more-or-less an

academic curiosity and has not attained the same widespread

use as Altman's ZETA model.

Zavgren (1985) extended Ohlson's work by including more

variables and extending the length of the study. Her work

looked for the important factors in the short- and long-term

predictions of bankruptcy. Zavgren found that profitability

was not significant in either the short- or long-run. Rather,

her study showed that the ability to meet obligations is

significant in the short-run, while efficiency ratios and

liquidity are important in the long-run. Zavgren's study,

then, reduces a company's bankruptcy risk to two issues, that

of short-term endurance (as measured by the ability to meet

obligations) and fundamental characteristics (as measured by

the efficiency ratio and basic liquidity.)



Significance of this Dissertation


While the existing literature is already quite advanced,

we believe a few areas have been left unexamined. First,

while work has been done on bond rating changes, there has

been no research that tries to link bankruptcy with financial

market reactions. No one to date has looked at the trend that






15

bond risk premia take as a company approaches bankruptcy, even

though bankruptcy risk, in theory, should be a primary risk

included in risk premia. Further, while researchers have

studied bond rating changes' effects on both the stock and

bond markets to see if such rating changes contained new

information, no study has linked the information these

downgrades provide with a company's risk of filing for Chapter

11 and thus declaring bankruptcy. Since bond downgrades are

meant to warn investors of possible default and bankruptcy,

whether such downgrades have any impact on financial markets

should be directly linked to the market's assessment of a

company's bankruptcy risk. So far, however, research has left

this area untouched.

Second, as we stated in the previous Chapter, current

bankruptcy prediction models have looked mostly at current

financial data. Only Zavgren (1985) has tried to examine

certain fundamental characteristics, and her study shows that

such information does indeed have a role in empirical studies

of bankruptcy, especially when we are dealing with long-term

bankruptcy prediction. Hence, we assert that fundamental

characteristics have largely been overlooked by present

bankruptcy research, and our dissertation will address this

area more systematically than Zavgren did.

Our research contributes to the financial research of

bankruptcy and market efficiency in several ways. By studying

the bond market and bankruptcy, we attempt to determine





16

whether the financial market can adequately assess bankruptcy

risk on its own and whether bond ratings play a part in this

assessment of risk. We then look at ways to augment or

reinforce market signals via prediction models with

significant early warning capabilities. In this regard, our

study covers a period longer than those of its predecessors.

Further, we introduce variables that assess the fundamental

characteristics of a company to forecast long-term bankruptcy.

On the theoretical side, this research can lead to

establishing a relationship between certain fundamental

characteristics of a company and its financial position a few

years into the future.

In the area of market efficiency, we attempt to assess

whether the markets are truly efficient in anticipating one

specific type of risk--bankruptcy risk. Further, in our event

study, we study whether the bond rating downgrades actually

do provide new information to the market. We do not, however,

do this by merely looking at whether the downgrade trailed or

led a rise in the risk premium, because we believe such

indications are in themselves not significant. After all, a

downgrade that trails a rise in risk premium might be regarded

as the leading downgrade to a subsequent rise in the risk

premium. Hence, we will instead concentrate on whether

downgrades make a significant impact on the market.















CHAPTER 3
METHODOLOGY TO STUDY FINANCIAL MARKETS AND BANKRUPTCY



Our research on financial markets and bankruptcy

encompasses two topics. First, we look at the trend of the

risk premia of corporate bonds of companies that later went

bankrupt. This trend tells us if the markets can correctly

assess increasing chances of bankruptcy and default as

bankruptcy nears. Then we examine the impact of bond

downgrades on the returns of a company's stock. We determine

if ratings play a significant role in providing the market

with new information.

To study whether bond risk premia increase as a company

approaches bankruptcy, we selected a sample of bonds based on

two criteria. First, they had to be publicly traded bonds

listed in the Standard & Poor's Bond Guide with a bond rating

from either S&P's or Moody's. The second criterion was that

the companies which issued the bonds later filed for Chapter

11 between September 1977 and October 1988. Only 50 corporate

bonds had bond ratings and other available data from S&P's or

Moody's adequate for our purposes. These 50 bonds, listed in

Table 1, are used to study risk premia and bankruptcy. Then,





18

from the Analytical Record of Bond Yields and Yield Spreads,

published by the Salomon Brothers, we obtained the monthly

yield-to-maturities for US government securities. The risk

premium for each of our companies is the excess of the yield-

to-maturity of its bond over the yield-to-maturity of an US

government bond with the same maturity.

We then studied the risk premia of our 50 companies as

they moved towards bankruptcy. We separated the companies

into two groups--those companies which later re-organized and

those that were later liquidated.1 Next, we compared the risk

premia of bonds in those two groups as the companies

approached bankruptcy to see if the market's assessment of

risk went so far as to differentiate companies which could

later re-organize from those that could not.

To study the impact of bond downgrades, we use the event

study methodology. An event study compares the impact of an

event on security holders with the predictions made by a model

that approximates what would have happened if the event had

not taken place. In effect, we try to compare what happened

with what a model tells us should have happened. Our event

is the first consistent downgrade rating change, and the size

of the impact is measured by the disturbance of the stock's

daily rates of return. The number of months between the first

downgrade bond rating change and the month of filing Chapter

11 for our sample is given in Table 2.

In our work, the Mean Adjusted Returns Model, as






19

discussed in Fama (1976) and Masulis (1980) is used as the

basis for the statistical studies. This model uses the mean

returns on an individual stock over a representative period

of time before the event period to estimate a stock's expected

mean return. This "comparison period" is then compared with

the daily rates of return over the period of rating change.

Because our research focuses on financial distress and

bankruptcy, both of which are long-term processes, we selected

a two-year time period before the event as the "comparison

period." Since there are a different number of business days

in any given year, we simplified things by defining 510

business days as "two years." Thus, our comparison period is

510 days to 11 days before the rating change. The actual

event, the bond rating change, is taken as the 21-day period

beginning ten days before and ending ten days after the

downgrade announcement.

For this study, we construct a sample of companies that

were listed on the New York or American Stock Exchanges, that

had bond downgrades, and that later filed for bankruptcy. We

then found a matching sample of companies that satisfied the

first two criteria but did not later file for bankruptcy.

Once we have used our comparison period to determine a

stock j's mean daily return, Aj, the event period disturbance

term Et, which measures the impact caused by the bond rating

change, is given by:

Ejt = Rjt ~j,





20

with t being the date in the comparison period,
t = -10..10,
where Rj is the realized daily return of the
stock j at time t, which was read from the
CRSP Daily Return Tape.

The average disturbance term for N events (firms) is:

avg E, = 1/N (E Eit)

with j = 1..N.

The null hypothesis, avg Et equals zero, means that a downward

bond rating change has no effect on shareholders' daily

returns. Since we believe that the first downgrade of a bond

gives the earliest signal and, hence, the most information to

stockholders about the risks of financial distress, we expect

the null hypothesis to be rejected for our Chapter 11 sample.

Conversely, we expect not to be able to reject the above null

hypothesis for our matching sample of firms that did not file

for Chapter 11.

The variance of avg E. is:

Var (E) = (1/499) E (avg Et X(E))

where X(E) = (1/500) Z (avg Et)

When t=0, we would be testing for the disturbance on event

date. The t-statistic used to determine whether avg E0

differs significantly from zero with 499 degree of freedom is:


t = avg E0 / J (Var (E))

The cumulative error over a particular event time interval is:

CE(a,b) = Z (avg Et)

where -10 5 a < b < +10






21

We hypothesize that the cumulative errors in the bankrupt and

matching groups are statistically different, implying

different effects of bond rating changes on stock rates of

return.

Finally, we separate the Chapter 11 group into two sub-

groups: one sub-group of companies that filed for Chapter 11

and later re-organized and another of companies that filed but

were later liquidated. We compute an average Et for bond

downgrades of companies in the two sub-groups. Then, we

employ the t-test and F-test to analyze the differences for

statistical significance between the two sub-groups. The null

hypothesis is that the means for the two sub-groups of

companies should become statistically equivalent. By

reasoning explained previously, we expect that the null

hypothesis will be rejected. Thus, we expect the means for

the two sub-groups of companies to become statistically

significantly different as we approach the filing of Chapter

11.






22




Note

1. A company, by our definition, is "liquidated" if it
satisfies one or more of these conditions:

1. acquired by another company or liquidated
2. listed on COMPUSTAT as "bankrupt"
3. no longer on the Wall Street Journal Index
4. no longer on the Predicasts F&S Index of Corporate
Change
5. no longer on Q-file
6. no longer on the Directory of Corporate Affiliations
7. no longer listed on the C-D System
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CHAPTER 4
RESULTS ON FINANCIAL MARKETS AND BANKRUPTCY



For our research on risk premia and bankruptcy, we

computed and drew risk premium curves for each of our 50

companies' bonds. (These curves are presented in the

Appendix.) A solid line indicates a bond rating change by

S&P, a dotted line one by Moody's. The arrows on the graphs

indicate a bond upgrade.

In 80% of our sample, or 40 of the risk premium curves,

there is a definite upward trend: risk premia rise steadily

as the company approaches bankruptcy. Nine (18%) have

ambiguous, fluctuating trends, and only one, or 2% of our

sample, shows a downward trend where the risk premium on its

bond actually fell as it moved towards bankruptcy. Hence, our

data suggest that the market generally incorporates the

likelihood of bankruptcy adequately in its overall assessment

of risk and includes this particular risk in the valuation of

securities.

When we compare the relationship between bond rating

changes and risk premia curves, we find that for most cases

where there was an obviously increasing risk premium, the





28

rating downgrade came after the risk premium had begun to

increase. Hence, in the short-term, a lag of one to seven

months does exist. This conclusion confirms that of Weinstein

(1977), who found that markets had anticipated bond rating

changes 18 to six months before the change. It, however,

conflicts with Katz (1974), who concluded that yield-to-

maturity adjusted to the rating change six-to-ten weeks after

it happened. We believe the reason for this discrepancy is

that for measuring market-assessed risk, our risk premium, a

relative value, is better than the yield-to-maturity, an

absolute value, used by Katz. This is because while factors

such as added risk and inflation would eat away the nominal

returns of yield-to-maturity and bias the results of any study

based on it, risk premium would account for such factors and

hence provide an accurate indication of the returns on the

bond.

Our data, then, seem to suggest that bond ratings, though

popular since the early 1900's, cannot predict risk premium

changes or any upcoming default. We believe, however, that

the lag phenomenon is not particularly meaningful. For

example, a bond downgrade that trails an increase in the risk

premium may lead a later increase. Since bond rating changes

should warn investors of coming bankruptcy and default, what

really matters in the long-run is whether a bond rating

provides new information to the market on companies that later

went bankrupt. That can be determined only by seeing if bond






29

rating changes have any impact on the market. Assuming that

the first bond downgrade provides the market with the greatest

amount of new information about changes in risk, we must

further study the impact of the first bond downgrade on the

market.

Our data can be used to compare the two rating agencies,

S&P and Moody's, to see which warns investors earlier. Table

3 gives the relevant information. On average, S&P gave the

first bond downgrade 24.54 months before a company filed for

Chapter 11, while Moody's gave the first consistent bond

downgrade 21.58 months, or 2.96 months after S&P, before a

company filed for Chapter 11. Out of a sample of 50

companies, there were five bonds that received no downgrades

whatsoever from S&P's and six that received no downgrades

whatsoever from Moody's before the companies which issued them

filed for Chapter 11 bankruptcy. Although there was no rating

change, the markets did foresee the coming bankruptcy, and the

risk premia on these bonds began increasing an average of

three to five months before Chapter 11. Finally, six

companies which S&P's rated were not rated at all by Moody's.

Hence, it would seem that in this specific instance S&P

provided more timely and more complete bond ratings and

changes than Moody's in the sample and for the period we

studied. We emphasize that this is a one-sided test only, and

that it by no means can be thought of as a definitive

conclusion.





30

As described earlier in Chapter 3, we divided the sample

of companies which filed Chapter 11 into those that later re-

organized and those that were liquidated. Nine out of the 50

companies in our sample were "liquidated," while the other 41

re-organized. The average risk premium curves for these two

groups are shown in Figure 1. From this graph, we can roughly

conclude some interesting patterns. Long before Chapter 11,

the companies that would eventually be liquidated had lower

risk premia than those which would later re-organize. The two

groups had about the same risk premia 41 to 27 months before

Chapter 11. Then, as the companies approached bankruptcy,

risk premia of companies which were later liquidated rose

steadily above those of later re-organized companies.

After performing t-tests with Montgomery's formula for

the three periods (65-to-42 months before bankruptcy, 41-to-

27 months before bankruptcy, and 26-to-i months before

bankruptcy), however, we found that this was not so. We had

tested for the null hypothesis that the means between the two

groups during each month were equal. During the first period

of 65-to-42 months before bankruptcy, 20 out of 24 (83%) t-

tests were significant, and all t values were negative. By

our definition for t, this means that the mean values of risk

premia for the later liquidated firms are lower than those for

later reorganized firms. During the second period, however,

12 out of 15 (80%) t-tests were significant, and 12 of those

15 t-tests were positive. This means, contrary to what might






31

be discerned from the graph, that the mean values of risk

premia for later liquidated and later reorganized firms were

different and that the mean risk premia of the later

liquidated firms were higher. Hence, although from just

looking at a graph we had thought that the differences, which

were clearly visible, would not be statistically significant,

the t-tests show that this is not so. Finally, during the

third period, 19 out of 26 (73%) t-tests are significant, and

only one of the 26 was negative. All other t-tests during

this final period were positive. This means that during the

final period, the mean risk premia of later liquidated firms

were also significantly greater than those of the later

reorganized firms, as we had expected from looking at the

graph. Table 4 gives the means and the t-tests.

This means that the market can sense the coming of

liquidation and therefore place an added risk premium to such

risk much earlier than the 27 months we had earlier expected.

For our event study of the effects of the bond downgrade

on the daily rates of return, we first had to find the exact

press release dates of the bond rating changes. We selected

only those companies that were listed on the New York or the

American Stock Exchanges.1 Because we could not find relevant

data for two continuous years from the COMPUSTAT Daily Return

tape for all our companies, some of the observations in our

sample had to be dropped. This left us a samples of 22 pair

of bankrupt and matching companies. The matching samples have






32

equivalent downgrades during the same time period, but did not

later file Chapter 11. The companies in the two samples are

listed in Tables 5 and 6.

Tables 7 through 10 give the statistical results of our

event study. In Table 7, the t-statistic for testing the null

hypothesis that the average disturbances at event day, E,(0),

equals zero for the Chapter 11 group is -21.81, with 499

degree of freedom. This t-statistic is significant at the

0.5% level. Thus, as expected in the Research Design and

Methodology section, the null hypothesis that the average

disturbance at the event day for the Chapter 11 group is zero

can be strongly rejected. For the matching sample, however,

the t-statistic for testing E2(0) equals zero is -1.45, which

is significant only at a marginal level. The negative signs

on both the t-statistics mean that bond downgrades negatively

affect shareholder wealth.

To see if the means in the Chapter 11 and matching

samples are equal, we employ a special t-test (see

Montgomery(1984)), which is suitable for cases when we cannot

assume equal variances and when the number of observations is

less than 30. The t-statistic for testing the equality of two

means is -15.545, with 42 degree of freedom. It is

significant at the 0.5% level, so the null hypothesis that the

two means are equal is rejected. This means that the daily

rates of return of companies in the Chapter 11 sample suffered

more with bond downgrades than those in the matching sample.






33

The variances of the two groups, as given by the F-test, were

not significantly different.2

Table 8 shows the statistical analysis of the two sub-

groups in the Chapter 11 sample, the companies which re-

organized and those that were liquidated. The t-statistics

are -4.98 for companies which later re-organized and -26.94

for companies which did not. Since both are significant, the

null hypotheses are rejected. Using Montgomery's formula, we

find that the t-test is -0.32 with 9 degree of freedom, which

is not significant. Hence, the two means are not

statistically significantly different. Finally, the variance

of the re-organized companies is lower than that of the

companies which were later liquidated.3

Tables 9 and 10 give the daily prediction error and

cumulative daily prediction errors in the 21 days surrounding

the downgrade announcement. Figure 2 shows the cumulative

error curves for both the Chapter 11 and the matching samples.

These curves show that the rating downgrades had a definite

negative impact on the daily rates of return. Most

importantly, the relationship between these two curves tells

us that the impact of the first bond downgrade is much more

severe on companies which would later file for Chapter 11 than

those that would not. Hence, we may conclude that the market

does react to downward rating changes and that the rating

agencies therefore do provide significant new information to

the market with rating changes. These results conflict with






34

those of previous works mentioned in Chapter 2. We believe,

however, that the issue is still very much unresolved, as can

be seen by the seemingly contradictory results of Griffin and

Sanvincente (1982). Therefore, our work should contribute to

the ongoing debate.












Notes

1. Our two criteria for selecting companies into the Chapter
11 and matching samples for event study were:

1. The companies had to be listed either on the New York
or the American Stock Exchanges.
2. There must be two years of continuous data available
for the companies.

2. The F-test value is 1.13, with degree of freedom (21, 20).
This F-value is not significant, so the variances of the two
groups are not significantly different.

3. The F-test value is 8.13 with a positive sign, and it is
significant at the 1% level.












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+ Reorganized Firms


Figure 1. Risk Premia Curves Comparison

Risk premia trends for companies that filed for Chapter 11
and later re-organized versus those that filed and were later
liquidated.









Table 4. T-Test of Risk Premia Trends


Time MeanI Mean2


16.70
11.46
10.38
6.08
8.31
7.12
6.80
6.80
6.86
5.98
7.42
7.33
6.73
6.19
6.14
6.42
4.73
5.10
5.04
4.88
5.74
4.49
4.23
4.32
4.32
4.46
4.54
3.99
4.04
3.95
3.33
3.50
3.80
3.80
3.83
3.82
3.44
3.51
3.70
3.50
3.56
3.32
2.56
1.87
1.72
1.89
1.71
2.08


11.18
8.08
7.43
7.11
6.22
5.68
5.55
4.89
4.78
4.65
4.47
4.41
4.45
4.42
4.23
4.00
4.04
3.81
3.74
3.66
3.49
3.73
3.49
3.58
3.58
3.57
3.77
3.75
3.49
3.48
3.53
3.34
3.34
3.30
3.29
3.25
3.72
3.53
3.39
3.49
3.46
3.45
3.49
3.20
3.26
3.12
2.89
3.08


Diff.


5.51858
3.37600
2.94731
-1.02914
2.08476
1.43333
1.25468
1.90249
2.08516
1.32662
2.94818
2.92675
2.28420
1.77084
1.90900
2.42500
0.68789
1.28795
1.30813
1.22106
2.25051
0.76234
0.74654
0.74654
0.74759
0.88553
0.77331
0.24753
0.55032
0.46810
-0.19686
0.16256
0.45914
0.50408
0.53727
0.56812
-0.28775
-0.01832
0.30900
0.01545
0.10248
-0.12621
-0.93164
-1.32963
-1.53593
-1.22093
-1.17630
-0.99972


t-test


5.969257
3.651703
3.188007
-1.113180
2.255015
1.550387
1.357147
2.059800
2.255444
1.434954
3.188950
3.165763
2.470741
1.915457
2.064899
2.623039
0.744070
1.393130
1.414961
1.320781
2.434302
0.824601
0.807508
0.807508
0.808646
0.957843
7.588362
2.428966
5.400186
4.593351
-1.931730
1.595207
4.505502
4.946421
5.272179
5.574928
-2.823640
-0.179790
3.032172
0.151591
1.005648
-0.897810
-6.627130
-9.458170
-10.925600
-8.684910
-8.367450
-7.111410


s.l.

0.5%
0.5%
0.5%

2.5%
10%
10%
5%
2.5%
10%
0.5%
0.5%
2.5%
5%
5%
2.5%

10%
10%
10%
2.5%





0.5%
2.5%
0.5%
0.5%
5%
10%
0.5%
0.5%
0.5%
0.5%
1%

1%



0.5%
0.5%
0.5%
0.5%
0.5%
0.5%








Table 4--continued.


1.68
1.97
1.74
1.80
1.84
1.84
1.80
1.74
1.88
2.08
2.49
2.00
2.45
1.83
2.45
2.49
2.72


2.79
2.52
2.79
2.68
2.89
2.73
2.93
2.86
2.76
2.77
2.50
2.57
2.62
2.73
3.04
2.91
2.87


"MeanI and Mean." are the risk premia means for the later
liquidated and later reorganized firms, respectively. "Diff."
is their difference. "t-test" is the value of the t-test, and
"s.l." is the significance level.


-1.10180
-0.55000
-1.04960
-0.87340
-1.04792
-0.88565
-10.14058
-1.11917
-0.87986
-0.69457
-0.10409
-0.57091
-0.17650
-0.89842
-0.58684
-0.42263
-0.14889


-7.837530
-3.912360
-7.466210
-6.212830
-7.454230
-6.299980
-7.996630
-7.961060
-6.258740
-4.940710
-0.100230
-4.061090
-1.255510
-6.390810
-4.174430
-3.006340
-1.059100


0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%

0.5%

0.5%
0.5%
1%






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Table 7. T-test for Chapter 11 (bankrupt)
and Matching Samples: Event Study Results


Chapter 11 Sample


Matching Sample


E1(0)
Std.


-0.03199700
0.00687700


H0: E,(0) =,0,
tI = -21.98
(d.f. = 499,
significant at 0.5%)


E2(0)
Std.


-0.00203900
0.00645500


Ho: E2(0) = 0,
tg = -1.45
(d.f. = 499,
significant at 10%)


HO: E1(0) = E2(0)
t-test = -15.545 (d.f.= 42)
(significant at 0.5%)









Table 8. T-test for Sub-Groups of Chapter 11
Companies: Those which were Liquidated and those which
Reorganized


Liquidated Group

E,(0) -0.03293800
Std. 0.01980400

Ho: E,(0) = 0,
t, = -4.98
(d.f.: 499,
significant at 0.5%)


Reorganized Group

E2(0) -0.02922600
Std. 0.00694700

H0: E2(0) = 0,
t2 = -26.94
(d.f.: 499,
significant at 0.5%)


Ho: E,(0) = E2(0)
t-test = -0.32 (d.f.: 9)









Table 9. Disturbance Resulting from Bond Downgrade on
Chapter 11 (Bankrupt Sample) and Statistical Analysis


Event
Day


CE
m%


avg E(t)
-Ml}

-0.006464
-0.007603
-0.001908
-0.001019
-0.016982
0.001227
-0.002338
-0.005651
-0.007840
-0.009647
-0.031997
0.018805
0.022623
0.002346
0.002065
-0.008776
-0.034234
0.014345
-0.029843
0.021802
-0.008666


Variable

E(-l)
E(0)
CE(-10,0)
CE(-5,0)
CE(-3,0)
CE(-1,0)
CE(+1,0)
CE(+3,0)
CE(+5,0)
CE(+10,0)
CE(-10,10)


Value(%)

-0.009674
-0.031997
-0.090222
-0.056246
-0.055135
-0.041644
-0.013192
0.011777
0.005066
-0.031530
-0.089755


t-statistic


-1.41
-4.65
-3.38
-2.11
-2.06
-1.56
-0.49
0.44
0.19
-1.18
-3.36


10.0%
1.0%
0.5%
2.5%
2.5%
10.0%


* 0.5%


The t-test for CE is:
t = CE*(N/2)/(Std(CE)* (T12))


-0.006464
-0.014067
-0.015975
-0.016994
-0.033976
-0.032749
-0.035087
-0.040738
-0.048578
-0.058225
-0.090222
-0.071417
-0.048794
-0.046448
-0.044383
-0.053159
-0.087393
-0.073048
-0.102891
-0.081089
-0.089755


-10
- 9
- 8
- 7
- 6
- 5
- 4
- 3
- 2
- 1
0
1
2
3
4
5
6
7
8
9
10








Table 10. Disturbance Resulting from Bond Downgrade on
Matching Sample and Statistical Analysis


Event
Day


CE
IAm


avg E(t)
Xll

-0.012418
-0.022204
0.018645
0.003892
0.010662
0.004340
0.013230
0.005412
-0.010702
0.002165
-0.002039
0.007029
-0.000817
-0.019285
0.001402
-0.003376
-0.000191
0.001111
0.005467
0.004831
-0.004599


Variable

E(-1)
E(0)
CE(-10,0)
CE(-5,0)
CE(-3,0)
CE(-1,0)
CE(+1, 0)
CE(+3, 0)
CE(+5, 0)
CE(+10,0)
CE(-10,10)


Value (%)


0.002165
-0.002039
0.010983
0.012406
-0.005164
0.000126
0.004990
-0.015112
-0.017086
-0.010467
0.002555


t-statistic


0.34
-0.32
1.13
1.28
-0.53
0.01
0.51
-1.56
-1.76
-1.08
0.26


* 10.0%
* 5.0%


The t-test for CE is:
t = CE*(N"1)/(Std(CE)* (T12))


-0.012418
-0.034622
-0.015977
-0.012085
-0.001423
0.002917
0.016147
0.021559
0.010857
0.013022
0.010983
0.018012
0.017195
-0.002090
-0.000688
-0.004064
-0.004255
-0.003144
0.002323
0.007154
0.002555


-10
- 9
- 8
- 7
- 6
- 5
- 4
- 3
- 2
- 1
0
1
2
3
4
5
6
7
8
9
10






















0.03

0.02

0.01

0

-0.01

-0.02

-0.03

-0.04

-0.05

-0.06 -

-0.07 -

-0.08 -

-0.09

-0.1

-0.11 I
-10 -9 -8 -7 -6


0 Chapter 11 Sample


-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10


Day Surrounding Event
+ Matching Somple


Figure 2. Disturbance Due to Bond Downgrade

This graph compares the disturbance caused by a bond downgrade
on companies in the sample which filed for Chapter 11 and in
the sample which did not file for bankruptcy.














CHAPTER 5
EMPIRICAL MODEL OF BANKRUPTCY


The evidence that bond rating downgrades provide new

information to the market suggests that proper analysis of

fundamental corporate factors, such as the ones presumably

used by S&P's and Moody's, can give an early warning of

impending financial difficulties. Even so, there are at least

four problems with using bond downgrades as the sole or

primary indicator of bankruptcy risk. First, many firms whose

bonds are downgraded never experience significant financial

stress. In fact, a company may simply be trying to modify its

risk-return balance and better reposition itself in the market

place to capitalize on future opportunities. Second, although

our event study identified a differential effect between the

companies that eventually filed for protection under Chapter

11 of the bankruptcy code and those which did not have to seek

protection, that does not mean we can easily tell between the

two before the fact. In other words, how much of a difference

is "significant?" Third, S&P's and Moody's sometimes give

conflicting signals, and there have been cases where the

downgrade either does not predate the bankruptcy filing by






49

very much time or there is no downgrade at all. Finally, it

appears that consistent signals start appearing only

approximately two years ahead of the Chapter 11 filing,

assuming, of course, that they can be correctly interpreted.

Thus, bond downgrades give us about as much forewarning as the

ZETA model of Altman et al., and the latter model is probably

more a practical predictor of bankruptcy than bond downgrades.

Hence, we believe that proper analysis of fundamental

corporate characteristics would provide us with a more

effective empirical model which could determine bankruptcy

risk. What we would need is an indicator which can alert

investors and managers of developing circumstances that would

normally lead to increased probabilities of bankruptcy long

before it actually becomes necessary to file for protection

under Chapter 11. Such an indicator would allow investors to

make more informed portfolio allocation decisions, and it

would signal to corporate managers that corrective actions

need to be taken before financial difficulties become serious.

We believe that if such an indicator can be found and used to

predict financial distress and possible bankruptcy up to five

years ahead of potential bankruptcy, then the scarce resources

in the economy can be better allocated.

Current bankruptcy prediction models, however, have not

shown that they can reliably forecast bankruptcy risk more

than two years ahead of filing of Chapter 11. In fact, there

is very little evidence to date that it is even possible to





50

detect the roots of financial distress up to five years ahead

of an actual crisis. Our main purpose in this part of the

dissertation, then, is to explore this issue: can a bankruptcy

prediction model be designed that maintains significant

forecasting powers up to five years ahead of the date of

Chapter 11 filing? While we would also like to develop a

model that can surpass the predictive powers of the ZETA model

in the short-run while also preserving that power over five

years, we do not, in this dissertation, intend to search

specifically for such a "best" model. That task will be left

for future research after we have shown that it is possible

to maintain high levels of accuracy over the long-run.

Present-day finance literature does not provide us with

many works that have looked at the relationship between

various types of risk, such as bankruptcy risk, and companies'

fundamental characteristics. Zavgren (1985) provides some

evidence that asset efficiency is an important indicator which

may be of use to us, but we believe that other variables would

also be needed. Derkinderen and Crum (1988) developed a

framework known as the Potential and Resilience Evaluation

(PARE) model on the issues of long-term risk-return balance.

This framework suggests some possible variables which can be

used to assess the fundamental and strategically crucial

characteristics of a company. Basing our views from such a

fundamental perspective, as suggested by Derkinderen and Crum

(1988) and Zavgren (1985), we have arrived at a list of eight






51

variables which can assess both the short- and long-run

dimensions of the bankruptcy problem. We now turn to a

discussion of these variables and the roles they would play

in our study of long-term bankruptcy risk.


Variable Definitions


We selected our eight variables out of many potential

candidates. In selecting them, we aimed to find the minimum

number of factors that together provide signals about both

short- and long-run aspects of the companies, in isolation as

well as relative to other companies in their core industry.

Our reasons for selecting these variables were also partially

based on the availability of data, although these variables

are considered to be good indicators of differences between

the more successful companies and those with lackluster

performance records. These variables can roughly be divided

into two groups: 1). those which assess company operating and

profitability characteristics (which will be referred to as

"the Group I variables"), and 2). those which assess

fundamental company characteristics (which will be referred

to as "the Group II variables.") Existing bankruptcy

prediction models focus mostly on relationships that would be

included in the first group. Although these factors are

obviously important to bankruptcy, particularly in the short-

run, we contend that the second group must also be considered

if the model is to have adequate long-term predictive powers.





52

Four variables are included in Group I to measure the

company's financial and operating positions. The first is

return on assets, or ROA, defined as EBIT/TA. This is the

basic earning power ratio and is a strong signal of

profitability. We consider that it is a particularly good

representation of the company's performance in implementing

growth in the past. The second variable in this category is

the fixed charge coverage ratio, FCC. This ratio measures

simultaneously a company's level of debt and how well its cash

flow covers the servicing requirements of debt. It is one of

the most important indicators of the ability of the firm to

survive adversity in the short-run. The third variable is the

market-to-book ratio. The market-to-book ratio measures

investors' confidence in the firm and, as a direct result, how

well the company can tap into the equity market for capital.

In other words, this ratio indicates the extent to which

investors believe that the firm has good growth opportunities

for the future. A ratio greater than one indicates that the

return from reinvested earnings is expected to exceed the

required rate of return. Finally, the balance ratio of

income and sales, defined as the difference between the growth

rates of income and sales, focuses on the profitability of

incremental sales. It measures whether the company is

boosting sales at the expense of profits and, therefore, may

be heading into financial problems even as it continues to

expand market share.






53

To assess the second category of difference indicators,

the Group II variables which measure company fundamental

characteristics, four additional variables are used. First,

ownership assesses the agency effects of the company's

management. According to the agency theory literature, such

as Jensen and Meckling (1976), when the shareholders contract

with the management for the latter to serve the former as

agents, some cost is inevitably involved, including a dead-

weight loss. This cost occurs because management and

shareholders in most corporations (particularly the larger

ones) are usually distinctly separate groups, and they likely

have differing, even conflicting, interests. For example,

management of America's top 200 firms own only 0.1 percent of

their companies' stock, and nearly one out of ten Fortune 500

Chief Executive Officers own no stock at all in their

companies. Because of such low ownership stakes, many

scholars have questioned whether such managements really serve

the shareholders' interests. As a result of questions such

as this, management ownership has become a topic of interest

and discussion in recent years. We agree that this topic is

important and relevant to our needs in this dissertation. We

believe, however, that absolute ownership measures are not as

significant as the net transfer of ownership, which measures

whether management, as a whole, increased or decreased its

ownership share of the corporation during a period of time.

Assuming that management has information the average





54

shareholder does not, then whether a management is a net

purchaser or a net seller of the company's stock shows

management's confidence in its own projects. Further, it also

shows whether management is committed to the success of the

company or whether it is simply "grabbing for parachutes."

To incorporate these ideas into the model, we include the net

rate of management stock acquisitions as a variable, defined

as the difference between management purchases and sales of

the company's stock, measured in percentages of total equity.

The second variable in this category is the capital

intensity ratio, defined as total assets divided by sales.

This ratio measures how much a company must invest in assets

to expand its sales. Thus, it indirectly tells us both the

structure of the industry and how much the company will have

to rely on fresh capital to fuel growth. In this

dissertation, though, we do not follow the traditional

definitions of industry as given by COMPUSTAT or Dun &

Bradstreet. Rather, developing from the ideas of Tse (1987),

we regroup the COMPUSTAT SIC codes so as to define 24 lines

of industry by the nature of the business. These definitions

of industry, along with the growth rate and bankruptcy rate

of each industry, are presented in Table 11. As Table 11 and

Figure 3 show, a company's line of business does impact

significantly on bankruptcy. While the specialty

manufacturing industry (code #19) had a 13% cumulative

bankruptcy rate during the 1968-1987 period, the chemicals






55

(code #4) and utilities (code #20) industries suffered only

about a 1% cumulative bankruptcy rate during the same period.

Expanding on the information about competitiveness

contained in the industry characteristics, and to assess a

company's position within its industry, we employ the relative

sales growth ratio. This ratio is the difference between the

sales growth rate for the primary or core industry in which

the company competes and the rate of growth of the company's

sales. It indicates the competitiveness of the company within

its major industry in terms of its ability to gain market

share. It also complements the balance ratio of income and

sales, the Group I variable that measures whether the company

has gained market share at the expense of profit margins.

The final variable in the Group II variables set is the

relatedness ratio, as described by Rumelt (1982). This

variable assesses a company's diversification program in that

it indicates the extent to which the company focuses its

efforts on a portfolio of related businesses that could be

expected to have synergistic interdependencies. It is

calculated as:

(% of assets in related segments)
-----------------------------x (number of segments 1)
(number of segments)

and determines whether a company is a "single business" (a

value of zero), "unrelated diversified" (a low positive

value), or "related diversified" (a high positive value). As

Rumelt (1980) points out, different strategies of





56

diversification can strongly affect a company's long-term

prospects, and the degree of relatedness should assess the

benefits of those diversifications. According to Rumelt, the

higher the relatedness ratio the greater the chances of good

performance.

The eight variables described above cover the two broad

categories and also collectively address the various

dimensions of the PARE framework, which are: 1) the extent to

which the firm has good growth opportunities available; 2)

whether or not the market perceives that the company can

exploit the growth opportunities successfully; 3) the degree

to which the fortunes of the firm are subject to foreseeable

adversities in the future; 4) whether or not the firm has the

ability to survive such adversities.

Role of Variables in the Model

The model of bankruptcy risk developed in this

dissertation includes the eight variables discussed above and

uses them to derive a summed probability of bankruptcy. Using

Logist Analysis, which will be discussed in Chapter 6, a

probabilistic function of a cumulative score of z is derived

which, in turn, is composed of these eight factors:

P = f(z), where f' > 0.

z = ao + biX, + b2X2 + ... + bSX8,

where bl.. are coefficients,
X1 is ROA (EBIT/TA),
X2 is FCC,
X3 is Balance Ratio,
X4 is Market/Book Ratio,
X5 is Relatedness Ratio,








X6 is Net Rate of Management Stock Acquisitions,
X7 is Relative Sales Growth Rate,
X8 is Capital Intensity.


Hypotheses


Because the methodology used in this dissertation, Logist

Analysis (discussed in Chapter 6), develops a model in which

the coefficients can reveal the role each variable plays, we

can hypothesize about how each factor in the model affects

overall assessment of bankruptcy risk. Specifically,

according to our model, a negative beta means that the larger

the variable, the less the chance of bankruptcy. Similarly,

a positive beta means that the larger the variable, the

greater the chance of bankruptcy. If any of the variables

are able to take on negative values, the rules given above

about the sign of the coefficient should be reversed. We

hypothesize that all coefficients bi through b8 should be

negative.

The coefficients for return on assets, fixed charge

coverage, and the market-to-book ratio should be obvious. In

principle, the sales-income balance ratio's coefficient is

negative because if income is growing more briskly than sales,

then the company is experiencing widening profit margins,

which would inevitably lead to higher profitability and even

more growth in the future. Since long-term considerations

sometimes make it necessary to sacrifice short-run

profitability to drive out the competition and gain market





58

share, however, even good, solid companies may have negative

values for this ratio. Hence, our confidence about the sign

of this particular coefficient is less than for those of the

first three variables. More important than the sign, though,

is the idea that the balance ratio for the bankrupt companies

should be significantly different than the ratio for non-

bankrupt companies.

The relatedness ratio's coefficient is negative because

a larger relatedness ratio indicates that a company is

diversified into related lines of business, which means, as

Rumelt (1982) shows, that the company will be able to achieve

real product synergy and counter-cyclicality. The net rate

of stock acquisition is also expected to be negative because

that signals net purchase of stock by management. This is a

signal that management expects the firm to be profitable in

the long-run.

The coefficient for by, relative sales growth, is

negative because we expect that companies with good relative

sales growth rate will have a negative value for the variable,

and a negative coefficient is needed to reverse the impact on

the chances of bankruptcy. Finally, the sign of the

coefficient for capital intensity is negative because, as

Ohlson (1980) points out, larger capital intensity is

associated with larger company size, and larger industrial

companies do not go bankrupt as easily as smaller ones. On

the other hand, though, to the extent that the reciprocal of






59

the capital intensity ratio is an indicator of asset

efficiency, the negative sign would be counter to the findings

of Zavgren (1985).








Table 11. Industry Classification,
Growth and Bankruptcy Rates


Industry
Number Industry


Food
Clothing & Textiles
Paper & Publishing
Chemicals

Drugs
Petroleum Refining
Rubber & Leather
Glass & Cement
Metals


COMPUSTAT Growth
SIC Rate

2000-2199 8.94%
2200-2399 5.41%
2600-2799 9.51%
2800-2839,
2840-2899 10.84%
2830-2839 11.42%
2900-2999 12.82%
3000-3199 5.33%
3200-3299 7.45%
3300-3499 6.28%


10 Industrial Machinery 3500-3569,
3580-3599 6.33%
11 Office Machinery & 3570-3579,
Electronic Equipment 3650-3679 8.71%
12 Electrical Equipment 3680-3699 14.38%
13 Motor Vehicles 3700-3799 7.96%
14 Scientific &
Surveying Equipment 3800-3899 8.58%
15 Transportation 4000-4599,


Agriculture
Extractive
Construction

Specialty Manuf.
Utilities
Wholesale
Consumer Products
Services
Financial


4700-4799 11.20%
0100-0999 10.42%
1000-1499 10.48%
1500-1799,
2400-2499 9.93%
3900-3999 7.02%
4800-4899 14.37%
5000-5199 10.51%
5200-5999 8.78%
7000-8999 12.39%
6000-6799 19.00%


Bankruptcy
Rate

2.3622%
8.1633%
3.9130%

1.1062%
N/A
1.6393%
0.9788%
2.5000%
3.3898%

2.3490%

6.8452%
8.7805%
6.2201%

3.9474%

11.2245%
2.6316%
5.4217%

5.2239%
13.0435%
1.3245%
6.5421%
4.4983%
3.7516%
2.5097%


Growth Rate is the average annual growth rate of the industry
between 1968 and 1987. Bankruptcy Rate is the percentage of
businesses that failed during that period.





















































I I I


I I II III I II I I III II


1 3 5 7 9 11 13 15 17 19 21 23
2 4 6 8 10 12 14 16 18 20 22 24
Industry Code


Industry and Bankruptcy Rate


14,



12


10


8


Ku
i6


ps________^ _____ &____
\ ^ \

^ ^ $

G n------ ^ -- --


Cum. %


Figure 3.














CHAPTER 6
METHODOLOGY TO TEST EMPIRICAL MODEL


The Logist Analysis Methodology


The methodology used in this dissertation to build the

empirical bankruptcy model is logist analysis.

Logist analysis is a statistical method that computes the

conditional probability that a given observation belongs to

a particular class of observations if certain variables about

the observation are known. Based on a cumulative probability

function, this model does not require that independent

variables be multivariate normals or that the classes have

equal covariance matrices. Instead, the model is solved using

the maximum likelihood method. Thus, logist analysis reduces

the fundamental bankruptcy estimation problem to the

following: given that a company belongs to some pre-specified

population, what is the probability that this company will

fail within some pre-specified period of time?

Ohlson (1980), which was discussed earlier in the

Literature Review section, was probably the first work on

bankruptcy to use logist analysis. Although the research did






63

not produce a significantly viable model, the work

nevertheless provided some interesting insights into the use

of logist analysis for empirical studies of bankruptcy. In

Ohlson's model, Xi denoted a vector of predictors for company

i, p denoted a vector of unknown parameters, and P(Xi, 8),

where P is a probability function (0 P < 1), denoted the

probability of bankruptcy for a given set of vectors Xi and P.

The logarithm of the likelihood of any specific outcome, as

reflected by the binary sample space of bankruptcy versus non-

bankruptcy, is given by:

L(3) = Z log P(Xi, P) + E log (1 P(Xj, P)),

where i, j are elements of the S1 index set of bankrupt

companies and S2 index set of non-bankrupt companies,

respectively. For any specified function P, the maximum

likelihood estimates of P1, P21, ** Pn are obtained by solving:

max, L(P).

Because we do not as yet have a full theory of

bankruptcy, however, we cannot easily find an appropriate

class of functions P. As a practical matter, therefore, we

can only select a function for the sake of computational and

interpretative simplicity. One such function is the logistic

function:

P = (1 + exp{-yi))',

where y, = EZ jXij = P'Xi.

This formula has two implications. First, P is increasing in

y. Second, y is equal to log (P / (1 P)).





64

Like discriminant analysis, logist analysis weights the

independent variables and creates a score for each company.

The Z score obtained may be used to determine the probability

of membership in a group where:

Probability of bankruptcy
= 1 / (1 + exp(-z))
= 1 / (1 + exp(-a + blX + ... + bpXp)).

The b coefficients are weighted so as to maximize the joint

probability of bankruptcy for the known bankrupt companies and

the probability of non-bankruptcy for those companies that did

not go bankrupt. Unlike the coefficients derived from

discriminant analysis, these coefficients tell us the role

that each individual variable plays in the overall empirical

model. Therefore, we can use them to analyze which factors

are the most significant in long-term bankruptcy forecasts.


Loqist versus Discriminant Analysis



Much previous bankruptcy work, most significantly Altman

et al. (1977), has employed the traditional linear

discriminant analysis, although both the linear and the

quadratic forms have been used. For our dissertation, though,

we consider that logist analysis can yield a superior model

because logist analysis does not share many of the problems

faced by discriminant analysis.

First, linear discrimination is basically a multivariate

technique that assigns a score to each element in a sample






65

using a linear combination of independent variables. The

multivariate approach is very appealing because it reduces

several financial dimensions of a problem to a single score.

In general, such reductions have been quite successful. The

bankruptcy models derived from discriminant analysis tend to

have high classification accuracies, at least in the short-

to medium-terms. Serious questions, however, have been raised

about whether so many factors and dimensions of a complex

financial problem like bankruptcy can validly be reduced to

a single score, or whether crucial information would be lost

during the process of such a reduction.

Second, discriminant analysis has several statistical

requirements that are difficult to meet for most samples.

For discriminant analysis to work, the independent variables

must be multivariate normals, and the covariance matrices of

the original and hold-out groups must be equivalent. In

practice, satisfying both assumptions is difficult. The

requirement that the independent variables have multivariate

normal distributions, for example, is frequently violated.

It will be violated whenever a dummy independent variable,

such as the time variable t, is used. Although some remedial

measures, such as log transformations, square root

transformations, and elimination of outliers can be used, such

methods have unclear economic implications which are often too

easily ignored. Further, in many cases the requirement that

covariance matrices be equal is also violated. This means





66

that the group covariances are not statistically equivalent,

as indicated by Box's F statistic.

A way to avoid the latter problem of unequal covariances

is to use quadratic discriminant analysis. Unlike linear

discrimination, the quadratic form does not require that

covariances must be equal. Instead, quadratic discriminant

analysis assesses the covariance of each group independently

as it builds a model. The problem, however, is that quadratic

discriminant analysis is not nearly as widely used as linear

discriminant analysis, and there are also questions about its

model-building powers. Altman et al. (1977) and Marks and

Dunn (1974) both reported that linear discriminant analysis

could achieve greater classification success than quadratic

discriminant analysis. The Marks and Dunn paper reached this

conclusion for samples where the group variances are similar,

the group means are far apart, the sample sizes are small, and

the number of variables is small. Although these two papers

do not conclusively show that linear discriminant analysis is

superior to quadratic discriminant analysis, they suggest that

there are significant problems with using the latter to build

an empirical model of bankruptcy.

We use the logist analysis method because it resolves

both major problems of discriminant analysis. First, unlike

discriminant analysis, it does not reduce all the financial

dimensions of bankruptcy to a single cut-off score. Rather,

it assesses each relevant independent variable and comes up






67

with a probability of bankruptcy, so that, given that a

company belongs to a certain sample, logist analysis provides

the probability of failure. Second, unlike linear

discriminant analysis, logist analysis does not require that

the independent variables be multivariate normals or that

groups have equal covariance matrices. Harrell and Lee (1985)

reported that even when all the assumptions of discriminant

analysis are met, logist analysis is at least as effective as

discriminant analysis. Hence, our results should be much more

significant than under discriminant analysis. Furthermore,

unlike the quadratic version of discriminant analysis, logist

analysis is a sound, proven technique that can provide good

classification accuracy.

Therefore, we believe that the logist analysis

methodology is significantly superior to discriminant analysis

for our research. For this reason, we employ it to build our

empirical model of bankruptcy.


Sample Design


Logist analysis in our research requires two groups of

companies, a bankrupt and a matching sample. Companies that

were on the COMPUSTAT Research Tape and which filed for

Chapter 11 between 1968 and 1987 are used as our bankrupt

companies sample. We select a matching sample of companies

in the same industries and with similar asset sizes but that

avoided bankruptcy.





68

Our data come from several sources. We use the COMPUSTAT

Research Tape and Industry Tape for basic data on financial

variables of both our samples. The COMPUSTAT Research Tape

provides such data for the bankrupt sample, while the Industry

Tape provides such data for our matching sample. We use the

Ownership Reporting System Tape, published by the National

Archives and Record Services, to obtain data on the management

acquisition of company stock. Next, we use the COMPUSTAT

Segments Information Tape to find the segments of our

companies and to compute their degree of diversification.

Finally, we use the COMPUSTAT Research and COMPUSTAT Industry

tapes again to calculate industry growth and bankruptcy rates.

At the start, we had 315 bankrupt companies that were

deleted from the COMPUSTAT Industry Tape and moved to the

COMPUSTAT Research Tape between 1968 and 1987 by a deletion

code of 02, which indicates bankruptcy. We could not,

however, find 5 years of continuous data for all 315 companies

because the information we needed was on several different

tapes, each of which had information on different time

periods. The COMPUSTAT Business Segments Information Tape,

for example, has data only from 1975 onward, as does the

Ownership Reporting System. The Master Current Tape of

Ownership Reporting System, however, offers data from January

1980 to August 1987, and the Master History Tape offers data

from January 1975 to April 1982. Even though we used every

available tape and even calculated several variables by hand,






69

we still could keep only 59 observations in our sample of

bankrupt companies. Most of the companies were "lost" because

we could not find ownership data about management purchase and

sale of stock or segment information about their lines of

business. After determining the composition of the bankruptcy

sample, we matched the sample by industry and asset size and

selected 63 companies that did not go bankrupt and had the

data we needed. Table 12 presents the companies in our

original bankrupt and matching samples.

Orthodox logist analysis requires that samples be

selected randomly from a population of bankrupt and non-

bankrupt companies. In almost all studies on bankruptcy which

have used the logist analysis methodology, however, the sample

has been selected using non-random, state-based criteria.

Therefore, the probability of bankruptcy derived by logist

analysis for any firm i is actually the probability in the

specific sample, not the general population. The relationship

between the probability of bankruptcy based on the population

and the probability of bankruptcy based on the sample depends

on how the sample of bankrupt companies was selected from the

population in general as well as how the sample of non-

bankrupt companies was selected. Because of this, the

probabilities from logist analysis must be adjusted for the

effects of the sample selection, or else they would become

meaningless because by selecting a sample differently, we can

derive completely different results. In the following





70

chapter, we explain how we adjusted our results and discuss

in greater detail how the selection process actually affects

the results of logist analysis.








Table 12. Original (Bankrupt) and Matching Sample
for Deriving Empirical Bankruptcy Model

Original Sample

MI CNUM Company Name To IndDNUM Asset

1 2073 ATI Inc. 84 237399 12.40
2 13900 Aldebaran Drilling Co. Inc. 87 171381 5.83
3 14419 Aldon Industries Inc. 87 22272 9.48
4 25909 American Fuel Technologies 86 42860 1.20
5 37460 Apache Energy & Minerals 84 246792 5.40
6 40150 Argonaut Energy Corp. 86 171311 15.47
7 77266 Beker Industries 85 42870 267.90
8 124187 Buttes Gas & Oil Co. 87 171311 389.52
9 140556 Capitol Air Inc. 84 154511 34.75
10 141602 Cardis Corp. 87 215013 195.20
11 159620 Chargit Inc. 87 237399 19.00
12 163742 Chemical Investors Inc. 83 32640 20.60
13 202666 Commodore Resources Corp. 82 171311 0.09
14 208106 Conner Corp. 87 182451 71.83
15221241 Cosmetic Sciences Inc. 86 238091 1.50
16 225015 Crawford Energy Inc. 85 171381 26.95
17 228885 Crutcher Resources Corp. 86 171389 99.80
18 232827 Cytox Corp. 85 215161 1.30
19 234230 Dakota Minerals Inc. 84 171311 4.70
20 236280 Danker Labs Inc. 85 143851 1.90
21238136 Datatron Inc. 85 215080 7.30
22 254674 Discovery Oil Ltd. 86 171311 15.16
23 278902 Econo Therm Energy Systems 86 93443 22.88
24 292009 Empire Oil & Gas Co. 83 171381 31.34
25 292666 Energy Exchange 85 171311 55.43
26 292935 End-Lase Inc. 86 215080 12.50
27 293799 Enterprise Technologies Inc. 85 215170 33.30
28 364652 Gamex Industries Inc. 82 193990 2.00
29 402274 Gulf Energy Corp. 84 171311 5.05
30 423276 Helionetics Inc. 86 123621 27.90
31 456704 Information Displays Inc. 84 123686 37.00
32 460380 Intl Stretch Prods 84 22200 5.88
33 460468 Intl Teldata Corp. 85 246794 0.65
34 461027 Interstate Motor Freight 84 154210 82.28
35 552813 MGF Oil Corp. 84 171311 342.92
36559150 Magic Marker Industries Inc. 86 193950 8.10
37 585163 Mego International 82 193944 46.00
38 595215 Mid-America Petroleum Inc. 86 171381 22.47
39 628300 Mutual Oil of America Inc. 86 171311 29.97
40 635080 National Business Comm. Corp. 85 225900 5.55
41 638777 NATPAC Inc. 86 225411 25.90
42 654048 Nicklos Oil & Gas Co. 85 171381 96.78
43 682121 OmniMedical 84 237600 9.00
44 712221 People's Restuarants Inc. 86 225812 41.79
45 747623 Quanta Systems Corp. 85 113664 2.40








Table 12--continued.


46 748379
47 761049
48 765361
49 771044
50 795872
51802828
52 805567
53 816068
54 817910
55 925523
56 929073
57 984010
58 984126
59 989875


QuikPrint of America Inc.
Reser's Fine Foods Inc.
Richmond Tank Car Co.
Roblin Industries
Sambo's Restaurants
Santec Corp.
Saxon Industries
Seiscom Delta, Inc.
Servamatic Systems Inc.
Viable Resources Inc.
Vuebotics Corp.
Xenerex Corp.
Xonics Inc.
Zytrex Corp.


Matching Sample


M# CNUM Company Name


1204682
2 866055
3 550819
4 524038
5255264
6870738
7 628850
8 136420
9443784
10 480827
11 205477
12 878504
13 69689
14 674098
15 872625
16 209705
17 786629
18 847660
19 192108
20 914802
21239133
22 971889
23 208258
24 739647
25 666416
26 46357
27 6351
28 250568
29 131069
30 458683
31 369032


Comptek Research Inc.
Summit Energy Inc.
Lydall Inc.
Lee Pharmaceuticals
Diversified Industries Inc.
Swift Energy Co.
NCH Corp.
Canadian Occidental Petroleum
Hudson General Corp.
Jorgensen (Earle M.) Co.
Computer Task Group Inc.
Technical Tape Inc.
Baruch-Foster Corp.
Oakwood Homes
TRC Cos Inc.
Consolidated Oil & Gas
Sage Energy Co.
Speed-O-Print Business Machines
Coeur D'Alene Mines Corp.
University Patents Inc.
Davis Water & Waste
Wilshire Oil of Texas
Conquest Exploration Co.
Prairie Oil Royalties Co. Ltd.
Northgate Exploration Ltd.
Astrex Inc.
Adams Resources & Energy Inc.
DesignCraft Industries
Callahan Mining Corp.
InterGraph Corp.
General Automation


T. IndDNUM Asset


237372
171311
22200
42844
246200
171311
42842
171311
154580
215051
237372
32640
171311
182451
238911
171311
171311
215081
171040
143851
215051
171311
9480
171311
171040
215065
215172
193911
171040
123686
123681


12.44
28.80
50.14
6.50
68.23
12.60
272.10
317.94
48.30
197.11
29.92
31.00
18.10
56.00
3.04
123.23
139.40
7.65
22.58
18.18
36.48
64.04
17.19
32.75
117.60
25.30
35.58
7.62
55.97
28.90
38.60


246794
12013
133743
93312
225812
123688
32600
171382
175900
171311
237391
171311
143861
113674


2.30
9.70
101.30
32.13
220.94
2.90
486.60
23.36
26.36
6.25
2.10
30.95
15.40
6.50








Table 12-continued.

32 732852 Pope, Evans & Robbins Inc. 84 22330 4.89
33 647072 New Mexico & Arizona Land 85 246519 36.49
34 893552 Transcon Inc.-California 84 154213 79.30
35960878 Westmoreland Coal Co. 84 171211 376.30
36 55716 BSN Corp. 86 193949 22.24
37 43147 Artra Group Inc. 82 193960 51.91
38 553748 MSR Explorations Ltd. 86 171311 26.90
39 655555 Nord Resources Corp. 86 171090 66.10
40204909 Computer Factory Inc. 85 225995 13.88
41885539 Three D Department 86 225700 21.15
42 379355 Global Natural Resources Inc. 85 171311 105.80
43 29429 American Science Engineering 84 237391 13.97
44 362232 G R I Corp 86 225961 49.34
45 362360 GTI Corp 85 113679 13.05
46 170819 Christiana Companies 83 246552 44.48
47 208093 Connelly Containers Inc. 86 12030 18.50
48 879369 TeleFlex Inc. 83 133714 109.30
49 707389 Penn Engineering & Mfg Corp. 85 93452 39.01
50476502 Jerrico Inc. 81 225812 238.50
51238085 Datametrics Corp. 85 123688 3.80
52 313693 Federal Paper Board Co. 82 32631 472.83
53 212576 Convest Energy Partners 86 171311 34.49
54 658136 North Canadian Oils Ltd. 86 171311 182.00
55 427879 Hershey Oil Corp. 84 171311 30.38
56 27258 American List Corp. 84 237331 2.39
57 208285 Conquest Exploration Co. 84 171311 123.16
58 942622 Watsco Inc. 84 143822 19.97
59 590262 Merrimac Industries Inc. 84 113663 9.34

"M#" is the matching number, which is used to match the
observations in the bankrupt and matching samples. "CNUM" and
"DNUM" are the company and industry classifications. "To" is
the year during which the company filed for Chapter 11 for
companies in the bankrupt sample, or the last year data was
collected for our research for companies in the matching
sample. "Ind." is the industry code according to our
definitions. "Asset" is the company's asset size.














CHAPTER 7
RESULTS OF EMPIRICAL MODELS OF BANKRUPTCY



Using the sample data described in Chapter 6, we were

able to derive five probabilistic models, designated P1

through P5. All of them are based on the factors described in

Chapter 5, and they assess bankruptcy risk one through five

years ahead of time corresponding to the subscription Pn. The

only difference among these distinct models is in their

coefficients: they all assume the form discussed in Chapter

5. Table 13 shows the signs of the coefficients of the

variables for each model P,.

Most of these coefficients conform to our expectations

as explained in Chapter 5, but others show significant

differences. The signs for the coefficients of the balance

ratio and the net rate of management stock acquisitions seem

to vary randomly but lean towards being positive, while we

expected both to be negative. Both of these variables can be

positive or negative, and our expectation was stated for the

"normal" case for which the expected value of the variable is

positive. Looking at the raw data, a significant number of

the values in both samples were negative, so we would have to






75

reverse the coefficient sign convention. Hence, the positive

signs give the expected signal and it is only our view of

"normal" values for the variables that could not be verified

empirically. We suspect that this result can be explained in

large part by the way the matching sample was constructed.

The match was made by industry and asset size, and it is

evident that many of the pairs came from "troubled"

industries. It is an empirical question, but we suspect that

a random sample from all industries would conform to the

original expectations.

The other sign anomalies are not as troubling. The first

four variables (Group I) are expected to be most significant

close to bankruptcy, and three of the four have the correct

signs in the first three years. Also, the last four variables

(Group II) are expected to be most significant in earlier

years, and three of the four have the correct sign in the last

four years. We believe that this pattern confirms the

validity of our expectations.

Logist analysis provides a technique that allows us to

find the most significant variables in any predictive model.

A variable is "most significant" if, by Chi-Square Q-statistic

and MLE's statistic, they meet the requirements of entry and

stay significance levels pre-specified for the model. Our

entry and stay significance levels were set at 0.05. Table

14 shows the most significant variables in each of our models.

Capital intensity is significant in all periods. This means





76

that the nature of a company's line of business always plays

a significant role. When bankruptcy is far into the future,

our data indicate that this factor plays the largest role of

the eight variables used in our model. As we approach

bankruptcy, especially one year ahead of bankruptcy, however,

ROA, FCC, and Market/Book Ratio become increasingly

significant. This confirms our view that in the short-term,

variables in the company operating and profitability

indicators group that are weighted toward a company's current

financial data would play significant roles. Other factors,

such as relative sales growth, balance ratio of income and

sales growth, and management stock acquisition, have also

played increasingly larger roles near the time of bankruptcy.

To investigate this timing phenomenon further, we built

and tested separate predictive models based on the groups

defined in Chapter 5. Group I was composed of company

operating and financial indicators and included ROA, market-

to-book ratio, FCC, and balance ratio. Group II was composed

of fundamental company characteristics indicators and included

the net rate of management stock acquisitions, the relative

sales growth rate, the relatedness ratio, and capital

intensity. We then compared the predictive power and

effectiveness of the main models built with all eight

variables with those of the Group I and Group II models.

Table 15 shows the predictive powers and effectiveness of all

three sets of models. Figure 4 shows the predictive power of






77

our main model, and Figure 5 compares the Group I and Group

II models.

We then investigated into the classification powers of

our model by examining the empirical probability density

functions for bankrupt and non-bankrupt firms. We divided the

range of probability of bankrupt from 0 to 1.0 into ten equal

intervals. The percentage of bankrupt and non-bankrupt firms

relative to the total number of firms that they present which

fall within each of these intervals for the five different

time periods ti through t5 are tabulated and shown in Tables

16 and 17. The percentages are plotted against the mid-value

of the interval to obtain the discrete approximation of the

distributions of the bankrupt and non-bankrupt probabilities

in Figures 6 to 15. The probabilities of the two groups are

shown to diverge significantly by their respective bar graphs.

The bankrupt group is clearly skewed toward the higher

probabilities of failure that our model derived, while the

non-bankrupt group is clearly skewed toward the lower

probabilities of failure. These results are similar to those

of Zavgren (1985). Her paper, however, only presented

original probabilities, while we present both the original

probabilities and those probabilities adjusted for sample

selection (as discussed below).

As mentioned in the previous chapter, because we

selected our data with non-random, state-based criteria, we

must adjust the probabilities derived from logist analysis.





78

For any given firm i in the general population with a

probability P of bankruptcy, logist analysis would give a

probability P' of bankruptcy for that company in our specific

sample. We must find ways of finding a relationship between

P and P' and also between the structures of our samples.

Assuming that there are N, bankrupt and N2 non-bankrupt firms

in the general population and n, bankrupt and n2 non-bankrupt

firms in our bankrupt and non-bankrupt samples, P', according

to Bayes' formula for conditional probability, is equal to:

P' = P (n,/N1) / {P (n,/N,)+ (l-P) (n2/N2)) (1)

Previous work, such as Palepu (1986), which tried to predict

merger targets using logist analysis models, have partially

explored this relationship, but he only gave a formula for P'

in the special case when n,=N,. We, however, derived a general

formula for P' for cases when nI is not equal to N1, and n2 is

not equal to N2:

Let al = n,/N,,
a2 = n2/N2,
Then formula (1) can rewritten as

P' = (a, P)/{(al*P) + (l-P) a2)} (2)

Substituting P = (1 + exp(-Yj))"' into (2), we derive the
formula for any value of a, and a2:

P' = (1 + exp{lg(a2/a1)-Yj}) 1. (3)

This formula implies the following relationships between the

samples and P' and P:

If aI = a2:
P' = P, Type I error will not change,
Type II error will not change.









If a, > ag:
P' > P, Type I error will increase,
Type II error will decrease.

If al < a.,
P' < P, Type I error will decrease,
Type II error will increase.

According to this formula, without adjustments, we can

derive a model with an artificially high or artificially low

type I error by settling for an artificially low or

artificially high type II error, or vice versa, simply by

selecting the right samples. After adjustments, artificial

type I and II errors are still possible because, even then,

a, and a2 are part of the model. Therefore, to have meaningful

probability models with the logist analysis methodology, we

must always first adjust for al and a2 and then report their

values along with our type I and type II errors. Table 18

presents such data for our sample.

Since a, > a2 in our samples, type I error increased after

adjustments were made, while type II error decreased. We can

observe this same phenomenon by comparing Figures 6 through

10 with Figures 11 through 12, respectively.

Our data lead to some interesting conclusions. First,

we have succeeded in building a model whose predictive power

does not fall precipitously as time before bankruptcy

increases. Whereas Altman's ZETA model, under optimal

conditions, is 96% accurate one year before bankruptcy but

only 60% accurate five years before bankruptcy, our model's





80

predictive power, based on data from one experimental sample,

is relative stable. It is most effective one year before

bankruptcy, with 96.0% accuracy (as measured by the C-Index

of logist analysis), but even at its lowest point, three years

before bankruptcy, it still has 89.0% accuracy, and five years

before bankruptcy it is 95.1% accurate.

Second, we have found that during different periods

before bankruptcy, different groups of variables become

important in predicting bankruptcy. When close to bankruptcy,

the Group I financial variables have very high predictive

power. As we move farther back in time and try to predict

bankruptcy farther ahead of time, we found that these

variables' predictive powers started to wane. The Group II

fundamental variables became increasingly more powerful as we

moved farther back in time. This demonstrates that there is

a time relationship between our fundamental variables and the

future financial position of the company.








Table 13. Signs of Coefficients

Model bI b2 b3 b4 b5 b6 b7 b_

P + + +

P2 + +

P3 + + -

P4 + + -

P5 + -

PI through P5 are models for predicting bankruptcy one to five
years ahead of time.

bI through b8 are coefficients of the following variables:
b,: ROA (EBIT/TA)
b2: FCC
b3: Balance Ratio
b4: Market/Book Ratio
b: Relatedness Ratio
b: Net Rate of Management Stock Acquisitions
b7: Relative Sales Growth Rate
b8: Capital Intensity.







Table 14. Most Significant Variables in
Forecasting Bankruptcy

Model Most Significant Variables

P, ROA, FCC, Balance Ratio, Capital Intensity,
Market/Book Ratio

P2 Relative Sales Growth, FCC, Capital Intensity

P3 ROA, Net Rate of Management Stock Acquisitions,
Relative Sales Growth, Capital Intensity

P4 Capital Intensity

P5 Capital Intensity
P through P5 are models for forecasting bankruptcy one through
five years ahead of time, respectively.









Table 15.


Predictive Power and Effectiveness
of Different Models


Years:


Eight-Variable Models:
C-Index: 0.960
X2 59.75
(SL with 8 DF) 0.50%
L.H. Ratio Index 0.5969

Group I Models:
C-Index: 0.929
X2 49.63
(SL with 4 DF) 0.50%
L.H. Ratio Index 0.4958

Group II Models:
C-Index: 0.819
X2 16.45
(SL with 4 DF) 0.50%
L.H. Ratio Index 0.1643


0.957
69.31
0.50%
0.6133


0.873
39.88
0.50%
0.3529


0.770
27.43
0.50%
0.2427


0.892
48.48
0.50%
0.4135


0.771
16.33
0.50%
0.1365


0.835
35.19
0.50%
0.3001


0.909
44.51
0.50%
0.4819


0.740
10.33
5.00%
0.1074


0.863
35.31
0.50%
0.3823


5


0.951
45.94
0.50%
0.5980


0.598
3.83
50.00%
0.0460


0.889
32.47
0.50%
0.4227


The C-Index comes from logist analysis and indicates the
classification accuracy of the model. X2 (or Chi-Square) is
the -2 log likelihood ratio chi-square statistic of the model.

























IUU




80 -




60-




40




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1 2 3 4 5


Yeors before Bankruptcy












Figure 4. Classification Accuracy of Empirical Model of
Bankruptcy


Accuracy

























Group I


Group II


1 2 3 4 5


Years before Bankruptcy











Figure 5. Classification Accuracy of Models Based on Group I
and Group II Variables






s 86



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0.25 0.45
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Probability Interval Mid-Volues










Figure 6. Unadjusted Empirical Probability Density
Function, 1 Year Before Bankruptcy


Non-bkpt

Bankrupt


0.7-


0.6-


0.5-


0.4-


0.3-


0.2-


0.1-


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Non-bkpt


Bankrupt


0.05 0.25 0.45 0.65 0.85
0.15 0.35 0.55 0.75 0.95


Probability Interval Mid-Values












Figure 7. Unadjusted Empirical Probability Density
Function, 2 Years Before Bankruptcy


























Non-bkpt


3arkrupt


0.05 0.25 0.45 0.65 0.85
0.15 0.35 0.55 0.75 0.95

Probability Interval Mid-Values











Figure 8. Unadjusted Empirical Probability Density
Function, 3 Years Before Bankruptcy



























Non-bkpt


Bankrupt


0.05 0.25 0.45 0.65 0.85
0.15 0.35 0.55 0.75 0.95


Probability Interval Mid-Values












Figure 9. Unadjusted Empirical Probability Density
Function, 4 Years Before Bankruptcy




























0.8


0.7Non-bkpt


Bankrupt
0.6
c

0
a 0.5-
o

0.4-
0
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0.3-
U


0.2-


0.1 -


0--
0.05 0.25 0.45 0.65 0.85
0.15 0.35 0.55 0.75 0.95


Probability Interval Mid-Values














Figure 10. Unadjusted Empirical Probability Density
Function, 5 Years Before Bankruptcy























0.7


0.6


0.5


0.4-


0.3-


0.2-


0.1-


0.05 0.25
0.15


7 urJ l~a


0.65 0.85
0.55 0.75


Prob'atlitly Interval Mid-Values











Figure 11. Adjusted Empirical Probability Density
Function, 1 Year Before Bankruptcy


Non-bkpt

Bankrupt


Y

























0.8


0.7


0.6


0.5-


0.4-


0.3-


0.2-


0.1-


Probability Interval Mid-Values













Figure 12. Adjusted Empirical Probability Density
Function, 2 Years Before Bankruptcy


15 0.25 0 45 0.65 0.85
0.15 0.35 0.55 0.75 0.95


Non-bkpt


Bankrupt



























Non-bkpt


Bankrupt


0.05 0.25 0.45 0.65 0.85
0.15 0.35 0.55 0.75 0.95


Probability Interval Mid-Values












Figure 13. Adjusted Empirical Probability Density
Function, 3 Years Before Bankruptcy