Financial Ratios as Predictors of Failure: Evidence from ... - ERIM

17 Nov 2008
Financial Ratios as Predictors of Failure:
Evidence from Hong Kong using Logit Regression
Student: Weiying Guo 292341
Coach: Dr. Ben Tims
Co-reader: Drs. Johannes Meuer
Finance and Investment
Rotterdam School of Management

Preface
The author 1 declares that the text and work presented in this master thesis is original and
that no sources other than those mentioned in the text and its references have been used in
creating the master thesis.
The copyright of the master thesis rests with the author. The author is responsible for its
contents. RSM Erasmus University is only responsible for the educational coaching and
beyond that cannot be held responsible for the content.
1
The author would like to thank Dr. Ben Tims, and Drs. Johannes Meuer for valuable suggestions and
helpful comments. All remaining errors are the author’s responsibility.
1

Abstract
This paper presents some empirical results of predicting corporate failure by using
various financial ratios. It aims to identify the characteristics that distinguish default and
non-default companies. Two samples (matched and non-matched) of Hong Kong based
companies are used in this research over the period 2001-2007. By using logistic
regression, it shows that level of debt, and return on equity increase corporate failure,
whereas bankruptcy decreases with firm size and profitability. The results are in support
of capital structure theory and risk-return tradeoff. The predictive power of the logit
model is reasonably high in three years prior to default.
Keywords: Risk Management, Probability of default, bankruptcy, logistic regression
2

Table of Contents
1. Introduction..................................................................................................................... 4
2. Probability of Default and Bankruptcy........................................................................... 5
3. Literature Review............................................................................................................ 6
3.1 Theories..................................................................................................................... 7
3.2 Multi factors in predicting PD and the methodologies ............................................. 9
3.2.1 Multiple Discriminant Analysis.......................................................................... 9
3.2.2 Logistic Regression .......................................................................................... 10
4. Data and Methodology.................................................................................................. 11
4.1 Methodology ........................................................................................................... 11
4.2 Data and Sample...................................................................................................... 12
4.3 Explanatory Variables and Hypotheses................................................................... 13
5. Empirical Results.......................................................................................................... 16
5.1 Descriptive Results.................................................................................................. 16
5.2 Estimation results of the Logit model ..................................................................... 19
5.3 Predictive power of the model ................................................................................ 23
5.4 Robustness Test....................................................................................................... 25
6. Conclusion .................................................................................................................... 27
Reference .......................................................................................................................... 30
Appendix One ................................................................................................................... 34
Appendix Two................................................................................................................... 36
Appendix Three ................................................................................................................ 37
Appendix Four .................................................................................................................. 38
Appendix Five................................................................................................................... 39
Appendix Six .................................................................................................................... 40
Appendix Seven................................................................................................................ 41
Appendix Eight ................................................................................................................. 42
Appendix Nine.................................................................................................................. 43
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1. Introduction
One year after the onset of the credit crunch, most Americans have still been suffering
from losing jobs, skyrocketing commodity prices, weakening dollar, all in all, a bad
economy. The downward trend has unfortunately crept to countries in Europe and Asia,
and fear of potential financial markets meltdown has reached its new level ever before
after the 1997 Asian financial crisis and 9/11. At the same time, credibility and risk
management have probably never caught such attention from investors and policymakers
in history. The credit crunch is prompting a new age of risk management, requiring risk
managers to measure risk in real time and help prevent future crises. The new Basel
framework, Basel II, intends to further strengthen the soundness and stability of the
international banking system (Basel committee, 2004) by promoting stronger risk
management practices in the banking industry. Under the Internal Rating Approach,
banks are given opportunities to estimate counterparties’ default probabilities by
themselves. Probability of default (PD) plays an important role not only because it is the
cornerstone when calculating regulatory capital requirements, but also when it comes to
making tough loan decisions it helps banks discriminate good borrowers from bad
borrowers.
For banks, one of the best ways to examine a company’s financial health is by looking at
its financial ratios. The objective of this paper is to explore the possibilities to predict
probability of default and to identify the characteristics distinguishing default companies
from non-default ones by using logistic regression. Relying on existing theories, such as
risk-return tradeoff, and capital structure theory, the study examines the relationship
between PD and different financial ratios in various industries in Hong Kong. Many
scholars have conducted default research in the United States and Western Europe (see
4

Beaver (1966), Marais (1979), Altman and Lavallee (1981) and Westgaard and Wijst
(2001) and others). Nevertheless, there has been little similar bankruptcy research in Asia.
One possible explanation could be that Asian financial markets just emerged in the last
decade, whereas most of the default analyses were conducted over 20 years ago. So far
there has been no comprehensive bankruptcy analysis performed in the context of Hong
Kong. However, being one of the first banking industries who adopted the new banking
regulation, Hong Kong deserves extra attention. Compared to most empirical studies in
the 70s and 80s, the data set used in this research (from 2001 to 2007) is rather
contemporary. Therefore, whether previous empirical results still stand in a modern
context is under question.
The rest of the paper is structured as follows. In the next section, I briefly introduce
probability of default and bankruptcy. Section 3 reviews literature. In section 4, I explain
the data, sample selection, and methodology used in the analysis. Section 5 presents the
empirical results. Section 6 concludes.
2. Probability of Default and Bankruptcy
Legally speaking, bankruptcy is described as a debtor not being able to meet its debt
obligations as they fall due. In an accounting sense, when the sum of the realized cash
flow and expected future cash flow is less than the debt obligations, bankruptcy occurs.
PD is used to measure the likelihood that a firm defaults under its debt obligations.
Different researchers have different definitions of failure 2 . Operationally, Beaver (1968
(1)) defined a failed firm when any of the following events has occurred: bankruptcies,
bond default, overdrawn bank account, or nonpayment of a preferred stock dividend.
2
See a summary of the definitions of failure in major empirical default analyses, by Castagna and Matolcsy
(1981)
5

However he did not find substantial differences in the empirical results even under this
boarder definition. Deakin (1972) only included those firms which experienced
bankruptcy, insolvency, or which were otherwise liquidated for the benefit of creditors in
his default analysis. I define default companies as those delisted (except for companies
that are taken over by others 3 ) from the Hong Kong Stock Exchange 4 , or as those listed
as “ceased place of business”, or “winding up” according to the Integrated Companies
Registry Information System (ICRIS) 5 . Therefore, the date of default is either the date of
delisting from the HKEx, or the date of winding up.
Bankruptcy of a company generates both direct and indirect costs. Assets of the firm are
usually being sold at a price well below the one that would be realized before the
bankruptcy announcement. Accountants and lawyers can cost huge amounts of money.
The companies’ brand name and long established reputation are often ruined. Of course,
failure of a company is costly to suppliers of capital, which in most cases are banks. It is
therefore in banks’ interest to predict borrowers’ probability of default when making loan
decisions.
3. Literature Review
Bankruptcies have been mostly explained by capital structure, risk-return tradeoff, cash
flow, and agency theory. Some scholars also tried to combine different proxy variables
that are derived from accounting data into their models for predicting corporate default.
These studies vary from time, countries, and industries. However they all proved that
3
Acquired companies will not be included in the sample selection. HKEx offers relevant takeover
information (last updated on 22 June 2007) regarding announcement date, name of offeror, name of offeree,
and offer type, etc.
4
This definition is also used by Izan (1984) for Australian companies, and Zeitun, Tian, & Keen (2007) for
Jordanian companies.
5
Official website offered by Hong Kong government. http://www.icris.cr.gov.hk/csci/
6

financial ratios can be used to predict PD.
3.1 Theories
In a world without tax and bankruptcy, there is no optimal capital structure under the
classic Modigliani-Miller irrelevance theorem 6 (Modigliani & Miller 1958, 1963).
Nevertheless, in the real world, most companies have to choose between tax advantages
and bankruptcy costs (trade-off theory, Kraus and Litzenberger, 1973). That is, debt
brings tax shields for a company, but at the same time it increases distress or bankruptcy
costs. The optimal amount of debt should produce the lowest weighted average cost of
capital. Kim (1978) claimed that the market value of a company decreases as financial
leverage becomes extreme, thus it should finance less debt than its debt capacity (the
optimum 7 ). The transfer of ownership from shareholders to debtholders also encourages
risk taking behavior, because shareholders have the limited downside risk while enjoying
unlimited upside potential, further reinforcing the conflict of interests between various
stakeholders in the company. Therefore, higher debt in one’s capital structure should be
associated with higher PD.
From external to internal financing, cash flow has been an important determinant of
bankruptcy. Scott (1981) claimed that cash flow variables involve estimates of the firm’s
future cash flow distribution, and that past and present cash flow should be able to predict
PD. Financial Accounting Standards Board (1981) stated that “the greater the amount of
future net cash inflows from operations, the greater the ability of the enterprise to
withstand adverse changes in operating conditions”. Other scholars have also shown
6
The total value of a firm will not change because of its capital structure. In other words, no capital
structure is better or worse than any other capital structure for the firm’s shareholders.
7
The breakeven point is where the marginal benefit of the tax shield equals the marginal cost of financial
distress.
7

interest in predicting bankruptcy by incorporating cash flow characteristics in their
predictive models (see e.g. Casey and Bartczak (1985), Gentry et al (1985), Gombola et
al (1987), and Aziz (1988), among others). Cash rich companies are assumed to be better
able to diversify their risks and therefore less likely to go bankrupt. Deakin (1972) used
several cash flow ratios (cash flow/total debt, cash/total assets, cash/current liabilities,
cash/sales) to test their coefficients with bankruptcy. The signs of the coefficients were
negative but did not seem to be consistent in all five years before companies’
bankruptcies. Recently, Zeitun et al (2007) demonstrated the negative relationship
between cash flow and default risk, however the results were not significant. Similar to
cash flow, a shortage of liquidity could also trigger corporate failure. Cash, the most
liquid form of assets is crucial to a company disregarding its size or industry type.
Furthermore, it also matters how quickly a company is able to covert other assets into
cash with no or little price discount. Therefore, the availability and convertibility of a
company’s assets are extremely important especially in crises. Becchetti and Sierra
(2003), among others used liquidity ratios for their bankruptcy analyses.
There are always trade-offs between internal and external financing. According to the
pecking order theory (Myers, 1984), a company should use relatively costless internal
financing over external financing. However internal financing is not without problem. If a
company’s cash flow cannot be distributed to its shareholders or debtholders, managers
are more likely to misuse retained earnings. Internal financing better sources free cash
flow (measured as operating cash flow minus the capital expenditures) and thereby
increases agency costs (Jensen, 1986) due to the asymmetric information between
managers and shareholders. A high level of free cash flow seems to destroy corporate
value, so it is expected to be positively related to bankruptcy.
Changes in market prices of stocks can also be used to predict failure (Beaver 1968 (2),
8

Altman and Brenner, 1981). According to the classic Capital Asset Pricing Model
(CAPM) 8 , investors would expect higher returns for bearing more risk. The first and most
well-know empirical tests can be traced back to over 30 years ago. For example, Black et
al (1972) provided empirical tests and additional insights based on the original CAPM
model. They confirmed that the beta factor (firm-specific risk) is important in
determining security returns using cross-sectional tests. More recently, Chava and
Purnanandam (2008) uncovered the risk-return relation by extending their sample period,
and suggested that expected returns are positively correlated with bankruptcy.
Consequently, there should be a positive relation between return on equity and default
risk.
3.2 Multi factors in predicting PD and the methodologies
3.2.1 Multiple Discriminant Analysis
Many scholars have incorporated various factors in terms of financial ratios into their
predicting model in order to discriminate default and non-default companies. Beaver
(1966) and Altman (1968) pioneered the studies. By using univariate analysis, Beaver
pairwisely compared failed and non-failed companies and found that ratios like cash
flow/total assets, net income/total assets, total debt/total assets, and cash flow/total debt 9
in particular were important indicators of failure. Later, based on his research, Altman
(1968) developed the classic Multiple Discriminant Analysis (MDA) and Z-score model.
Being more advanced than univariate analysis, MDA examines the entire variable profile
simultaneously instead of sequentially testing individual variables. The five accounting
8
E(R)=Rf+β*(Rm- Rf), E(R) is the expected return of the capital asset, Rf is the risk-free rate of interest, β is
the sensitivity of the asset returns to market returns, Rm is the expected return of the market, (Rm- Rf) is the
difference between expected return on market and risk-free rate, or also known as risk premium. Since most
investors are diversified, the expected return on a security should be positively related to its beta.
The model was introduced by Treynor (1962), Sharpe (1964), Lintner (1965), and Mossin (1966).
9
Cash flow/total debt has predictive power up to five years before bankruptcy.
9

atios he employed in the research were working capital/total assets, retained
earnings/total assets, earning before interest and taxes/total assets, market value
equity/book value of total debt, and sales/total assets. The model proved very accurate
when tested on a sample of US manufacturing firms, and the predictive value of the
model for the first two years prior to bankruptcy was quite high (correct prediction: 95%
for year one and 72% for year two). Following his previous research, Altman et al (1977)
constructed a second-generation model, called ZETA. ZETA model was effective in
classifying bankrupt companies up to five years prior to failure on a sample of
corporations consisting of manufacturers and retailers. Many other scholars have also
applied multidimensional models in their studies (see for example, Deakin (1972) and
Sinkey (1975)).
3.2.2 Logistic Regression
Later, new econometric methodology of logit and probit analysis has been introduced into
this field. There is no fundamental difference between logit and probit models, except
that the conditional probability p approaches zero or one at a slower rate in logit than in
probit. In practice many researchers choose logit model because of its comparative
mathematical simplicity (Gujarati, 2003). Comparing to quantitative explanatory
variables in normal regression, dependent variables in logistic regression are normally
qualitative (or dummy). Martin (1977) first intended to build an early warning model for
predicting future bank failure based on current period’s balance sheet and income
statement by using logistic regression. Ohlson (1980) tested the 1970-1976 industrial
sample data, and found that the predictive power of the default risk model (two years
before default) based on financial ratios seemed to be robust. Meanwhile, he found four
basic factors being significant with probability of failure (within one year), namely firm
10

size, financial structure, performance 10 , and current liquidity.
In their empirical analysis, Westgaard and Wijst (2001) used the 1996 accounting data
and the 1998 bankruptcy information (2-year prior to default) and illustrated that
financial ratios (cash flow to debt, financial coverage, liquidity, and equity ratio) were
negatively and significantly correlated with PD in a corporate bank portfolio in Norway.
One year later, Westgaard and Wijst together with Hol (2002) did another research for
Norwegian limited liability companies, but with different proxy variables and time
horizon (1995-2000). Their main finding was that leverage and cash flow standard
deviation had a significantly positive effect on default probability, while cash flow had a
significant negative effect. Similarly, Zeitun et al (2007) proved that firms’ cash flow
decreased corporate failure in Jordanian companies. Their main contribution, however,
was that they addressed the issue of free cash flow 11 and default risk. They concluded
that firms’ PD increased with firms’ free cash flow, which also seemed to be consistent
with agency theory. The predictive power of their models (three years prior to default) for
both matched and non-matched is very high (91.5%, 80%, and 81%). A summary of the
previous researches is presented in Table One in Appendix One.
4. Data and Methodology
4.1 Methodology
Multiple Discriminant Analysis has been widely used in default research. Nevertheless
the usefulness of MDA is quite limited, since such a technique only provides qualitative
differentiation among counterparties, and does not produce probabilities. Furthermore,
10 Measured as net income to total assets
11 Free cash flow was measured as retained earning to total assets (also see Dhumale, 1998).
11

there are specific statistical requirements under this approach. For example, it assumes
predictors have normal distributions which would restrict the use of dummy independent
variables (Ohlson, 1980).
Probability of default is characterized as a non-linear S-shaped cumulative distribution
function with probabilities varying from 0 to 1, therefore a logit regression suits best.
Logit regression can specify a dichotomous dependent variable as a function of various
explanatory variables. More importantly, logit solves the problem with linear probability
model that is inherently unbounded. Different counterparties can be mapped into the
regression model within a boundary between 0 and 1. By taking the natural log of the
odds ratio (p/(1-p)) 12 , the logit model is linear in X and in parameters, facilitating the
interpretation of coefficients. The model can be written as Li=ln[pi/(1-pi)]=βXi+ui, with
two states, L=1 if the firm defaults, L=0 otherwise. As p goes from 0 to 1, the logit L
goes from -∞ to +∞. The models are estimated by using the SPSS software. Early
examples of the use of logit regression are for instance, Martin (1977), Ohlson (1980),
Westgaard and Wijst (2001), and Zeitun et al (2007) as mentioned in section 3.2.2.
4.2 Data and Sample
The companies in this study are publicly traded and listed on the Hong Kong Stock
Exchange (HKEx) 13 over the period 2001-2007. Their accounting data (for three years
prior to default) is collected by Thomson One Banker (TOB). TOB provides basic
company information such as company name, industry code, income statements and
balance sheets. However, TOB does not specify a company’s financial health (default or
non-default). Instead it only states whether the company is active or inactive 14 . According
12 P as in probability
13 http://www.hkex.com.hk/index.htm
14 Although inactive companies are usually default.
12

to the definition of default (see section two) in this study, 30 default companies with
complete financial data have been found over 2001-2007. They are in ten different
industries 15 . For each default company, the first three fiscal year-end financial data before
its default announcement is used.
The first sample selection is similar to Beaver (1966) and Altman et al (1977)’s. In order
to isolate the characteristics of default companies, each default company is matched with
a non-default company from the same industry group, with similar asset size, and in the
same year. The purpose of matching is that there could be a potential bias in certain of the
ratios. For example, some financial ratios could vary dramatically cross industries.
Therefore, industry and time dummies are added in the first sample to control the bias.
However, the “matching procedures” tend to be somewhat arbitrary (Ohlson, 1980). It is
also interesting to see the effect of excluding matching. In the second sample, I pool
cross-sectional and time-series data for all the companies over the period 2001-2007. 71 16
non-failed companies are randomly selected for the second sample over the same time
period. Similar to sample one, non-default companies are chosen from the same ten
industries, but without controlling time and firm size.
4.3 Explanatory Variables and Hypotheses
The variables used in this study are summarized and presented in Table 2 at the end of
this section. The variables selected for the regression model are related to “cash flow”,
15
Industries (number of observations): Capital Goods (3), Consumer Durables & Apparel (7), Diversified
Financials (2), Food Beverage & Tobacco (3), Materials (3), Real Estate (2), Software & Services (2),
Technology & Hardware Equipment (4), Telecommunication Services (2), Transportation (2)
16
Due to the limitation of collecting information of default companies, in the second sample the number of
default companies is still 30. However we cannot unilaterally and infinitely increase the number of
non-default companies. It would lead to a biased result. Therefore, randomly picked 71 non-default firms
are included in sample two.
13

“returns”, “values” and “debt obligations”. The sign of the coefficients of the different
ratios is based on previous studies. The regression model can also be specified as Li = ln
[pi/(1-pi)] = β1TDTAi - β2EQTCi + β3RETAi + β4ROEi - β5CFTDi – β6NITAi – β7SATAi –
β8WCTAi – β9CRi – β10Sizei + dummy (year) + dummy (industry) + ui.
Hypothesis 1: Highly leveraged firms are more likely to fail.
Firms with heavy debt obligation have higher distress cost, thus are more likely to go
bankrupt. Empirical studies proved the positive relationship between total debt to total
assets (TDTA) and probability of default (Martin (1977), and Hol et al (2002)). A
company’s financial leverage can also be measured by solidity. It estimates the extent by
which the company’s assets are funded by equity (EQTC). Westgaard and Wijst (2001)
found a negative and significant relationship between solidity and default probabilities.
Hypothesis 2: Those Companies with more free cash flow have higher probability to
fail.
Managers probably would rather invest in projects with negative NPV instead of paying
back companies’ shareholders. Free cash flow is estimated by retained earnings to total
assets (RETA). It is hypothesized to have a positive correlation with probability of default
(Altman (1968), Altman et al (1977), and Zeitun et al (2007)).
Hypothesis 3: Abnormal and high equity returns may indicate high default risk.
Stock returns can be used to classify firms’ potential failure. A positive risk premium is
required when investors detect potential high risks (Black et al (1972), and Chava and
Purnanandam (2008)). Therefore equity returns (ROE) are supposed to be positively
related to default probabilities.
Hypothesis 4: A company’s cash flow is negatively related to bankruptcy.
14

Cash flow over total debt (CFTD) measures the ability of a company to pay back its
debtholders. Westgaard and Wijst (2001), and Zeitun et al (2007) used the same ratio and
found a negative relation between these two variables (although the empirical result from
Zeitun et al was not statistically significant).
Hypothesis 5: The ability to generate income helps prevent bankruptcies.
Net income to total assets (NITA) and sales to total assets (SATA) are used to measure
profitability (see Altman (1968), Deakin (1972), Martin (1977), and Ohlson (1980)).
Profitable firms seem to be associated with low probability of default as they have great
flexibility in allocating money and diversifying their investment.
Hypothesis 6: Companies’ liquidity has a negative relationship with PD.
Bankruptcies ought to depend on how fast a company can generate cash. Liquidity risk is
measured by working capital to total assets (WCTA) and current ratio (CA/CL) in this
study. Altman (1968) and Becchetti & Sierra (2003) used WCTA to distinguish default
and non-default firms, and they found it negatively and significantly impacted on PD.
Current ratio also indicates a negative correlation with PD, but the coefficient was not
significant in Deakin (1972)’s study.
Hypothesis 7: Large firms tend to survive compared with small firms.
A company’s size is expected to be negatively related to probability of default. In many
previous studies, researchers used the base 10 logarithm of a company’s total assets when
estimating firm size (Altman (1984), Westgaard and Wijst (2001), and Manzoni (2004)),
and they confirmed this negative correlation.
15

Table 2 Explanatory Variables
Variables Description Expected Sign
TDTA Total Debt to Total Assets +
EQTC Equity to Total Capital -
RETA Retained Earnings to Total Assets +
ROE Return on Equity +
CFTD Cash Flow (Net Income+Depreciation) to Total Debt -
NITA Net Income to Total Assets -
SATA Sales to Total Assets -
WCTA Working Capital (Current Assets-Current Liabilities) to Total Assets -
CR Current Ratio (Current Assets/Current Liabilities) -
Size The base 10 logarithm of the Total Assets -
5. Empirical Results
5.1 Descriptive Results
Table 3(a) illustrates informative descriptive statistics for default firms first year 17 prior
to bankruptcy and their matched non-default firms. Comparing both types of firms
(default vs. non-default), the majority of the mean values supports the expected signs of
explanatory independent variables as shown in Table 2 (e.g. NITA for non-bankrupt
companies is higher than that of the default firms. TDTA is the other way around). In
general, the financial ratios of the default companies tend to fluctuate more than those of
the non-default ones. It means that for the default companies, their financial figures are
more likely to be different from each others’. This result is not surprising because
extreme values seem to be easily found on the failed companies’ balance sheets and
income statements, especially right before their failures. However extreme values can
still be detected in non-default companies (Table 3(a) right, Sample One, 30 companies),
17
For the comparisons between bankrupt and non-bankrupt companies two and three years before
bankruptcy events, see Table 4 and 5 in Appendix Two and Three.
16

such instability in terms of high standard deviation is reduced to some extent by including
more observations (Table 3(b) right, Sample Two, 71 companies).
Table 3(a) Descriptive Statistics (Sample One, 1 st year before default)
Default Companies Non-Default Companies
Minimum Maximum Mean Std.
Deviation
Variance Minimum Maximum Mean Std.
Deviation
Variance
CFTD1 -1.96 11.95 0.26 2.36 5.56 -0.74 327.10 14.18 59.73 3567.81
RETA1 -20.10 0.42 -1.00 3.70 13.67 -3.81 0.71 0.01 0.89 0.79
WCTA1 -8.77 0.40 -0.47 1.65 2.71 -0.34 0.58 0.20 0.21 0.04
CR1 0.01 2.95 1.03 0.80 0.64 0.06 26.10 2.54 4.55 20.68
NITA1 -554.77 15.47 -34.97 103.61 10735.72 -12.67 57.48 7.97 12.82 164.35
TDTA1 0.60 897.53 65.22 160.72 25830.92 0.03 45.75 15.74 11.72 137.40
SATA1 0.06 5.10 0.81 1.01 1.02 0.01 3.95 0.95 0.88 0.77
Size1 1.37 4.17 2.89 0.71 0.50 1.32 5.78 3.10 0.86 0.74
EQTC1 9.60 100.00 76.69 26.04 678.16 39.34 100.00 83.80 15.85 251.28
ROE1 -1017.34 65.71 -76.30 215.30 46353.62 -176.03 47.23 5.01 41.56 1727.08
Table 3(b) Descriptive Statistics (Sample Two, 1 st year before default)
CFTD1 -1.96 11.95 0.26 2.36 5.56 -0.49 111.30 5.54 15.75 247.91
RETA1 -20.10 0.42 -1.00 3.70 13.67 -3.81 0.71 0.08 0.72 0.52
WCTA1 -8.77 0.40 -0.47 1.65 2.71 -0.34 0.78 0.19 0.24 0.06
CR1 0.01 2.95 1.03 0.80 0.64 0.06 15.54 2.28 2.48 6.15
NITA1 -554.77 15.47 -34.97 103.61 10735.72 -7.00 65.74 9.58 11.73 137.62
TDTA1 0.60 897.53 65.22 160.72 25830.92 0.07 52.54 17.79 13.60 185.03
SATA1 0.06 5.10 0.81 1.01 1.02 0.01 3.95 0.86 0.77 0.59
Size1 1.37 4.17 2.89 0.71 0.50 1.32 5.78 3.40 0.83 0.69
EQTC1 9.60 100.00 76.69 26.04 678.16 27.28 100.00 83.14 16.61 276.00
ROE1 -1017.34 65.71 -76.30 215.30 46353.62 -176.03 3894.62 68.00 461.46 212947.93
Unlike ordinary least square (OLS) method, the variance inflation factors (VIF) 18 cannot
be computed in logistic regression as there is no direct counterpart to R 2 . Nevertheless,
the problem of multicollinearity 19 potentially exists in either OLS or logistic regression
18
VIF shows how the variance of an estimator is inflated by the presence of multicollinearity. As the extent
of collinearity increases, the variance of an estimator increases, and in the limit it can become infinite
(Gujarati, 2003.)
19
Multicollinearity is the phenomenon that one independent variable is highly and linearly correlated with
17

which results in high standard errors of coefficients β and thus leads to an unreliable
interpretation of final results. In logistic regression, large standard errors signal the
possibility of multicollinearity (Studenmund, 2000, and Gujarati, 2003). Multicollinearity
cannot be eliminated entirely, however it should be reduced as much as possible.
Therefore before selecting variables for the model, it seems necessary to look at the
correlations between individual variables (see Table 6(a) and (b)). Variables that show
high correlation with the others might be dropped out of the model. For example, RETA
and WCTA are highly correlated with other seven variables respectively. However it
needs to be kept in mind that correlations only indicate the connections between two
single variables, instead of a single variable and the rest of the variables. The elimination
procedure based on the correlation table therefore is rather subjective. Another
observation from Table 6(a) and (b) is that the correlations between individual variables
decline as more companies are included in the sample, implying that multicollinearity
decreases with sample size.
Table 6(a) Correlations (Sample One, 1 st year before default)
CFTD1 RETA1 WCTA1 CR1 NITA1 TDTA1 SATA1 Size1 EQTC1 ROE1
CFTD1 1.000 0.068 0.094 0.961** 0.058 -0.062 -0.036 -0.073 0.141 0.055
RETA1 0.068 1.000 0.949** 0.127 0.955** -0.953** 0.000 0.388** 0.284* 0.299*
WCTA1 0.094 0.949** 1.000 0.188 0.965** -0.969** -0.003 0.322* 0.311* 0.354**
CR1 0.961** 0.127 0.188 1.000 0.127 -0.118 -0.044 -0.073 0.172 0.116
NITA1 0.058 0.955** 0.965** 0.127 1.000 -0.233 -0.041 0.342** 0.262* 0.262*
TDTA1 -0.062 -0.953** -0.969** -0.118 -0.233 1.000 0.026 -0.307* -0.323* -0.312*
SATA1 -0.036 0.000 -0.003 -0.044 -0.041 0.026 1.000 -0.223 0.057 -0.233
Size1 -0.073 0.388** 0.322* -0.073 0.342** -0.307* -0.223 1.000 -0.024 0.257*
EQTC1 0.141 0.284* 0.311* 0.172 0.262* -0.323* 0.057 -0.024 1.000 0.318*
ROE1 0.055 0.299 0.354** 0.116 0.431** -0.312** -0.233 0.257* 0.318* 1.000
other independent variables. Serious multicollinearity endangers the reliability of the estimators. However,
multicollinearity is not a serious problem when the purpose is prediction only (see for example, Geary,
1963)
18

Table 6(b) Correlations (Sample Two, 1 st year before default)
CFTD1 RETA1 WCTA1 CR1 NITA1 TDTA1 SATA1 Size1 EQTC1 ROE1
CFTD1 1.000 0.100 0.113 0.219* 0.087 -0.104 0.038 0.044 0.218* 0.015
RETA1 0.100 1.000 0.930** 0.167 0.927** -0.940** -0.003 0.352** 0.257** 0.032
WCTA1 0.113 0.930** 1.000 0.281** 0.944** -0.956** -0.021 0.281** 0.287** 0.092
CR1 0.219* 0.167 0.281** 1.000 0.175 -0.163 -0.128 0.070 0.215* -0.009
NITA1 0.087 0.927** 0.944** 0.175 1.000 -0.212 -0.043 0.293** 0.238* 0.249*
TDTA1 -0.104 -0.940** -0.956** -0.163 -0.212 1.000 0.033 -0.266** -0.313** -0.108
SATA1 0.038 -0.003 -0.021 -0.128 -0.043 0.033 1.000 -0.215* 0.090 -0.075
Size1 0.044 0.352** 0.281** 0.070 0.293** -0.266** -0.215* 1.000 -0.139 -0.032
EQTC1 0.218* 0.257** 0.287** 0.215* 0.238* -0.313** 0.090 -0.139 1.000 0.104
ROE1 0.015 0.032 0.092 -0.009 0.249 -0.108 -0.075 -0.032 0.104 1.000
*. Correlation is significant at the 0.05 level (2-tailed).
**. Correlation is significant at the 0.01 level (2-tailed).
5.2 Estimation results of the Logit model
Similar to linear regression, logistic regression also gives estimation for the coefficient of
each parameter and its relevant significance (based on t-ratios) to the dependent variable
(PD). But the interpretation of logit regression is different, since it assumes a non-linear
relationship between probability and the independent variables. Remember that
Li=ln[pi/(1-pi)], after taking the antilog of the estimated logit, we get pi/(1-pi) (that is, the
odds ratio). In this case, since p represents probability of default, pi/(1-pi) can also be
called as odds of default. Therefore, instead of looking at parameter β (which is used to
explain the ln(odds of default)), Exp(β) should be considered the equivalent value when
interpreting odds of default directly. Table 7 shows the logit results by using matched
samples (sample one). The variables included in the model (RETA, NITA, TDTA, and
ROE) are those which jointly make the model valid and maximize the predictive power
of the model.
19

Table 7 Variables in the Equation (Sample One, 1 st year before default)
B S.E. Wald df Sig. Exp(B)
RETA1 0.979 0.775 1.597 1.000 0.206 2.662
NITA1 -0.227** 0.079 8.164 1.000 0.004 0.797**
TDTA1 0.041* 0.020 4.083 1.000 0.043 1.042*
ROE1 0.020* 0.010 4.005 1.000 0.045 1.021*
RE -0.346 1.763 0.039 1.000 0.844 0.707
TH -0.011 1.190 0.000 1.000 0.993 0.989
MT -0.570 1.409 0.164 1.000 0.686 0.565
CD 0.713 0.938 0.578 1.000 0.447 2.041
DF 0.784 1.446 0.294 1.000 0.588 2.191
CG -1.312 1.263 1.080 1.000 0.299 0.269
TS 0.466 1.575 0.087 1.000 0.767 1.593
2001 -0.941 1.269 0.549 1.000 0.459 0.390
2002 -1.968 1.571 1.570 1.000 0.210 0.140
2003 -0.632 1.159 0.297 1.000 0.586 0.532
2006 -0.719 1.351 0.283 1.000 0.595 0.487
2007 -1.795 1.313 1.868 1.000 0.172 0.166
Omnibus Tests of Model
Coefficients
Hosmer and Lemeshow
Test
Model Summary
Chi-square 33.352 Chi-square 6.732 -2 Log Likelihood 49.825
df 16.000 df 8.000 Cox & Snell R 2
significance 0.007** significance 0.566 Nagelkerke R 2
0.426
0.569
Notes: *, and ** significant at 5, and 1 percent level respectively. The sample includes 60 companies over period
2001-2007. Industry and time dummies are included in the model, however they are not statistically significant.
RE: Real Estate; TH: Technology & Hardware Equipment; MT: Materials; CD: Consumer Durables & Apparel; DF:
Diversified Financials; CG: Capital Goods; TS: Telecommunication Services
For Hypothesis One, highly leveraged companies are more prone to go bankrupt.
According to the logit results, one additional TDTA increases the odds of default by about
4.2%. To put it another way, the odds of default are 1.042 times as large for companies
with high TDTA as for those with low ratio. The result is consistent with the trade-off
theory that PD increases as more debt in a company’s capital structure (Beaver (1966),
Martin (1977), Hol (2002)). The ratio, ROE, has seldom been used in previous MDA or
logit regression empirical analyses. In this study, ROE is at least at 5% significance level,
and it has a positive relationship with odds of default. Specifically, one unit change in
20

ROE increases the odds of default 1.021 times, or an extra ROE increases the odds of
default by 2.1%. This positive relation is in support of the classic risk-return tradeoff
promoted by Black et al (1972) and Chava and Purnanandam (2008). As predicted by
Hypothesis Five, the ability to generate cash/income should negatively influence
corporate failure. The representative variable for the first sample is NITA, and it is
negatively and significantly correlated with odds of default at 1% level. Each additional
NITA decreases the odds of default by 20.3% ((0.797-1)*100), controlling for other
variables in the model. This is consistent with the results in previous studies such as
Deakin (1972), and Ohlson (1980), among others. Free cash flow is not found to have any
significant impact on probability of default. This is different from Altman (1968) and
Zeitun et al (2007)’s results, since they concluded that companies with high free cash
flow measured by RETA have higher default risk. Most scholars applied bankruptcy
research on single industry. However, others (Zeitun, 2007) who believed financial ratios
vary dramatically cross industries and used industry dummies found significant results. In
this analysis, time and industry dummies do not seem to be significant, meaning that no
particular industry or year is significantly different from others in predicting bankruptcy.
Hol et al (2002) did not find industry dummies significantly different from zero either,
and they gave a possible explanation that these variables mostly capture the inter-industry
differences in default probability.
The Omnibus test in Table 7 illustrates that the model is significant at the 1% level,
meaning that at least one of the independent variables is significantly correlated with the
dependent variable, and all the variables in the model jointly are capable of predicting the
dependent variable. The Hosmer and Lemeshow chi-square test of goodness of fit as well
as the classification tables which will be introduced in Section 5.3 assess the models’ fit.
A finding of non-significance, as can be seen in Table 7, indicates that the model
adequately fits the data. It is less straight forward to interpret the ratios under Model
21

Summary. -2 log likelihood (-2LL) is crucial when comparing different logistic models,
but it cannot be used directly in significance test and thus is not very informative in
assessing a single model. SPSS in Logistic regression also outputs R 2 like that in OLS
regression. However the Cox & Snell R 2 and Nagelkerke R 2 can only be seen as
approximations to OLS R 2 , not as the actual percentage of variance explained. Thus, they
are not informative in indicating model fit. For Sample One, the Cox & Snell R 2 and
Nagelkerke R 2 are 42.6% and 56.9% respectively, which are reasonably high.
In the second sample, after adding observations in non-default companies and without
controlling factors such as firm size and time, coefficients of individual variables become
more significant (see Table 8). Interestingly, when randomly picking non-default
companies, we see that size seems to be a significant factor in predicting default. Its
negative coefficient with odds of default is also consistent with Westgaard and Wijst
(2001)’s findings that small firms have limited access to capital markets and are more
likely to fail. It can be concluded that each additional Size (measured by log10(total
assets)) decreases the odds of default by a factor of 0.488, controlling for other variables
in the model. Ratios such as NITA and TDTA are significant at least at 5% level in
sample two as well. However, unlike the result in Table 7, ROE does not have a
significant relationship with odds of default despite of its positive sign. RETA, SATA,
EQTC are not found to be significant either.
Empirical results for two years and three years before default in both samples are
presented in Table 9 and 10 respectively (see Appendix Four to Seven). The main
conclusion is that TDTA seems to be positively and significantly related with odds of
default over all three years in both matched and non-matched sample. Another
observation is that in Table 9 (Appendix Four), the coefficients (β) of 2001 under two and
three years before default are significant. The exponential values are 0.034 (e -3.371 ) and
22

0.0856 (e -2.458 ) respectively. It means that the odds for bankruptcy in 2001 could be 3.4%
(or 8.56%) higher than that in the other years.
Table 8 Variables in the Equation (Sample Two, 1 st year before default)
B S.E. Wald df Sig. Exp(B)
NITA1 -0.232** 0.079 8.629 1.000 0.003 0.793**
Size1 -0.717* 0.332 4.681 1.000 0.031 0.488*
RETA1 0.976 0.594 2.702 1.000 0.100 2.653
TDTA1 0.039* 0.019 4.079 1.000 0.043 1.040*
SATA1 -0.694 0.794 0.764 1.000 0.382 0.500
EQTC1 0.016 0.014 1.430 1.000 0.232 1.016
ROE1 0.003 0.003 1.031 1.000 0.310 1.003
CD 1.206 0.951 1.607 1.000 0.205 3.340
DF 1.137 1.197 0.902 1.000 0.342 3.117
MT -0.895 1.121 0.638 1.000 0.424 0.409
SS -1.126 1.562 0.520 1.000 0.471 0.324
TPT 1.439 1.134 1.610 1.000 0.204 4.217
TH -0.455 1.225 0.138 1.000 0.710 0.635
Omnibus Tests of Model
Coefficients
Hosmer and Lemeshow
Test
Model Summary
Chi-square 71.835 Chi-square 16.268 -2 Log Likelihood 68.181
df 13.000 df 8.000 Cox & Snell R 2
significance 0.000*** significance 0.066 Nagelkerke R 2
Notes: *, **, and *** significant at 10, 5, and 1 percent level respectively. The sample includes 101 companies over
period 2001-2007. Industry dummies are included in the model, however they are not statistically significant.
CD: Consumer Durables & Apparel; DF: Diversified Financials; MT: Materials; SS: Software & Services; TPT:
Transportation; TH: Technology & Hardware Equipment.
5.3 Predictive power of the model
As one year prior to default in sample one, the predictive success according to table 11
comprises 86.7% correct prediction of non-default companies and 76.7% default
companies, with an overall 81.7% accuracy. Table 11 also displays two types of
prediction error, Type I and Type II errors. In this case, Type I error (n=7) occurs when a
0.509
0.679
default company is misclassified as non-default, and when a non-default company is
23

predicted to be default, it is called Type II error (n=4). The overall predictive success in
sample two (86.1%, see Table 12 in Appendix Eight) is relatively higher than that in
sample one. However, as mentioned before, unilaterally increasing the number of
observations (in this case, non-default companies) could somehow bias the interpretation
of the results 20 . Consequently, the number of compared observations (default &
non-default) in each sample should not be different from each other too much.
Table 11 Classification (Sample One, 1 st year before default)
Predicted
Default
Observed 0 1 Percentage Correct
Default 0 26 4 86.7
The cut value is .500
1 7 23 76.7
Overall Percentage 81.7
An alternative way to look at the prediction is through the histogram of predicted
probabilities (Figure 1, representing sample one). The x axis represents the probability
from 0 (non- default) to 1 (default). The y axis is the frequency of the cases. Ideally,
failed (non-failed) companies should be clustered on the right (left) side of the x axis.
Moreover a U-shaped distribution with well differentiated predictions is more desirable
over normal distribution. Because a model where predictions are close to 0 or 1 provides
more information than one with predictions all cluster around the cut value 0.5. This
U-shaped distribution might be less obvious in Figure 1, mostly because the sample size
is rather small. As more observations are included in the model, a more desirable
distribution can be clearly seen in Figure 2 (representing sample two) in Appendix Eight.
20
The overall accuracy of the logit in Sample One equals 86.7%*0.5+76.7% *0.5=81.7%, because the
default and non-default companies represent half of the total observations respectively. In Sample Two, the
overall predictive success=95.8%*(71/101)+63.3%*(30/101)=86.1%. The increase in predictive power is
mostly due to the uneven weights distribution.
24

In this study, the predictive success of the models for all three years prior to default in
both samples is reasonably high (all above 70%). In general, models in sample two have
higher predictive power than those in sample one. Within each sample, the further the
distance is to bankruptcy, the less powerful the predictive power becomes. Although the
difference between year two and year three is quite small, this result is consistent with
Zeitun et al (2007)’s. In their matched sample, the percent of predictive successes in year
two and year three are 80% and 81% respectively.
5.4 Robustness Test
The robustness of the model depends on if it can be applied in multi-period. That is, the
longer the accuracy of the model could be maintained, the better the model becomes. In
this study, as the predictive powers of the model in all three years prior to bankruptcy are
above 70% in both samples, we conclude that the model seem to be robust across
25

estimation procedure. However it is interesting to check what impact of outliers to the
model prediction would be. After excluding observations with standardized residuals
greater than 2 (Table 13), the predictive power of the entire model improves, and Type I
(n=3) and Type II errors (n=3) decrease at the same time (Table 14).
Case Selected
Status a
Table 13 Casewise List b (Sample One, 1 st year, outliers)
Observed Predicted Predicted Temporary Variable
Default
Group
Resid ZResid
34 S 0** 0.859 1 -0.859 -2.469
37 S 1** 0.243 0 0.757 1.764
41 S 1** 0.190 0 0.810 2.067
55 S 1** 0.194 0 0.806 2.038
a. S = Selected, U = Unselected cases, and ** = Misclassified cases.
b. Cases with studentized residuals greater than 2.000 are listed.
Table 14 Classification (Sample One, 1 st year, excluding outliers)
Predicted
Default
Observed 0 1 Percentage Correct
Default 0 26 3 89.7
The cut value is .500
1 3 23 88.9
Overall Percentage 89.3
Nonetheless, such improvements are not costless. The results generated by the new model
(excluding outliers) do not seem to be as stable as the original results. Especially for the
industry and time dummies, their standard errors slightly increase (see Table 15). This is
probably because of the limited number of companies in sample one. Elimination of
outliers could cause large fluctuations in the estimation of the parameters. When more
observations are used in the sample (see Appendix Nine), the model is robust after
excluding outliers.
26

Table 15 Variables in the Equation (Sample One, 1 st year, excluding outliers)
B S.E. Wald df Sig. Exp(B)
RETA1 1.453 1.008 2.076 1.000 0.150 4.276
NITA1 -0.473*** 0.173 7.464 1.000 0.006 0.623
TDTA1 0.116** 0.048 5.892 1.000 0.015 1.123
ROE1 0.047** 0.020 5.817 1.000 0.016 1.048
RE -1.877 2.157 0.757 1.000 0.384 0.153
TH 1.575 1.602 0.967 1.000 0.325 4.831
MT -2.110 2.186 0.932 1.000 0.334 0.121
CD -0.944 1.484 0.405 1.000 0.525 0.389
DF 0.662 1.663 0.159 1.000 0.690 1.939
CG -2.431 1.525 2.542 1.000 0.111 0.088
TS 0.429 6.419 0.004 1.000 0.947 1.535
2001 -1.875 1.628 1.327 1.000 0.249 0.153
2002 -2.207 2.386 0.855 1.000 0.355 0.110
2003 -0.333 1.468 0.051 1.000 0.820 0.717
2006 -1.563 3.371 0.215 1.000 0.643 0.209
2007 -6.996** 3.404 4.223 1.000 0.040 0.001
6. Conclusion
The article focused on predicting bankruptcies for Hong Kong based companies. It
examines the relationship between default risk and various financial ratios. Logistic
regression is the main methodology in this research for testing different theories and
hypotheses. The result is in support of capital structure theory and risk-return tradeoff. To
be specific, TDTA, representing capital structure, has a positive and significant impact on
bankruptcy, which is consistent with the results of Martin (1977) and Hol et al (2002).
Shareholders’ expected return, as reflected by ROE, is also an important determinant of
corporate failure. ROE has not been used extensively in previous MDA or logit analyses.
But its positive relationship with PD as estimated in the study is consistent with the
classic risk-return tradeoff. Moreover, profitability, as measured by NITA, is significantly
and negatively related to default probabilities in both samples (Altman (1968), and
27

Ohlson (1980)). In the second sample, it has been proved that firm size plays an
important role in predicting PD. Small firms are more prone to go bankrupt because of
the limited access to capital market. Westgaard and Wijst (2001) and others illustrate the
same result. Other variable, such as free cash flow (as measured by RETA), does not
seem to be related to default risk for companies in Hong Kong, since it is not significant
in both samples. Contrary to previous empirical results, such as Zeitun et al (2007), this
inconsistency should be explained by a Hong Kong specific factor. Because most of the
Hong Kong companies (even large publicly traded) are family controlled 21 , agency
problem raised by free cash flow does not seem to be severe in such context (without the
principal and agent relationship). In that case, free cash flow, measured by RETA, should
not threaten a company’s default probability. Industry dummies do not explain
bankruptcy in this study. The result is consistent with Hol (2002)’s, meaning that industry
variables capture the inter-industry differences in default probability. The majority of the
time dummies are not significantly correlated with bankruptcy, except for the year 2001
for two and three years before bankruptcy in sample one. The result may imply that firms
in Hong Kong have higher probabilities to go bankrupt in 2001 compared with those in
other years. Interestingly, in 2001 the real GDP increase by percentage was the lowest
over 2000-2007 according to Census and Statistics Department (Hong Kong) 22 .
Intuitively, this indicates that macroeconomic factors could influence default probability.
The predictive power for all three years before bankruptcy in both samples is reasonably
high, and generally increases as time approaching to the bankruptcy event. The result is
21
70% of Hong Kong listed companies were majority controlled by a family or an individual (Hong Kong
Society of Accountants, 1996). 53% of all listed companies had one shareholder or one family group of
shareholders that owned 50% or more of the entire issued capital (Hong Kong Society of Accountants,
1997). Also see publications of Ho (2003), and the presentation at International Financial Corporation IO
Training Session on 30 April 2004, “Corporate governance in Hong Kong”, by Patrick Contoy, Hong Kong
Exchanges and Clearing.
22
Official website: http://www.censtatd.gov.hk/hong_kong_statistics/statistical_tables/
2000+: Real GDP increases by percentage: 2000 (7.95), 2001 (0.50), 2002 (1.84), 2003 (3.01), 2004 (8.46),
2005 (7.12), 2006 (6.75), 2007 (6.83)
28

useful in describing default risk in the context of Hong Kong. As a risk manager of a
bank, he or she would first look at borrowers (companies)’ capital structure, profitability,
firm size, and equity returns over other characters, such as retained earnings, or industry
type according to the empirical results in this study.
The limitations of the research need to be taken into consideration. One of the limitations
is that the multicollinearity problem cannot be fully dealt with. Two main solutions
adopted in the research are reducing explanatory variables in the models and increasing
sample size, ensuring that multicollinearity is to a large extent under control. Another
limitation is from the dataset. Only 30 publicly traded companies have been defined as
default in the study (due to mostly missing value, and the definition of bankruptcy) over
period 2001 to 2007. This results in a relatively small sample size in both matched and
non-matched sample. However, because bankruptcies are scarce activities, the problem of
limited sample observations also exists in previous studies 23 .
The models in this study will only be viewed as a static and myopic way in predicting
bankruptcies in short term. In future research, macroeconomic risk factors should also be
incorporated in estimating corporate default (see e.g., Fama (1986)). Macroeconomic
conditions have an impact not only on firms’ default risk but also on their financial
decisions (Hackbarth et al, 2006). The model would then provide more insights in
predicting future default under different scenarios. Meanwhile, with more and more
countries are adopting Basel II, similar bankruptcy analyses should also be encouraged in
Asia, where risk management practices are relatively weak compared with those in
western countries.
23
For example, Altman (1968)’s sample comprises 66 corporations with 33 firms in each of the two groups.
Castagna and Matolcsy (1981) analyzed 21 failed and non-failed firms respectively in their MDA analysis.
In Zeitun et al (2007)’s first sample, it is composed of 29 failed and 30 non-failed firms.
29

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banks”, Journal of Finance
Studenmund, A. H., 2000, “Using Econometrics: A Practical Guide”, 4 th Edition, Addison
Wesley
Treynor, J. L., 1962, “Toward a Theory of Market Value of Risky Assets”, unpublished
manuscript
Westgaard, S., and N. Wijst, 2001, “Default probabilities in a corporate bank portfolio: A
logistic model approach”, European Journal of Operational Research 135, p338-349
Zeitun, R., G. Tian, and S. Keen, 2007, “Default Probability for the Jordanian Companies:
A Test of Cash Flow Theory”, International Research Journal of Finance and
Economics 8
33

MDA
Appendix One
Table 1 Literature Summary
Author Year Ratios
Beaver 1966
Altman 1968
Deakin 1972
Sinkey 1975
Altman et al 1977
cash flow/total assets, net income/total assets, total debt/total assets,
and cash flow/total debt
working capital/total assets, retained earnings/total assets, earning
before interest and taxes/total assets, market value equity/book
value of total debt, and sales/total assets
Working capital/Total assets, current assets/current liabilities, total
debt/total assets, quick assets/sales, quick assets/total assets,
cash/total assets, cash/sales, current assets/total assets, cash/current
liabilities, net income/total assets, current assets/sales, cash
flow/total debt
Other expenses as % of revenue, loans as % of revenue, operating
expense/operating income, loans/(capital + reserve), state and local
obligations as % of revenue, (cash + U.S. treasury securities)/total
assets, loans/total assets, provision for loan losses/operating
expense, U.S. treasury securities as % of revenue, interest paid on
deposits as % in revenue
Return on assets, stability of earnings (measured by a normalized
measure of the standard error of estimate around a ten-year trend,
debt service (measured by the familiar interest coverage ratio,
cumulative profitability (measured by the firm’s retained earnings),
liquidity, capitalization, size
34

Logistic
regression
Appendix One (continued)
Author Year Ratios
Martin 1977
Ohlson 1980
Westgaard and
Wijst
2001
Hol et al 2002
Zeitun et al 2007
Net income/total assets, gross
charge-offs/net operating income,
expenses/operating revenues,
loans/total assets, commercial
loans/total loans, loss
provision/loans+securities, net liquid
assets/total assets, gross capital/risk
assets
Size, total liabilities to total assets,
working capital to total assets,
current liabilities to current assets,
OENEG (one if total liabilities
exceeds total assets, zero otherwise),
net income to total assets, funds
provided by operations to total
liabilities, INTWO (one if net income
was negative for the last two years,
zero otherwise)
cash flow to debt, financial coverage,
liquidity, and equity ratio
total debt/total assets, tax/earnings
before interest and tax, cash flow (net
income+depreciation/total assets),
standard deviation of cash flow,
bankruptcy cost (ln(sales))
Net income to total liabilities, cash
flow to total debt, sales to total
assets, current assets minus current
liabilities to total assets, , long-term
liabilities to total assets, total debt to
total equity, firms age in years, log
the assets of the firm, retained
earning to total assets
Significant &
Positive
expenses/operating
revenues,
loans/total assets
current liabilities
to current assets,
INTWO
total debt/total
assets, standard
deviation of cash
flow, and
bankruptcy cost
retained earning to
total assets
Significant &
Negative
gross
capital/risk
assets
working capital
to total assets
all
cash flow
sales to total
assets, net
income to total
liabilities
35

Appendix Two
Table 4 Descriptive Statistics (Sample One, 2 nd and 3 rd year)
Default Companies Non-Default Companies
Minimum Maximum Mean STDV Variance Minimum Maximum Mean STDV Variance
CFTD2 -513.12 125.90 -12.35 97.35 9476.50 -11.80 19.23 1.64 5.36 28.77
CFTD3 -4.57 9.29 0.36 2.09 4.39 -10.68 36.35 2.28 8.23 67.73
RETA2 -24.60 0.55 -0.95 4.50 20.29 -38.82 0.67 -1.38 7.15 51.08
RETA3 -8.89 0.51 -0.44 1.83 3.34 -29.47 0.78 -0.98 5.44 29.55
WCTA2 -1.21 0.54 -0.10 0.43 0.18 -0.43 0.61 0.12 0.23 0.05
WCTA3 -0.94 0.99 0.06 0.38 0.14 -0.44 0.73 0.17 0.25 0.06
CR2 0.03 3.89 1.20 0.88 0.77 0.15 3.47 1.56 0.85 0.71
CR3 0.16 67.21 4.37 12.76 162.69 0.16 6.52 1.75 1.19 1.41
NITA2 -257.04 31.96 -17.25 62.04 3848.38 -85.28 41.94 -0.06 24.72 610.83
NITA3 -205.59 28.30 -10.87 45.93 2109.58 -124.05 27.01 -3.19 28.17 793.38
TDTA2 0.01 113.25 33.34 28.42 807.88 0.34 56.01 16.40 13.42 180.00
TDTA3 0.22 277.39 37.82 49.67 2467.28 0.00 71.25 17.43 15.82 250.40
SATA2 0.02 2.84 0.89 0.77 0.59 0.04 3.11 1.00 0.78 0.61
SATA3 0.02 2.84 0.88 0.68 0.46 0.03 4.55 0.96 0.86 0.73
Size2 1.60 4.07 2.93 0.61 0.38 1.14 5.69 2.97 0.89 0.79
Size3 -1.08 3.98 2.86 0.94 0.88 1.34 5.60 2.93 0.86 0.74
EQTC2 30.79 100.00 77.24 22.48 505.56 37.35 100.00 83.18 16.85 283.81
EQTC3 18.89 100.00 74.56 22.36 499.77 -652.16 100.00 56.89 135.77 18434.32
ROE2 -610.38 84.34 -31.73 127.36 16220.59 -1593.75 68.05 -52.14 295.40 87261.91
ROE3 -2537.76 58.16 -110.31 476.83 227364.26 -424.07 93.25 -11.49 91.22 8321.36
36

Appendix Three
Table 5 Descriptive Statistics (Sample Two, 2 nd and 3 rd year)
Default Companies Non-Default Companies
Minimum Maximum Mean STDV Variance Minimum Maximum Mean STDV Variance
CFTD2 -513.12 125.90 -12.35 97.35 9476.50 -4.55 158.32 6.50 24.00 575.98
CFTD3 -4.57 9.29 0.36 2.09 4.39 -10.68 64.07 4.51 13.14 172.57
RETA2 -24.60 0.55 -0.95 4.50 20.29 -3.94 0.73 -0.02 0.91 0.82
RETA3 -8.89 0.51 -0.44 1.83 3.34 -3.87 0.78 -0.02 0.83 0.69
WCTA2 -1.21 0.54 -0.10 0.43 0.18 -0.43 0.71 0.17 0.25 0.06
WCTA3 -0.94 0.99 0.06 0.38 0.14 -0.42 0.66 0.16 0.23 0.05
CR2 0.03 3.89 1.20 0.88 0.77 0.15 23.32 2.42 3.18 10.10
CR3 0.16 67.21 4.37 12.76 162.69 0.01 11.26 2.16 2.12 4.47
NITA2 -257.04 31.96 -17.25 62.04 3848.38 -85.28 41.94 3.96 16.72 279.46
NITA3 -205.59 28.30 -10.87 45.93 2109.58 -124.05 41.34 4.42 20.76 431.18
TDTA2 0.01 113.25 33.34 28.42 807.88 0.08 66.50 20.85 16.12 259.76
TDTA3 0.22 277.39 37.82 49.67 2467.28 0.00 60.24 21.30 16.04 257.37
SATA2 0.02 2.84 0.89 0.77 0.59 0.01 3.18 0.87 0.72 0.52
SATA3 0.02 2.84 0.88 0.68 0.46 0.00 3.55 0.86 0.72 0.51
Size2 1.60 4.07 2.93 0.61 0.38 1.14 5.69 3.34 0.84 0.71
Size3 -1.08 3.98 2.86 0.94 0.88 1.34 5.60 3.29 0.82 0.67
EQTC2 30.79 100.00 77.24 22.48 505.56 23.55 100.00 80.55 18.17 330.29
EQTC3 18.89 100.00 74.56 22.36 499.77 10.39 100.00 80.10 19.98 399.03
ROE2 -610.38 84.34 -31.73 127.36 16220.59 -202.77 68.05 5.64 39.61 1568.70
ROE3 -2537.76 58.16 -110.31 476.83 227364.26 -196.74 93.25 11.46 39.46 1556.94
37

Appendix Four
Table 9 Coefficients two or three years before default (Sample One)
Variables Two years before default Three years before default
RETA 0.447 1.214**
(0.206) (0.006)
NITA -0.074 0.156*
(0.339) (0.019)
TDTA 0.097** 0.084**
(0.007) (0.001)
ROE 0.023 -0.089*
(0.509) (0.011)
FBT -1.558 dropped
(0.274)
TPT 1.540 dropped
(0.293)
MT dropped -2.267
(0.159)
CD dropped -0.583
(0.469)
CG dropped -0.451
(0.683)
TS dropped -1.128
(0.422)
2001 -3.371* -2.458*
(0.041) (0.043)
2002 -1.651 -1.183
(0.170) (0.334)
2003 -1.501 -1.521
(0.060) (0.083)
2004 dropped dropped
2005 -1.577 -0.962
(0.108) (0.302)
2006 -2.275 -0.834
(0.052) (0.406)
2007 -2.475* -1.810
(0.050) (0.099)
38

Appendix Five
Table 9 (continued) Model Summary
Percentage Correct 73.333 73.333
-2 Log likelihood 62.294 58.940
Cox & Snell R Square 0.294 0.332
Nagelkerke R Square 0.392 0.443
Omnibus Tests of Model Coefficients
Chi-square 20.883 24.237
df 12.000 14.000
sig 0.050* 0.043*
Hosmer and Lemeshow Test
Chi-square 3.654 9.892
df 8.000 8.000
sig 0.887 0.273
39

Appendix Six
Table 10 Coefficients two or three years before default (Sample Two)
Variables Two years before default Three years before default
NITA -0.068 0.036
-0.077 -0.316
Size -0.604* -0.609
(0.026) -0.067
ROE 0.018 -0.029
-0.147 -0.122
TDTA 0.037** 0.043**
(0.006) (0.010)
SATA -0.367 -0.67
-0.349 -0.183
EQTC 0.004 -0.001
-0.741 -0.956
RETA 0.247 0.464
-0.344 -0.382
CD 1.391 1.745*
-0.055 (0.049)
MT -0.199 -0.094
-0.825 -0.924
RE -0.35 0.146
-0.77 -0.915
TH -0.016 dropped
-0.984
DF -0.057 dropped
-0.96
CG dropped 1.099
-0.252
FBT dropped 0.669
-0.513
SS dropped -0.15
-0.898
TS dropped 0.314
-0.779
TPT dropped 0.117
-0.916
40

Appendix Seven
Table 10 (continued) Model Summary
Percentage Correct 78.218 79.208
-2 Log likelihood 101.122 97.363
Cox & Snell R Square 0.320 0.344
Nagelkerke R Square 0.426 0.459
Omnibus Tests of Model Coefficients
Chi-square 38.894 42.653
df 12.000 15.000
sig 0.000** 0.000**
Hosmer and Lemeshow Test
Chi-square 4.774 4.556
df 8.000 8.000
sig 0.781 0.804
41

Appendix Eight
Table 12 Classification (Sample Two, 1 st year before default)
Predicted
Default
Observed 0 1 Percentage Correct
Default 0 68 3 95.8
The cut value is .500
1 11 19 63.3
Overall Percentage 86.1
42

Case Selected
Status a
Appendix Nine
Table 16 Casewise List b (Sample Two, 1 st year, outliers)
Observed Predicted Predicted Temporary Variable
Default
Group
Resid ZResid
67 S 1** 0.020 0 0.980 6.992
99 S 1** 0.013 0 0.987 8.757
a. S = Selected, U = Unselected cases, and ** = Misclassified cases.
b. Cases with studentized residuals greater than 2.000 are listed.
Table 17 Classification (Sample Two, 1 st year, excluding outliers)
Predicted
Default
Observed 0 1 Percentage Correct
Default 0 68 3 95.8
The cut value is .500
1 6 22 78.6
Overall Percentage 90.9
Table 18 Variables in the Equation (Sample Two, 1 st year, excluding outliers)
B S.E. Wald df Sig. Exp(B)
NITA1 -0.488** 0.164 8.866 1.000 0.003 0.614**
Size1 -1.227* 0.484 6.433 1.000 0.011 0.293*
RETA1 2.130 1.208 3.107 1.000 0.078 8.412
TDTA1 0.095** 0.032 8.650 1.000 0.003 1.099**
SATA1 -3.280* 1.530 4.594 1.000 0.032 0.038*
EQTC1 0.033 0.019 3.118 1.000 0.077 1.033
ROE1 0.008 0.005 2.424 1.000 0.119 1.008
CD 3.654* 1.583 5.330 1.000 0.021 38.613*
DF 2.086 1.604 1.692 1.000 0.193 8.057
MT -1.440 1.388 1.076 1.000 0.300 0.237
SS -2.411 1.891 1.625 1.000 0.202 0.090
TPT 3.198* 1.612 3.937 1.000 0.047 24.479*
TH -1.324 2.330 0.323 1.000 0.570 0.266
43