Financial Ratios as Predictors of Failure: Evidence from ... - ERIM
Financial Ratios as Predictors of Failure: Evidence from ... - ERIM
Financial Ratios as Predictors of Failure: Evidence from ... - ERIM
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17 Nov 2008<br />
<strong>Financial</strong> <strong>Ratios</strong> <strong>as</strong> <strong>Predictors</strong> <strong>of</strong> <strong>Failure</strong>:<br />
<strong>Evidence</strong> <strong>from</strong> Hong Kong using Logit Regression<br />
Student: Weiying Guo 292341<br />
Coach: Dr. Ben Tims<br />
Co-reader: Drs. Johannes Meuer<br />
Finance and Investment<br />
Rotterdam School <strong>of</strong> Management
Preface<br />
The author 1 declares that the text and work presented in this m<strong>as</strong>ter thesis is original and<br />
that no sources other than those mentioned in the text and its references have been used in<br />
creating the m<strong>as</strong>ter thesis.<br />
The copyright <strong>of</strong> the m<strong>as</strong>ter thesis rests with the author. The author is responsible for its<br />
contents. RSM Er<strong>as</strong>mus University is only responsible for the educational coaching and<br />
beyond that cannot be held responsible for the content.<br />
1<br />
The author would like to thank Dr. Ben Tims, and Drs. Johannes Meuer for valuable suggestions and<br />
helpful comments. All remaining errors are the author’s responsibility.<br />
1
Abstract<br />
This paper presents some empirical results <strong>of</strong> predicting corporate failure by using<br />
various financial ratios. It aims to identify the characteristics that distinguish default and<br />
non-default companies. Two samples (matched and non-matched) <strong>of</strong> Hong Kong b<strong>as</strong>ed<br />
companies are used in this research over the period 2001-2007. By using logistic<br />
regression, it shows that level <strong>of</strong> debt, and return on equity incre<strong>as</strong>e corporate failure,<br />
where<strong>as</strong> bankruptcy decre<strong>as</strong>es with firm size and pr<strong>of</strong>itability. The results are in support<br />
<strong>of</strong> capital structure theory and risk-return trade<strong>of</strong>f. The predictive power <strong>of</strong> the logit<br />
model is re<strong>as</strong>onably high in three years prior to default.<br />
Keywords: Risk Management, Probability <strong>of</strong> default, bankruptcy, logistic regression<br />
2
Table <strong>of</strong> Contents<br />
1. Introduction..................................................................................................................... 4<br />
2. Probability <strong>of</strong> Default and Bankruptcy........................................................................... 5<br />
3. Literature Review............................................................................................................ 6<br />
3.1 Theories..................................................................................................................... 7<br />
3.2 Multi factors in predicting PD and the methodologies ............................................. 9<br />
3.2.1 Multiple Discriminant Analysis.......................................................................... 9<br />
3.2.2 Logistic Regression .......................................................................................... 10<br />
4. Data and Methodology.................................................................................................. 11<br />
4.1 Methodology ........................................................................................................... 11<br />
4.2 Data and Sample...................................................................................................... 12<br />
4.3 Explanatory Variables and Hypotheses................................................................... 13<br />
5. Empirical Results.......................................................................................................... 16<br />
5.1 Descriptive Results.................................................................................................. 16<br />
5.2 Estimation results <strong>of</strong> the Logit model ..................................................................... 19<br />
5.3 Predictive power <strong>of</strong> the model ................................................................................ 23<br />
5.4 Robustness Test....................................................................................................... 25<br />
6. Conclusion .................................................................................................................... 27<br />
Reference .......................................................................................................................... 30<br />
Appendix One ................................................................................................................... 34<br />
Appendix Two................................................................................................................... 36<br />
Appendix Three ................................................................................................................ 37<br />
Appendix Four .................................................................................................................. 38<br />
Appendix Five................................................................................................................... 39<br />
Appendix Six .................................................................................................................... 40<br />
Appendix Seven................................................................................................................ 41<br />
Appendix Eight ................................................................................................................. 42<br />
Appendix Nine.................................................................................................................. 43<br />
3
1. Introduction<br />
One year after the onset <strong>of</strong> the credit crunch, most Americans have still been suffering<br />
<strong>from</strong> losing jobs, skyrocketing commodity prices, weakening dollar, all in all, a bad<br />
economy. The downward trend h<strong>as</strong> unfortunately crept to countries in Europe and Asia,<br />
and fear <strong>of</strong> potential financial markets meltdown h<strong>as</strong> reached its new level ever before<br />
after the 1997 Asian financial crisis and 9/11. At the same time, credibility and risk<br />
management have probably never caught such attention <strong>from</strong> investors and policymakers<br />
in history. The credit crunch is prompting a new age <strong>of</strong> risk management, requiring risk<br />
managers to me<strong>as</strong>ure risk in real time and help prevent future crises. The new B<strong>as</strong>el<br />
framework, B<strong>as</strong>el II, intends to further strengthen the soundness and stability <strong>of</strong> the<br />
international banking system (B<strong>as</strong>el committee, 2004) by promoting stronger risk<br />
management practices in the banking industry. Under the Internal Rating Approach,<br />
banks are given opportunities to estimate counterparties’ default probabilities by<br />
themselves. Probability <strong>of</strong> default (PD) plays an important role not only because it is the<br />
cornerstone when calculating regulatory capital requirements, but also when it comes to<br />
making tough loan decisions it helps banks discriminate good borrowers <strong>from</strong> bad<br />
borrowers.<br />
For banks, one <strong>of</strong> the best ways to examine a company’s financial health is by looking at<br />
its financial ratios. The objective <strong>of</strong> this paper is to explore the possibilities to predict<br />
probability <strong>of</strong> default and to identify the characteristics distinguishing default companies<br />
<strong>from</strong> non-default ones by using logistic regression. Relying on existing theories, such <strong>as</strong><br />
risk-return trade<strong>of</strong>f, and capital structure theory, the study examines the relationship<br />
between PD and different financial ratios in various industries in Hong Kong. Many<br />
scholars have conducted default research in the United States and Western Europe (see<br />
4
Beaver (1966), Marais (1979), Altman and Lavallee (1981) and Westgaard and Wijst<br />
(2001) and others). Nevertheless, there h<strong>as</strong> been little similar bankruptcy research in Asia.<br />
One possible explanation could be that Asian financial markets just emerged in the l<strong>as</strong>t<br />
decade, where<strong>as</strong> most <strong>of</strong> the default analyses were conducted over 20 years ago. So far<br />
there h<strong>as</strong> been no comprehensive bankruptcy analysis performed in the context <strong>of</strong> Hong<br />
Kong. However, being one <strong>of</strong> the first banking industries who adopted the new banking<br />
regulation, Hong Kong deserves extra attention. Compared to most empirical studies in<br />
the 70s and 80s, the data set used in this research (<strong>from</strong> 2001 to 2007) is rather<br />
contemporary. Therefore, whether previous empirical results still stand in a modern<br />
context is under question.<br />
The rest <strong>of</strong> the paper is structured <strong>as</strong> follows. In the next section, I briefly introduce<br />
probability <strong>of</strong> default and bankruptcy. Section 3 reviews literature. In section 4, I explain<br />
the data, sample selection, and methodology used in the analysis. Section 5 presents the<br />
empirical results. Section 6 concludes.<br />
2. Probability <strong>of</strong> Default and Bankruptcy<br />
Legally speaking, bankruptcy is described <strong>as</strong> a debtor not being able to meet its debt<br />
obligations <strong>as</strong> they fall due. In an accounting sense, when the sum <strong>of</strong> the realized c<strong>as</strong>h<br />
flow and expected future c<strong>as</strong>h flow is less than the debt obligations, bankruptcy occurs.<br />
PD is used to me<strong>as</strong>ure the likelihood that a firm defaults under its debt obligations.<br />
Different researchers have different definitions <strong>of</strong> failure 2 . Operationally, Beaver (1968<br />
(1)) defined a failed firm when any <strong>of</strong> the following events h<strong>as</strong> occurred: bankruptcies,<br />
bond default, overdrawn bank account, or nonpayment <strong>of</strong> a preferred stock dividend.<br />
2<br />
See a summary <strong>of</strong> the definitions <strong>of</strong> failure in major empirical default analyses, by C<strong>as</strong>tagna and Matolcsy<br />
(1981)<br />
5
However he did not find substantial differences in the empirical results even under this<br />
boarder definition. Deakin (1972) only included those firms which experienced<br />
bankruptcy, insolvency, or which were otherwise liquidated for the benefit <strong>of</strong> creditors in<br />
his default analysis. I define default companies <strong>as</strong> those delisted (except for companies<br />
that are taken over by others 3 ) <strong>from</strong> the Hong Kong Stock Exchange 4 , or <strong>as</strong> those listed<br />
<strong>as</strong> “ce<strong>as</strong>ed place <strong>of</strong> business”, or “winding up” according to the Integrated Companies<br />
Registry Information System (ICRIS) 5 . Therefore, the date <strong>of</strong> default is either the date <strong>of</strong><br />
delisting <strong>from</strong> the HKEx, or the date <strong>of</strong> winding up.<br />
Bankruptcy <strong>of</strong> a company generates both direct and indirect costs. Assets <strong>of</strong> the firm are<br />
usually being sold at a price well below the one that would be realized before the<br />
bankruptcy announcement. Accountants and lawyers can cost huge amounts <strong>of</strong> money.<br />
The companies’ brand name and long established reputation are <strong>of</strong>ten ruined. Of course,<br />
failure <strong>of</strong> a company is costly to suppliers <strong>of</strong> capital, which in most c<strong>as</strong>es are banks. It is<br />
therefore in banks’ interest to predict borrowers’ probability <strong>of</strong> default when making loan<br />
decisions.<br />
3. Literature Review<br />
Bankruptcies have been mostly explained by capital structure, risk-return trade<strong>of</strong>f, c<strong>as</strong>h<br />
flow, and agency theory. Some scholars also tried to combine different proxy variables<br />
that are derived <strong>from</strong> accounting data into their models for predicting corporate default.<br />
These studies vary <strong>from</strong> time, countries, and industries. However they all proved that<br />
3<br />
Acquired companies will not be included in the sample selection. HKEx <strong>of</strong>fers relevant takeover<br />
information (l<strong>as</strong>t updated on 22 June 2007) regarding announcement date, name <strong>of</strong> <strong>of</strong>feror, name <strong>of</strong> <strong>of</strong>feree,<br />
and <strong>of</strong>fer type, etc.<br />
4<br />
This definition is also used by Izan (1984) for Australian companies, and Zeitun, Tian, & Keen (2007) for<br />
Jordanian companies.<br />
5<br />
Official website <strong>of</strong>fered by Hong Kong government. http://www.icris.cr.gov.hk/csci/<br />
6
financial ratios can be used to predict PD.<br />
3.1 Theories<br />
In a world without tax and bankruptcy, there is no optimal capital structure under the<br />
cl<strong>as</strong>sic Modigliani-Miller irrelevance theorem 6 (Modigliani & Miller 1958, 1963).<br />
Nevertheless, in the real world, most companies have to choose between tax advantages<br />
and bankruptcy costs (trade-<strong>of</strong>f theory, Kraus and Litzenberger, 1973). That is, debt<br />
brings tax shields for a company, but at the same time it incre<strong>as</strong>es distress or bankruptcy<br />
costs. The optimal amount <strong>of</strong> debt should produce the lowest weighted average cost <strong>of</strong><br />
capital. Kim (1978) claimed that the market value <strong>of</strong> a company decre<strong>as</strong>es <strong>as</strong> financial<br />
leverage becomes extreme, thus it should finance less debt than its debt capacity (the<br />
optimum 7 ). The transfer <strong>of</strong> ownership <strong>from</strong> shareholders to debtholders also encourages<br />
risk taking behavior, because shareholders have the limited downside risk while enjoying<br />
unlimited upside potential, further reinforcing the conflict <strong>of</strong> interests between various<br />
stakeholders in the company. Therefore, higher debt in one’s capital structure should be<br />
<strong>as</strong>sociated with higher PD.<br />
From external to internal financing, c<strong>as</strong>h flow h<strong>as</strong> been an important determinant <strong>of</strong><br />
bankruptcy. Scott (1981) claimed that c<strong>as</strong>h flow variables involve estimates <strong>of</strong> the firm’s<br />
future c<strong>as</strong>h flow distribution, and that p<strong>as</strong>t and present c<strong>as</strong>h flow should be able to predict<br />
PD. <strong>Financial</strong> Accounting Standards Board (1981) stated that “the greater the amount <strong>of</strong><br />
future net c<strong>as</strong>h inflows <strong>from</strong> operations, the greater the ability <strong>of</strong> the enterprise to<br />
withstand adverse changes in operating conditions”. Other scholars have also shown<br />
6<br />
The total value <strong>of</strong> a firm will not change because <strong>of</strong> its capital structure. In other words, no capital<br />
structure is better or worse than any other capital structure for the firm’s shareholders.<br />
7<br />
The breakeven point is where the marginal benefit <strong>of</strong> the tax shield equals the marginal cost <strong>of</strong> financial<br />
distress.<br />
7
interest in predicting bankruptcy by incorporating c<strong>as</strong>h flow characteristics in their<br />
predictive models (see e.g. C<strong>as</strong>ey and Bartczak (1985), Gentry et al (1985), Gombola et<br />
al (1987), and Aziz (1988), among others). C<strong>as</strong>h rich companies are <strong>as</strong>sumed to be better<br />
able to diversify their risks and therefore less likely to go bankrupt. Deakin (1972) used<br />
several c<strong>as</strong>h flow ratios (c<strong>as</strong>h flow/total debt, c<strong>as</strong>h/total <strong>as</strong>sets, c<strong>as</strong>h/current liabilities,<br />
c<strong>as</strong>h/sales) to test their coefficients with bankruptcy. The signs <strong>of</strong> the coefficients were<br />
negative but did not seem to be consistent in all five years before companies’<br />
bankruptcies. Recently, Zeitun et al (2007) demonstrated the negative relationship<br />
between c<strong>as</strong>h flow and default risk, however the results were not significant. Similar to<br />
c<strong>as</strong>h flow, a shortage <strong>of</strong> liquidity could also trigger corporate failure. C<strong>as</strong>h, the most<br />
liquid form <strong>of</strong> <strong>as</strong>sets is crucial to a company disregarding its size or industry type.<br />
Furthermore, it also matters how quickly a company is able to covert other <strong>as</strong>sets into<br />
c<strong>as</strong>h with no or little price discount. Therefore, the availability and convertibility <strong>of</strong> a<br />
company’s <strong>as</strong>sets are extremely important especially in crises. Becchetti and Sierra<br />
(2003), among others used liquidity ratios for their bankruptcy analyses.<br />
There are always trade-<strong>of</strong>fs between internal and external financing. According to the<br />
pecking order theory (Myers, 1984), a company should use relatively costless internal<br />
financing over external financing. However internal financing is not without problem. If a<br />
company’s c<strong>as</strong>h flow cannot be distributed to its shareholders or debtholders, managers<br />
are more likely to misuse retained earnings. Internal financing better sources free c<strong>as</strong>h<br />
flow (me<strong>as</strong>ured <strong>as</strong> operating c<strong>as</strong>h flow minus the capital expenditures) and thereby<br />
incre<strong>as</strong>es agency costs (Jensen, 1986) due to the <strong>as</strong>ymmetric information between<br />
managers and shareholders. A high level <strong>of</strong> free c<strong>as</strong>h flow seems to destroy corporate<br />
value, so it is expected to be positively related to bankruptcy.<br />
Changes in market prices <strong>of</strong> stocks can also be used to predict failure (Beaver 1968 (2),<br />
8
Altman and Brenner, 1981). According to the cl<strong>as</strong>sic Capital Asset Pricing Model<br />
(CAPM) 8 , investors would expect higher returns for bearing more risk. The first and most<br />
well-know empirical tests can be traced back to over 30 years ago. For example, Black et<br />
al (1972) provided empirical tests and additional insights b<strong>as</strong>ed on the original CAPM<br />
model. They confirmed that the beta factor (firm-specific risk) is important in<br />
determining security returns using cross-sectional tests. More recently, Chava and<br />
Purnanandam (2008) uncovered the risk-return relation by extending their sample period,<br />
and suggested that expected returns are positively correlated with bankruptcy.<br />
Consequently, there should be a positive relation between return on equity and default<br />
risk.<br />
3.2 Multi factors in predicting PD and the methodologies<br />
3.2.1 Multiple Discriminant Analysis<br />
Many scholars have incorporated various factors in terms <strong>of</strong> financial ratios into their<br />
predicting model in order to discriminate default and non-default companies. Beaver<br />
(1966) and Altman (1968) pioneered the studies. By using univariate analysis, Beaver<br />
pairwisely compared failed and non-failed companies and found that ratios like c<strong>as</strong>h<br />
flow/total <strong>as</strong>sets, net income/total <strong>as</strong>sets, total debt/total <strong>as</strong>sets, and c<strong>as</strong>h flow/total debt 9<br />
in particular were important indicators <strong>of</strong> failure. Later, b<strong>as</strong>ed on his research, Altman<br />
(1968) developed the cl<strong>as</strong>sic Multiple Discriminant Analysis (MDA) and Z-score model.<br />
Being more advanced than univariate analysis, MDA examines the entire variable pr<strong>of</strong>ile<br />
simultaneously instead <strong>of</strong> sequentially testing individual variables. The five accounting<br />
8<br />
E(R)=Rf+β*(Rm- Rf), E(R) is the expected return <strong>of</strong> the capital <strong>as</strong>set, Rf is the risk-free rate <strong>of</strong> interest, β is<br />
the sensitivity <strong>of</strong> the <strong>as</strong>set returns to market returns, Rm is the expected return <strong>of</strong> the market, (Rm- Rf) is the<br />
difference between expected return on market and risk-free rate, or also known <strong>as</strong> risk premium. Since most<br />
investors are diversified, the expected return on a security should be positively related to its beta.<br />
The model w<strong>as</strong> introduced by Treynor (1962), Sharpe (1964), Lintner (1965), and Mossin (1966).<br />
9<br />
C<strong>as</strong>h flow/total debt h<strong>as</strong> predictive power up to five years before bankruptcy.<br />
9
atios he employed in the research were working capital/total <strong>as</strong>sets, retained<br />
earnings/total <strong>as</strong>sets, earning before interest and taxes/total <strong>as</strong>sets, market value<br />
equity/book value <strong>of</strong> total debt, and sales/total <strong>as</strong>sets. The model proved very accurate<br />
when tested on a sample <strong>of</strong> US manufacturing firms, and the predictive value <strong>of</strong> the<br />
model for the first two years prior to bankruptcy w<strong>as</strong> quite high (correct prediction: 95%<br />
for year one and 72% for year two). Following his previous research, Altman et al (1977)<br />
constructed a second-generation model, called ZETA. ZETA model w<strong>as</strong> effective in<br />
cl<strong>as</strong>sifying bankrupt companies up to five years prior to failure on a sample <strong>of</strong><br />
corporations consisting <strong>of</strong> manufacturers and retailers. Many other scholars have also<br />
applied multidimensional models in their studies (see for example, Deakin (1972) and<br />
Sinkey (1975)).<br />
3.2.2 Logistic Regression<br />
Later, new econometric methodology <strong>of</strong> logit and probit analysis h<strong>as</strong> been introduced into<br />
this field. There is no fundamental difference between logit and probit models, except<br />
that the conditional probability p approaches zero or one at a slower rate in logit than in<br />
probit. In practice many researchers choose logit model because <strong>of</strong> its comparative<br />
mathematical simplicity (Gujarati, 2003). Comparing to quantitative explanatory<br />
variables in normal regression, dependent variables in logistic regression are normally<br />
qualitative (or dummy). Martin (1977) first intended to build an early warning model for<br />
predicting future bank failure b<strong>as</strong>ed on current period’s balance sheet and income<br />
statement by using logistic regression. Ohlson (1980) tested the 1970-1976 industrial<br />
sample data, and found that the predictive power <strong>of</strong> the default risk model (two years<br />
before default) b<strong>as</strong>ed on financial ratios seemed to be robust. Meanwhile, he found four<br />
b<strong>as</strong>ic factors being significant with probability <strong>of</strong> failure (within one year), namely firm<br />
10
size, financial structure, performance 10 , and current liquidity.<br />
In their empirical analysis, Westgaard and Wijst (2001) used the 1996 accounting data<br />
and the 1998 bankruptcy information (2-year prior to default) and illustrated that<br />
financial ratios (c<strong>as</strong>h flow to debt, financial coverage, liquidity, and equity ratio) were<br />
negatively and significantly correlated with PD in a corporate bank portfolio in Norway.<br />
One year later, Westgaard and Wijst together with Hol (2002) did another research for<br />
Norwegian limited liability companies, but with different proxy variables and time<br />
horizon (1995-2000). Their main finding w<strong>as</strong> that leverage and c<strong>as</strong>h flow standard<br />
deviation had a significantly positive effect on default probability, while c<strong>as</strong>h flow had a<br />
significant negative effect. Similarly, Zeitun et al (2007) proved that firms’ c<strong>as</strong>h flow<br />
decre<strong>as</strong>ed corporate failure in Jordanian companies. Their main contribution, however,<br />
w<strong>as</strong> that they addressed the issue <strong>of</strong> free c<strong>as</strong>h flow 11 and default risk. They concluded<br />
that firms’ PD incre<strong>as</strong>ed with firms’ free c<strong>as</strong>h flow, which also seemed to be consistent<br />
with agency theory. The predictive power <strong>of</strong> their models (three years prior to default) for<br />
both matched and non-matched is very high (91.5%, 80%, and 81%). A summary <strong>of</strong> the<br />
previous researches is presented in Table One in Appendix One.<br />
4. Data and Methodology<br />
4.1 Methodology<br />
Multiple Discriminant Analysis h<strong>as</strong> been widely used in default research. Nevertheless<br />
the usefulness <strong>of</strong> MDA is quite limited, since such a technique only provides qualitative<br />
differentiation among counterparties, and does not produce probabilities. Furthermore,<br />
10 Me<strong>as</strong>ured <strong>as</strong> net income to total <strong>as</strong>sets<br />
11 Free c<strong>as</strong>h flow w<strong>as</strong> me<strong>as</strong>ured <strong>as</strong> retained earning to total <strong>as</strong>sets (also see Dhumale, 1998).<br />
11
there are specific statistical requirements under this approach. For example, it <strong>as</strong>sumes<br />
predictors have normal distributions which would restrict the use <strong>of</strong> dummy independent<br />
variables (Ohlson, 1980).<br />
Probability <strong>of</strong> default is characterized <strong>as</strong> a non-linear S-shaped cumulative distribution<br />
function with probabilities varying <strong>from</strong> 0 to 1, therefore a logit regression suits best.<br />
Logit regression can specify a dichotomous dependent variable <strong>as</strong> a function <strong>of</strong> various<br />
explanatory variables. More importantly, logit solves the problem with linear probability<br />
model that is inherently unbounded. Different counterparties can be mapped into the<br />
regression model within a boundary between 0 and 1. By taking the natural log <strong>of</strong> the<br />
odds ratio (p/(1-p)) 12 , the logit model is linear in X and in parameters, facilitating the<br />
interpretation <strong>of</strong> coefficients. The model can be written <strong>as</strong> Li=ln[pi/(1-pi)]=βXi+ui, with<br />
two states, L=1 if the firm defaults, L=0 otherwise. As p goes <strong>from</strong> 0 to 1, the logit L<br />
goes <strong>from</strong> -∞ to +∞. The models are estimated by using the SPSS s<strong>of</strong>tware. Early<br />
examples <strong>of</strong> the use <strong>of</strong> logit regression are for instance, Martin (1977), Ohlson (1980),<br />
Westgaard and Wijst (2001), and Zeitun et al (2007) <strong>as</strong> mentioned in section 3.2.2.<br />
4.2 Data and Sample<br />
The companies in this study are publicly traded and listed on the Hong Kong Stock<br />
Exchange (HKEx) 13 over the period 2001-2007. Their accounting data (for three years<br />
prior to default) is collected by Thomson One Banker (TOB). TOB provides b<strong>as</strong>ic<br />
company information such <strong>as</strong> company name, industry code, income statements and<br />
balance sheets. However, TOB does not specify a company’s financial health (default or<br />
non-default). Instead it only states whether the company is active or inactive 14 . According<br />
12 P <strong>as</strong> in probability<br />
13 http://www.hkex.com.hk/index.htm<br />
14 Although inactive companies are usually default.<br />
12
to the definition <strong>of</strong> default (see section two) in this study, 30 default companies with<br />
complete financial data have been found over 2001-2007. They are in ten different<br />
industries 15 . For each default company, the first three fiscal year-end financial data before<br />
its default announcement is used.<br />
The first sample selection is similar to Beaver (1966) and Altman et al (1977)’s. In order<br />
to isolate the characteristics <strong>of</strong> default companies, each default company is matched with<br />
a non-default company <strong>from</strong> the same industry group, with similar <strong>as</strong>set size, and in the<br />
same year. The purpose <strong>of</strong> matching is that there could be a potential bi<strong>as</strong> in certain <strong>of</strong> the<br />
ratios. For example, some financial ratios could vary dramatically cross industries.<br />
Therefore, industry and time dummies are added in the first sample to control the bi<strong>as</strong>.<br />
However, the “matching procedures” tend to be somewhat arbitrary (Ohlson, 1980). It is<br />
also interesting to see the effect <strong>of</strong> excluding matching. In the second sample, I pool<br />
cross-sectional and time-series data for all the companies over the period 2001-2007. 71 16<br />
non-failed companies are randomly selected for the second sample over the same time<br />
period. Similar to sample one, non-default companies are chosen <strong>from</strong> the same ten<br />
industries, but without controlling time and firm size.<br />
4.3 Explanatory Variables and Hypotheses<br />
The variables used in this study are summarized and presented in Table 2 at the end <strong>of</strong><br />
this section. The variables selected for the regression model are related to “c<strong>as</strong>h flow”,<br />
15<br />
Industries (number <strong>of</strong> observations): Capital Goods (3), Consumer Durables & Apparel (7), Diversified<br />
<strong>Financial</strong>s (2), Food Beverage & Tobacco (3), Materials (3), Real Estate (2), S<strong>of</strong>tware & Services (2),<br />
Technology & Hardware Equipment (4), Telecommunication Services (2), Transportation (2)<br />
16<br />
Due to the limitation <strong>of</strong> collecting information <strong>of</strong> default companies, in the second sample the number <strong>of</strong><br />
default companies is still 30. However we cannot unilaterally and infinitely incre<strong>as</strong>e the number <strong>of</strong><br />
non-default companies. It would lead to a bi<strong>as</strong>ed result. Therefore, randomly picked 71 non-default firms<br />
are included in sample two.<br />
13
“returns”, “values” and “debt obligations”. The sign <strong>of</strong> the coefficients <strong>of</strong> the different<br />
ratios is b<strong>as</strong>ed on previous studies. The regression model can also be specified <strong>as</strong> Li = ln<br />
[pi/(1-pi)] = β1TDTAi - β2EQTCi + β3RETAi + β4ROEi - β5CFTDi – β6NITAi – β7SATAi –<br />
β8WCTAi – β9CRi – β10Sizei + dummy (year) + dummy (industry) + ui.<br />
Hypothesis 1: Highly leveraged firms are more likely to fail.<br />
Firms with heavy debt obligation have higher distress cost, thus are more likely to go<br />
bankrupt. Empirical studies proved the positive relationship between total debt to total<br />
<strong>as</strong>sets (TDTA) and probability <strong>of</strong> default (Martin (1977), and Hol et al (2002)). A<br />
company’s financial leverage can also be me<strong>as</strong>ured by solidity. It estimates the extent by<br />
which the company’s <strong>as</strong>sets are funded by equity (EQTC). Westgaard and Wijst (2001)<br />
found a negative and significant relationship between solidity and default probabilities.<br />
Hypothesis 2: Those Companies with more free c<strong>as</strong>h flow have higher probability to<br />
fail.<br />
Managers probably would rather invest in projects with negative NPV instead <strong>of</strong> paying<br />
back companies’ shareholders. Free c<strong>as</strong>h flow is estimated by retained earnings to total<br />
<strong>as</strong>sets (RETA). It is hypothesized to have a positive correlation with probability <strong>of</strong> default<br />
(Altman (1968), Altman et al (1977), and Zeitun et al (2007)).<br />
Hypothesis 3: Abnormal and high equity returns may indicate high default risk.<br />
Stock returns can be used to cl<strong>as</strong>sify firms’ potential failure. A positive risk premium is<br />
required when investors detect potential high risks (Black et al (1972), and Chava and<br />
Purnanandam (2008)). Therefore equity returns (ROE) are supposed to be positively<br />
related to default probabilities.<br />
Hypothesis 4: A company’s c<strong>as</strong>h flow is negatively related to bankruptcy.<br />
14
C<strong>as</strong>h flow over total debt (CFTD) me<strong>as</strong>ures the ability <strong>of</strong> a company to pay back its<br />
debtholders. Westgaard and Wijst (2001), and Zeitun et al (2007) used the same ratio and<br />
found a negative relation between these two variables (although the empirical result <strong>from</strong><br />
Zeitun et al w<strong>as</strong> not statistically significant).<br />
Hypothesis 5: The ability to generate income helps prevent bankruptcies.<br />
Net income to total <strong>as</strong>sets (NITA) and sales to total <strong>as</strong>sets (SATA) are used to me<strong>as</strong>ure<br />
pr<strong>of</strong>itability (see Altman (1968), Deakin (1972), Martin (1977), and Ohlson (1980)).<br />
Pr<strong>of</strong>itable firms seem to be <strong>as</strong>sociated with low probability <strong>of</strong> default <strong>as</strong> they have great<br />
flexibility in allocating money and diversifying their investment.<br />
Hypothesis 6: Companies’ liquidity h<strong>as</strong> a negative relationship with PD.<br />
Bankruptcies ought to depend on how f<strong>as</strong>t a company can generate c<strong>as</strong>h. Liquidity risk is<br />
me<strong>as</strong>ured by working capital to total <strong>as</strong>sets (WCTA) and current ratio (CA/CL) in this<br />
study. Altman (1968) and Becchetti & Sierra (2003) used WCTA to distinguish default<br />
and non-default firms, and they found it negatively and significantly impacted on PD.<br />
Current ratio also indicates a negative correlation with PD, but the coefficient w<strong>as</strong> not<br />
significant in Deakin (1972)’s study.<br />
Hypothesis 7: Large firms tend to survive compared with small firms.<br />
A company’s size is expected to be negatively related to probability <strong>of</strong> default. In many<br />
previous studies, researchers used the b<strong>as</strong>e 10 logarithm <strong>of</strong> a company’s total <strong>as</strong>sets when<br />
estimating firm size (Altman (1984), Westgaard and Wijst (2001), and Manzoni (2004)),<br />
and they confirmed this negative correlation.<br />
15
Table 2 Explanatory Variables<br />
Variables Description Expected Sign<br />
TDTA Total Debt to Total Assets +<br />
EQTC Equity to Total Capital -<br />
RETA Retained Earnings to Total Assets +<br />
ROE Return on Equity +<br />
CFTD C<strong>as</strong>h Flow (Net Income+Depreciation) to Total Debt -<br />
NITA Net Income to Total Assets -<br />
SATA Sales to Total Assets -<br />
WCTA Working Capital (Current Assets-Current Liabilities) to Total Assets -<br />
CR Current Ratio (Current Assets/Current Liabilities) -<br />
Size The b<strong>as</strong>e 10 logarithm <strong>of</strong> the Total Assets -<br />
5. Empirical Results<br />
5.1 Descriptive Results<br />
Table 3(a) illustrates informative descriptive statistics for default firms first year 17 prior<br />
to bankruptcy and their matched non-default firms. Comparing both types <strong>of</strong> firms<br />
(default vs. non-default), the majority <strong>of</strong> the mean values supports the expected signs <strong>of</strong><br />
explanatory independent variables <strong>as</strong> shown in Table 2 (e.g. NITA for non-bankrupt<br />
companies is higher than that <strong>of</strong> the default firms. TDTA is the other way around). In<br />
general, the financial ratios <strong>of</strong> the default companies tend to fluctuate more than those <strong>of</strong><br />
the non-default ones. It means that for the default companies, their financial figures are<br />
more likely to be different <strong>from</strong> each others’. This result is not surprising because<br />
extreme values seem to be e<strong>as</strong>ily found on the failed companies’ balance sheets and<br />
income statements, especially right before their failures. However extreme values can<br />
still be detected in non-default companies (Table 3(a) right, Sample One, 30 companies),<br />
17<br />
For the comparisons between bankrupt and non-bankrupt companies two and three years before<br />
bankruptcy events, see Table 4 and 5 in Appendix Two and Three.<br />
16
such instability in terms <strong>of</strong> high standard deviation is reduced to some extent by including<br />
more observations (Table 3(b) right, Sample Two, 71 companies).<br />
Table 3(a) Descriptive Statistics (Sample One, 1 st year before default)<br />
Default Companies Non-Default Companies<br />
Minimum Maximum Mean Std.<br />
Deviation<br />
Variance Minimum Maximum Mean Std.<br />
Deviation<br />
Variance<br />
CFTD1 -1.96 11.95 0.26 2.36 5.56 -0.74 327.10 14.18 59.73 3567.81<br />
RETA1 -20.10 0.42 -1.00 3.70 13.67 -3.81 0.71 0.01 0.89 0.79<br />
WCTA1 -8.77 0.40 -0.47 1.65 2.71 -0.34 0.58 0.20 0.21 0.04<br />
CR1 0.01 2.95 1.03 0.80 0.64 0.06 26.10 2.54 4.55 20.68<br />
NITA1 -554.77 15.47 -34.97 103.61 10735.72 -12.67 57.48 7.97 12.82 164.35<br />
TDTA1 0.60 897.53 65.22 160.72 25830.92 0.03 45.75 15.74 11.72 137.40<br />
SATA1 0.06 5.10 0.81 1.01 1.02 0.01 3.95 0.95 0.88 0.77<br />
Size1 1.37 4.17 2.89 0.71 0.50 1.32 5.78 3.10 0.86 0.74<br />
EQTC1 9.60 100.00 76.69 26.04 678.16 39.34 100.00 83.80 15.85 251.28<br />
ROE1 -1017.34 65.71 -76.30 215.30 46353.62 -176.03 47.23 5.01 41.56 1727.08<br />
Table 3(b) Descriptive Statistics (Sample Two, 1 st year before default)<br />
CFTD1 -1.96 11.95 0.26 2.36 5.56 -0.49 111.30 5.54 15.75 247.91<br />
RETA1 -20.10 0.42 -1.00 3.70 13.67 -3.81 0.71 0.08 0.72 0.52<br />
WCTA1 -8.77 0.40 -0.47 1.65 2.71 -0.34 0.78 0.19 0.24 0.06<br />
CR1 0.01 2.95 1.03 0.80 0.64 0.06 15.54 2.28 2.48 6.15<br />
NITA1 -554.77 15.47 -34.97 103.61 10735.72 -7.00 65.74 9.58 11.73 137.62<br />
TDTA1 0.60 897.53 65.22 160.72 25830.92 0.07 52.54 17.79 13.60 185.03<br />
SATA1 0.06 5.10 0.81 1.01 1.02 0.01 3.95 0.86 0.77 0.59<br />
Size1 1.37 4.17 2.89 0.71 0.50 1.32 5.78 3.40 0.83 0.69<br />
EQTC1 9.60 100.00 76.69 26.04 678.16 27.28 100.00 83.14 16.61 276.00<br />
ROE1 -1017.34 65.71 -76.30 215.30 46353.62 -176.03 3894.62 68.00 461.46 212947.93<br />
Unlike ordinary le<strong>as</strong>t square (OLS) method, the variance inflation factors (VIF) 18 cannot<br />
be computed in logistic regression <strong>as</strong> there is no direct counterpart to R 2 . Nevertheless,<br />
the problem <strong>of</strong> multicollinearity 19 potentially exists in either OLS or logistic regression<br />
18<br />
VIF shows how the variance <strong>of</strong> an estimator is inflated by the presence <strong>of</strong> multicollinearity. As the extent<br />
<strong>of</strong> collinearity incre<strong>as</strong>es, the variance <strong>of</strong> an estimator incre<strong>as</strong>es, and in the limit it can become infinite<br />
(Gujarati, 2003.)<br />
19<br />
Multicollinearity is the phenomenon that one independent variable is highly and linearly correlated with<br />
17
which results in high standard errors <strong>of</strong> coefficients β and thus leads to an unreliable<br />
interpretation <strong>of</strong> final results. In logistic regression, large standard errors signal the<br />
possibility <strong>of</strong> multicollinearity (Studenmund, 2000, and Gujarati, 2003). Multicollinearity<br />
cannot be eliminated entirely, however it should be reduced <strong>as</strong> much <strong>as</strong> possible.<br />
Therefore before selecting variables for the model, it seems necessary to look at the<br />
correlations between individual variables (see Table 6(a) and (b)). Variables that show<br />
high correlation with the others might be dropped out <strong>of</strong> the model. For example, RETA<br />
and WCTA are highly correlated with other seven variables respectively. However it<br />
needs to be kept in mind that correlations only indicate the connections between two<br />
single variables, instead <strong>of</strong> a single variable and the rest <strong>of</strong> the variables. The elimination<br />
procedure b<strong>as</strong>ed on the correlation table therefore is rather subjective. Another<br />
observation <strong>from</strong> Table 6(a) and (b) is that the correlations between individual variables<br />
decline <strong>as</strong> more companies are included in the sample, implying that multicollinearity<br />
decre<strong>as</strong>es with sample size.<br />
Table 6(a) Correlations (Sample One, 1 st year before default)<br />
CFTD1 RETA1 WCTA1 CR1 NITA1 TDTA1 SATA1 Size1 EQTC1 ROE1<br />
CFTD1 1.000 0.068 0.094 0.961** 0.058 -0.062 -0.036 -0.073 0.141 0.055<br />
RETA1 0.068 1.000 0.949** 0.127 0.955** -0.953** 0.000 0.388** 0.284* 0.299*<br />
WCTA1 0.094 0.949** 1.000 0.188 0.965** -0.969** -0.003 0.322* 0.311* 0.354**<br />
CR1 0.961** 0.127 0.188 1.000 0.127 -0.118 -0.044 -0.073 0.172 0.116<br />
NITA1 0.058 0.955** 0.965** 0.127 1.000 -0.233 -0.041 0.342** 0.262* 0.262*<br />
TDTA1 -0.062 -0.953** -0.969** -0.118 -0.233 1.000 0.026 -0.307* -0.323* -0.312*<br />
SATA1 -0.036 0.000 -0.003 -0.044 -0.041 0.026 1.000 -0.223 0.057 -0.233<br />
Size1 -0.073 0.388** 0.322* -0.073 0.342** -0.307* -0.223 1.000 -0.024 0.257*<br />
EQTC1 0.141 0.284* 0.311* 0.172 0.262* -0.323* 0.057 -0.024 1.000 0.318*<br />
ROE1 0.055 0.299 0.354** 0.116 0.431** -0.312** -0.233 0.257* 0.318* 1.000<br />
other independent variables. Serious multicollinearity endangers the reliability <strong>of</strong> the estimators. However,<br />
multicollinearity is not a serious problem when the purpose is prediction only (see for example, Geary,<br />
1963)<br />
18
Table 6(b) Correlations (Sample Two, 1 st year before default)<br />
CFTD1 RETA1 WCTA1 CR1 NITA1 TDTA1 SATA1 Size1 EQTC1 ROE1<br />
CFTD1 1.000 0.100 0.113 0.219* 0.087 -0.104 0.038 0.044 0.218* 0.015<br />
RETA1 0.100 1.000 0.930** 0.167 0.927** -0.940** -0.003 0.352** 0.257** 0.032<br />
WCTA1 0.113 0.930** 1.000 0.281** 0.944** -0.956** -0.021 0.281** 0.287** 0.092<br />
CR1 0.219* 0.167 0.281** 1.000 0.175 -0.163 -0.128 0.070 0.215* -0.009<br />
NITA1 0.087 0.927** 0.944** 0.175 1.000 -0.212 -0.043 0.293** 0.238* 0.249*<br />
TDTA1 -0.104 -0.940** -0.956** -0.163 -0.212 1.000 0.033 -0.266** -0.313** -0.108<br />
SATA1 0.038 -0.003 -0.021 -0.128 -0.043 0.033 1.000 -0.215* 0.090 -0.075<br />
Size1 0.044 0.352** 0.281** 0.070 0.293** -0.266** -0.215* 1.000 -0.139 -0.032<br />
EQTC1 0.218* 0.257** 0.287** 0.215* 0.238* -0.313** 0.090 -0.139 1.000 0.104<br />
ROE1 0.015 0.032 0.092 -0.009 0.249 -0.108 -0.075 -0.032 0.104 1.000<br />
*. Correlation is significant at the 0.05 level (2-tailed).<br />
**. Correlation is significant at the 0.01 level (2-tailed).<br />
5.2 Estimation results <strong>of</strong> the Logit model<br />
Similar to linear regression, logistic regression also gives estimation for the coefficient <strong>of</strong><br />
each parameter and its relevant significance (b<strong>as</strong>ed on t-ratios) to the dependent variable<br />
(PD). But the interpretation <strong>of</strong> logit regression is different, since it <strong>as</strong>sumes a non-linear<br />
relationship between probability and the independent variables. Remember that<br />
Li=ln[pi/(1-pi)], after taking the antilog <strong>of</strong> the estimated logit, we get pi/(1-pi) (that is, the<br />
odds ratio). In this c<strong>as</strong>e, since p represents probability <strong>of</strong> default, pi/(1-pi) can also be<br />
called <strong>as</strong> odds <strong>of</strong> default. Therefore, instead <strong>of</strong> looking at parameter β (which is used to<br />
explain the ln(odds <strong>of</strong> default)), Exp(β) should be considered the equivalent value when<br />
interpreting odds <strong>of</strong> default directly. Table 7 shows the logit results by using matched<br />
samples (sample one). The variables included in the model (RETA, NITA, TDTA, and<br />
ROE) are those which jointly make the model valid and maximize the predictive power<br />
<strong>of</strong> the model.<br />
19
Table 7 Variables in the Equation (Sample One, 1 st year before default)<br />
B S.E. Wald df Sig. Exp(B)<br />
RETA1 0.979 0.775 1.597 1.000 0.206 2.662<br />
NITA1 -0.227** 0.079 8.164 1.000 0.004 0.797**<br />
TDTA1 0.041* 0.020 4.083 1.000 0.043 1.042*<br />
ROE1 0.020* 0.010 4.005 1.000 0.045 1.021*<br />
RE -0.346 1.763 0.039 1.000 0.844 0.707<br />
TH -0.011 1.190 0.000 1.000 0.993 0.989<br />
MT -0.570 1.409 0.164 1.000 0.686 0.565<br />
CD 0.713 0.938 0.578 1.000 0.447 2.041<br />
DF 0.784 1.446 0.294 1.000 0.588 2.191<br />
CG -1.312 1.263 1.080 1.000 0.299 0.269<br />
TS 0.466 1.575 0.087 1.000 0.767 1.593<br />
2001 -0.941 1.269 0.549 1.000 0.459 0.390<br />
2002 -1.968 1.571 1.570 1.000 0.210 0.140<br />
2003 -0.632 1.159 0.297 1.000 0.586 0.532<br />
2006 -0.719 1.351 0.283 1.000 0.595 0.487<br />
2007 -1.795 1.313 1.868 1.000 0.172 0.166<br />
Omnibus Tests <strong>of</strong> Model<br />
Coefficients<br />
Hosmer and Lemeshow<br />
Test<br />
Model Summary<br />
Chi-square 33.352 Chi-square 6.732 -2 Log Likelihood 49.825<br />
df 16.000 df 8.000 Cox & Snell R 2<br />
significance 0.007** significance 0.566 Nagelkerke R 2<br />
0.426<br />
0.569<br />
Notes: *, and ** significant at 5, and 1 percent level respectively. The sample includes 60 companies over period<br />
2001-2007. Industry and time dummies are included in the model, however they are not statistically significant.<br />
RE: Real Estate; TH: Technology & Hardware Equipment; MT: Materials; CD: Consumer Durables & Apparel; DF:<br />
Diversified <strong>Financial</strong>s; CG: Capital Goods; TS: Telecommunication Services<br />
For Hypothesis One, highly leveraged companies are more prone to go bankrupt.<br />
According to the logit results, one additional TDTA incre<strong>as</strong>es the odds <strong>of</strong> default by about<br />
4.2%. To put it another way, the odds <strong>of</strong> default are 1.042 times <strong>as</strong> large for companies<br />
with high TDTA <strong>as</strong> for those with low ratio. The result is consistent with the trade-<strong>of</strong>f<br />
theory that PD incre<strong>as</strong>es <strong>as</strong> more debt in a company’s capital structure (Beaver (1966),<br />
Martin (1977), Hol (2002)). The ratio, ROE, h<strong>as</strong> seldom been used in previous MDA or<br />
logit regression empirical analyses. In this study, ROE is at le<strong>as</strong>t at 5% significance level,<br />
and it h<strong>as</strong> a positive relationship with odds <strong>of</strong> default. Specifically, one unit change in<br />
20
ROE incre<strong>as</strong>es the odds <strong>of</strong> default 1.021 times, or an extra ROE incre<strong>as</strong>es the odds <strong>of</strong><br />
default by 2.1%. This positive relation is in support <strong>of</strong> the cl<strong>as</strong>sic risk-return trade<strong>of</strong>f<br />
promoted by Black et al (1972) and Chava and Purnanandam (2008). As predicted by<br />
Hypothesis Five, the ability to generate c<strong>as</strong>h/income should negatively influence<br />
corporate failure. The representative variable for the first sample is NITA, and it is<br />
negatively and significantly correlated with odds <strong>of</strong> default at 1% level. Each additional<br />
NITA decre<strong>as</strong>es the odds <strong>of</strong> default by 20.3% ((0.797-1)*100), controlling for other<br />
variables in the model. This is consistent with the results in previous studies such <strong>as</strong><br />
Deakin (1972), and Ohlson (1980), among others. Free c<strong>as</strong>h flow is not found to have any<br />
significant impact on probability <strong>of</strong> default. This is different <strong>from</strong> Altman (1968) and<br />
Zeitun et al (2007)’s results, since they concluded that companies with high free c<strong>as</strong>h<br />
flow me<strong>as</strong>ured by RETA have higher default risk. Most scholars applied bankruptcy<br />
research on single industry. However, others (Zeitun, 2007) who believed financial ratios<br />
vary dramatically cross industries and used industry dummies found significant results. In<br />
this analysis, time and industry dummies do not seem to be significant, meaning that no<br />
particular industry or year is significantly different <strong>from</strong> others in predicting bankruptcy.<br />
Hol et al (2002) did not find industry dummies significantly different <strong>from</strong> zero either,<br />
and they gave a possible explanation that these variables mostly capture the inter-industry<br />
differences in default probability.<br />
The Omnibus test in Table 7 illustrates that the model is significant at the 1% level,<br />
meaning that at le<strong>as</strong>t one <strong>of</strong> the independent variables is significantly correlated with the<br />
dependent variable, and all the variables in the model jointly are capable <strong>of</strong> predicting the<br />
dependent variable. The Hosmer and Lemeshow chi-square test <strong>of</strong> goodness <strong>of</strong> fit <strong>as</strong> well<br />
<strong>as</strong> the cl<strong>as</strong>sification tables which will be introduced in Section 5.3 <strong>as</strong>sess the models’ fit.<br />
A finding <strong>of</strong> non-significance, <strong>as</strong> can be seen in Table 7, indicates that the model<br />
adequately fits the data. It is less straight forward to interpret the ratios under Model<br />
21
Summary. -2 log likelihood (-2LL) is crucial when comparing different logistic models,<br />
but it cannot be used directly in significance test and thus is not very informative in<br />
<strong>as</strong>sessing a single model. SPSS in Logistic regression also outputs R 2 like that in OLS<br />
regression. However the Cox & Snell R 2 and Nagelkerke R 2 can only be seen <strong>as</strong><br />
approximations to OLS R 2 , not <strong>as</strong> the actual percentage <strong>of</strong> variance explained. Thus, they<br />
are not informative in indicating model fit. For Sample One, the Cox & Snell R 2 and<br />
Nagelkerke R 2 are 42.6% and 56.9% respectively, which are re<strong>as</strong>onably high.<br />
In the second sample, after adding observations in non-default companies and without<br />
controlling factors such <strong>as</strong> firm size and time, coefficients <strong>of</strong> individual variables become<br />
more significant (see Table 8). Interestingly, when randomly picking non-default<br />
companies, we see that size seems to be a significant factor in predicting default. Its<br />
negative coefficient with odds <strong>of</strong> default is also consistent with Westgaard and Wijst<br />
(2001)’s findings that small firms have limited access to capital markets and are more<br />
likely to fail. It can be concluded that each additional Size (me<strong>as</strong>ured by log10(total<br />
<strong>as</strong>sets)) decre<strong>as</strong>es the odds <strong>of</strong> default by a factor <strong>of</strong> 0.488, controlling for other variables<br />
in the model. <strong>Ratios</strong> such <strong>as</strong> NITA and TDTA are significant at le<strong>as</strong>t at 5% level in<br />
sample two <strong>as</strong> well. However, unlike the result in Table 7, ROE does not have a<br />
significant relationship with odds <strong>of</strong> default despite <strong>of</strong> its positive sign. RETA, SATA,<br />
EQTC are not found to be significant either.<br />
Empirical results for two years and three years before default in both samples are<br />
presented in Table 9 and 10 respectively (see Appendix Four to Seven). The main<br />
conclusion is that TDTA seems to be positively and significantly related with odds <strong>of</strong><br />
default over all three years in both matched and non-matched sample. Another<br />
observation is that in Table 9 (Appendix Four), the coefficients (β) <strong>of</strong> 2001 under two and<br />
three years before default are significant. The exponential values are 0.034 (e -3.371 ) and<br />
22
0.0856 (e -2.458 ) respectively. It means that the odds for bankruptcy in 2001 could be 3.4%<br />
(or 8.56%) higher than that in the other years.<br />
Table 8 Variables in the Equation (Sample Two, 1 st year before default)<br />
B S.E. Wald df Sig. Exp(B)<br />
NITA1 -0.232** 0.079 8.629 1.000 0.003 0.793**<br />
Size1 -0.717* 0.332 4.681 1.000 0.031 0.488*<br />
RETA1 0.976 0.594 2.702 1.000 0.100 2.653<br />
TDTA1 0.039* 0.019 4.079 1.000 0.043 1.040*<br />
SATA1 -0.694 0.794 0.764 1.000 0.382 0.500<br />
EQTC1 0.016 0.014 1.430 1.000 0.232 1.016<br />
ROE1 0.003 0.003 1.031 1.000 0.310 1.003<br />
CD 1.206 0.951 1.607 1.000 0.205 3.340<br />
DF 1.137 1.197 0.902 1.000 0.342 3.117<br />
MT -0.895 1.121 0.638 1.000 0.424 0.409<br />
SS -1.126 1.562 0.520 1.000 0.471 0.324<br />
TPT 1.439 1.134 1.610 1.000 0.204 4.217<br />
TH -0.455 1.225 0.138 1.000 0.710 0.635<br />
Omnibus Tests <strong>of</strong> Model<br />
Coefficients<br />
Hosmer and Lemeshow<br />
Test<br />
Model Summary<br />
Chi-square 71.835 Chi-square 16.268 -2 Log Likelihood 68.181<br />
df 13.000 df 8.000 Cox & Snell R 2<br />
significance 0.000*** significance 0.066 Nagelkerke R 2<br />
Notes: *, **, and *** significant at 10, 5, and 1 percent level respectively. The sample includes 101 companies over<br />
period 2001-2007. Industry dummies are included in the model, however they are not statistically significant.<br />
CD: Consumer Durables & Apparel; DF: Diversified <strong>Financial</strong>s; MT: Materials; SS: S<strong>of</strong>tware & Services; TPT:<br />
Transportation; TH: Technology & Hardware Equipment.<br />
5.3 Predictive power <strong>of</strong> the model<br />
As one year prior to default in sample one, the predictive success according to table 11<br />
comprises 86.7% correct prediction <strong>of</strong> non-default companies and 76.7% default<br />
companies, with an overall 81.7% accuracy. Table 11 also displays two types <strong>of</strong><br />
prediction error, Type I and Type II errors. In this c<strong>as</strong>e, Type I error (n=7) occurs when a<br />
0.509<br />
0.679<br />
default company is miscl<strong>as</strong>sified <strong>as</strong> non-default, and when a non-default company is<br />
23
predicted to be default, it is called Type II error (n=4). The overall predictive success in<br />
sample two (86.1%, see Table 12 in Appendix Eight) is relatively higher than that in<br />
sample one. However, <strong>as</strong> mentioned before, unilaterally incre<strong>as</strong>ing the number <strong>of</strong><br />
observations (in this c<strong>as</strong>e, non-default companies) could somehow bi<strong>as</strong> the interpretation<br />
<strong>of</strong> the results 20 . Consequently, the number <strong>of</strong> compared observations (default &<br />
non-default) in each sample should not be different <strong>from</strong> each other too much.<br />
Table 11 Cl<strong>as</strong>sification (Sample One, 1 st year before default)<br />
Predicted<br />
Default<br />
Observed 0 1 Percentage Correct<br />
Default 0 26 4 86.7<br />
The cut value is .500<br />
1 7 23 76.7<br />
Overall Percentage 81.7<br />
An alternative way to look at the prediction is through the histogram <strong>of</strong> predicted<br />
probabilities (Figure 1, representing sample one). The x axis represents the probability<br />
<strong>from</strong> 0 (non- default) to 1 (default). The y axis is the frequency <strong>of</strong> the c<strong>as</strong>es. Ideally,<br />
failed (non-failed) companies should be clustered on the right (left) side <strong>of</strong> the x axis.<br />
Moreover a U-shaped distribution with well differentiated predictions is more desirable<br />
over normal distribution. Because a model where predictions are close to 0 or 1 provides<br />
more information than one with predictions all cluster around the cut value 0.5. This<br />
U-shaped distribution might be less obvious in Figure 1, mostly because the sample size<br />
is rather small. As more observations are included in the model, a more desirable<br />
distribution can be clearly seen in Figure 2 (representing sample two) in Appendix Eight.<br />
20<br />
The overall accuracy <strong>of</strong> the logit in Sample One equals 86.7%*0.5+76.7% *0.5=81.7%, because the<br />
default and non-default companies represent half <strong>of</strong> the total observations respectively. In Sample Two, the<br />
overall predictive success=95.8%*(71/101)+63.3%*(30/101)=86.1%. The incre<strong>as</strong>e in predictive power is<br />
mostly due to the uneven weights distribution.<br />
24
In this study, the predictive success <strong>of</strong> the models for all three years prior to default in<br />
both samples is re<strong>as</strong>onably high (all above 70%). In general, models in sample two have<br />
higher predictive power than those in sample one. Within each sample, the further the<br />
distance is to bankruptcy, the less powerful the predictive power becomes. Although the<br />
difference between year two and year three is quite small, this result is consistent with<br />
Zeitun et al (2007)’s. In their matched sample, the percent <strong>of</strong> predictive successes in year<br />
two and year three are 80% and 81% respectively.<br />
5.4 Robustness Test<br />
The robustness <strong>of</strong> the model depends on if it can be applied in multi-period. That is, the<br />
longer the accuracy <strong>of</strong> the model could be maintained, the better the model becomes. In<br />
this study, <strong>as</strong> the predictive powers <strong>of</strong> the model in all three years prior to bankruptcy are<br />
above 70% in both samples, we conclude that the model seem to be robust across<br />
25
estimation procedure. However it is interesting to check what impact <strong>of</strong> outliers to the<br />
model prediction would be. After excluding observations with standardized residuals<br />
greater than 2 (Table 13), the predictive power <strong>of</strong> the entire model improves, and Type I<br />
(n=3) and Type II errors (n=3) decre<strong>as</strong>e at the same time (Table 14).<br />
C<strong>as</strong>e Selected<br />
Status a<br />
Table 13 C<strong>as</strong>ewise List b (Sample One, 1 st year, outliers)<br />
Observed Predicted Predicted Temporary Variable<br />
Default<br />
Group<br />
Resid ZResid<br />
34 S 0** 0.859 1 -0.859 -2.469<br />
37 S 1** 0.243 0 0.757 1.764<br />
41 S 1** 0.190 0 0.810 2.067<br />
55 S 1** 0.194 0 0.806 2.038<br />
a. S = Selected, U = Unselected c<strong>as</strong>es, and ** = Miscl<strong>as</strong>sified c<strong>as</strong>es.<br />
b. C<strong>as</strong>es with studentized residuals greater than 2.000 are listed.<br />
Table 14 Cl<strong>as</strong>sification (Sample One, 1 st year, excluding outliers)<br />
Predicted<br />
Default<br />
Observed 0 1 Percentage Correct<br />
Default 0 26 3 89.7<br />
The cut value is .500<br />
1 3 23 88.9<br />
Overall Percentage 89.3<br />
Nonetheless, such improvements are not costless. The results generated by the new model<br />
(excluding outliers) do not seem to be <strong>as</strong> stable <strong>as</strong> the original results. Especially for the<br />
industry and time dummies, their standard errors slightly incre<strong>as</strong>e (see Table 15). This is<br />
probably because <strong>of</strong> the limited number <strong>of</strong> companies in sample one. Elimination <strong>of</strong><br />
outliers could cause large fluctuations in the estimation <strong>of</strong> the parameters. When more<br />
observations are used in the sample (see Appendix Nine), the model is robust after<br />
excluding outliers.<br />
26
Table 15 Variables in the Equation (Sample One, 1 st year, excluding outliers)<br />
B S.E. Wald df Sig. Exp(B)<br />
RETA1 1.453 1.008 2.076 1.000 0.150 4.276<br />
NITA1 -0.473*** 0.173 7.464 1.000 0.006 0.623<br />
TDTA1 0.116** 0.048 5.892 1.000 0.015 1.123<br />
ROE1 0.047** 0.020 5.817 1.000 0.016 1.048<br />
RE -1.877 2.157 0.757 1.000 0.384 0.153<br />
TH 1.575 1.602 0.967 1.000 0.325 4.831<br />
MT -2.110 2.186 0.932 1.000 0.334 0.121<br />
CD -0.944 1.484 0.405 1.000 0.525 0.389<br />
DF 0.662 1.663 0.159 1.000 0.690 1.939<br />
CG -2.431 1.525 2.542 1.000 0.111 0.088<br />
TS 0.429 6.419 0.004 1.000 0.947 1.535<br />
2001 -1.875 1.628 1.327 1.000 0.249 0.153<br />
2002 -2.207 2.386 0.855 1.000 0.355 0.110<br />
2003 -0.333 1.468 0.051 1.000 0.820 0.717<br />
2006 -1.563 3.371 0.215 1.000 0.643 0.209<br />
2007 -6.996** 3.404 4.223 1.000 0.040 0.001<br />
6. Conclusion<br />
The article focused on predicting bankruptcies for Hong Kong b<strong>as</strong>ed companies. It<br />
examines the relationship between default risk and various financial ratios. Logistic<br />
regression is the main methodology in this research for testing different theories and<br />
hypotheses. The result is in support <strong>of</strong> capital structure theory and risk-return trade<strong>of</strong>f. To<br />
be specific, TDTA, representing capital structure, h<strong>as</strong> a positive and significant impact on<br />
bankruptcy, which is consistent with the results <strong>of</strong> Martin (1977) and Hol et al (2002).<br />
Shareholders’ expected return, <strong>as</strong> reflected by ROE, is also an important determinant <strong>of</strong><br />
corporate failure. ROE h<strong>as</strong> not been used extensively in previous MDA or logit analyses.<br />
But its positive relationship with PD <strong>as</strong> estimated in the study is consistent with the<br />
cl<strong>as</strong>sic risk-return trade<strong>of</strong>f. Moreover, pr<strong>of</strong>itability, <strong>as</strong> me<strong>as</strong>ured by NITA, is significantly<br />
and negatively related to default probabilities in both samples (Altman (1968), and<br />
27
Ohlson (1980)). In the second sample, it h<strong>as</strong> been proved that firm size plays an<br />
important role in predicting PD. Small firms are more prone to go bankrupt because <strong>of</strong><br />
the limited access to capital market. Westgaard and Wijst (2001) and others illustrate the<br />
same result. Other variable, such <strong>as</strong> free c<strong>as</strong>h flow (<strong>as</strong> me<strong>as</strong>ured by RETA), does not<br />
seem to be related to default risk for companies in Hong Kong, since it is not significant<br />
in both samples. Contrary to previous empirical results, such <strong>as</strong> Zeitun et al (2007), this<br />
inconsistency should be explained by a Hong Kong specific factor. Because most <strong>of</strong> the<br />
Hong Kong companies (even large publicly traded) are family controlled 21 , agency<br />
problem raised by free c<strong>as</strong>h flow does not seem to be severe in such context (without the<br />
principal and agent relationship). In that c<strong>as</strong>e, free c<strong>as</strong>h flow, me<strong>as</strong>ured by RETA, should<br />
not threaten a company’s default probability. Industry dummies do not explain<br />
bankruptcy in this study. The result is consistent with Hol (2002)’s, meaning that industry<br />
variables capture the inter-industry differences in default probability. The majority <strong>of</strong> the<br />
time dummies are not significantly correlated with bankruptcy, except for the year 2001<br />
for two and three years before bankruptcy in sample one. The result may imply that firms<br />
in Hong Kong have higher probabilities to go bankrupt in 2001 compared with those in<br />
other years. Interestingly, in 2001 the real GDP incre<strong>as</strong>e by percentage w<strong>as</strong> the lowest<br />
over 2000-2007 according to Census and Statistics Department (Hong Kong) 22 .<br />
Intuitively, this indicates that macroeconomic factors could influence default probability.<br />
The predictive power for all three years before bankruptcy in both samples is re<strong>as</strong>onably<br />
high, and generally incre<strong>as</strong>es <strong>as</strong> time approaching to the bankruptcy event. The result is<br />
21<br />
70% <strong>of</strong> Hong Kong listed companies were majority controlled by a family or an individual (Hong Kong<br />
Society <strong>of</strong> Accountants, 1996). 53% <strong>of</strong> all listed companies had one shareholder or one family group <strong>of</strong><br />
shareholders that owned 50% or more <strong>of</strong> the entire issued capital (Hong Kong Society <strong>of</strong> Accountants,<br />
1997). Also see publications <strong>of</strong> Ho (2003), and the presentation at International <strong>Financial</strong> Corporation IO<br />
Training Session on 30 April 2004, “Corporate governance in Hong Kong”, by Patrick Contoy, Hong Kong<br />
Exchanges and Clearing.<br />
22<br />
Official website: http://www.censtatd.gov.hk/hong_kong_statistics/statistical_tables/<br />
2000+: Real GDP incre<strong>as</strong>es by percentage: 2000 (7.95), 2001 (0.50), 2002 (1.84), 2003 (3.01), 2004 (8.46),<br />
2005 (7.12), 2006 (6.75), 2007 (6.83)<br />
28
useful in describing default risk in the context <strong>of</strong> Hong Kong. As a risk manager <strong>of</strong> a<br />
bank, he or she would first look at borrowers (companies)’ capital structure, pr<strong>of</strong>itability,<br />
firm size, and equity returns over other characters, such <strong>as</strong> retained earnings, or industry<br />
type according to the empirical results in this study.<br />
The limitations <strong>of</strong> the research need to be taken into consideration. One <strong>of</strong> the limitations<br />
is that the multicollinearity problem cannot be fully dealt with. Two main solutions<br />
adopted in the research are reducing explanatory variables in the models and incre<strong>as</strong>ing<br />
sample size, ensuring that multicollinearity is to a large extent under control. Another<br />
limitation is <strong>from</strong> the dat<strong>as</strong>et. Only 30 publicly traded companies have been defined <strong>as</strong><br />
default in the study (due to mostly missing value, and the definition <strong>of</strong> bankruptcy) over<br />
period 2001 to 2007. This results in a relatively small sample size in both matched and<br />
non-matched sample. However, because bankruptcies are scarce activities, the problem <strong>of</strong><br />
limited sample observations also exists in previous studies 23 .<br />
The models in this study will only be viewed <strong>as</strong> a static and myopic way in predicting<br />
bankruptcies in short term. In future research, macroeconomic risk factors should also be<br />
incorporated in estimating corporate default (see e.g., Fama (1986)). Macroeconomic<br />
conditions have an impact not only on firms’ default risk but also on their financial<br />
decisions (Hackbarth et al, 2006). The model would then provide more insights in<br />
predicting future default under different scenarios. Meanwhile, with more and more<br />
countries are adopting B<strong>as</strong>el II, similar bankruptcy analyses should also be encouraged in<br />
Asia, where risk management practices are relatively weak compared with those in<br />
western countries.<br />
23<br />
For example, Altman (1968)’s sample comprises 66 corporations with 33 firms in each <strong>of</strong> the two groups.<br />
C<strong>as</strong>tagna and Matolcsy (1981) analyzed 21 failed and non-failed firms respectively in their MDA analysis.<br />
In Zeitun et al (2007)’s first sample, it is composed <strong>of</strong> 29 failed and 30 non-failed firms.<br />
29
Reference<br />
Altman, E. I., 1968, “<strong>Financial</strong> ratios, Discriminant Analysis and the Prediction <strong>of</strong><br />
Corporate Bankruptcy”, The Journal <strong>of</strong> Finance, Vol.23, No.4, p589-609<br />
Altman E. I., and M. Brenner, 1981, “Information effects and stock market response to<br />
signs <strong>of</strong> firm deterioration“, Journal <strong>of</strong> Finance and Quantitative Analysis 16, p35-51<br />
Altman, E. I., R. G.. Haldeman, and P. Narayanan, 1977, ZETA analysis: “A new model<br />
to identify bankruptcy risk <strong>of</strong> corporations”, Journal <strong>of</strong> Banking and Finance 1, p25-94<br />
Altman, E. I., and M. Lavallee, 1981, “Business <strong>Failure</strong> Cl<strong>as</strong>sification in Canada”,<br />
Journal <strong>of</strong> Business Administration, p147-164<br />
Altman, E. I., 1984, “The Success <strong>of</strong> Business <strong>Failure</strong> Prediction Models”, Journal <strong>of</strong><br />
Banking and Finance 8, 171-198<br />
Aziz, A., D. Emanuel, and G. Lawson, 1988, “Bankruptcy prediction: an investigation <strong>of</strong><br />
c<strong>as</strong>h flow b<strong>as</strong>ed models”, Journal <strong>of</strong> Management Studies, Vol.25, p35-51<br />
B<strong>as</strong>el Committee on Banking Supervision, 2004, International Convergence <strong>of</strong> Capital<br />
Me<strong>as</strong>urement and Capital Standards – A Revised Framework, B<strong>as</strong>el<br />
Beaver, W. H., 1966, “<strong>Financial</strong> <strong>Ratios</strong> <strong>as</strong> <strong>Predictors</strong> <strong>of</strong> <strong>Failure</strong>, Empirical Research in<br />
Accounting: Selected Studies, Supplement”, Journal <strong>of</strong> Accounting Research 5,<br />
p71-127<br />
Beaver, W. H., 1968 (1), “Alternative <strong>Financial</strong> <strong>Ratios</strong> <strong>as</strong> <strong>Predictors</strong> <strong>of</strong> <strong>Failure</strong>”,<br />
Accounting Review, p113-122<br />
Beaver, W. H., 1968 (2), “Market Prices, <strong>Financial</strong> <strong>Ratios</strong>, and the Prediction <strong>of</strong> <strong>Failure</strong>”,<br />
Journal <strong>of</strong> Accounting Research, p179-192<br />
Becchetti, L., and J. Sierra, 2003, “Bankruptcy Risk and Productive Efficiency in<br />
Manufacturing Firms, Journal <strong>of</strong> Banking and Finance 27, p2099-2120<br />
Black, F., M. C. Jensen, and M. S. Scholes, 1972, “The Capital Asset Pricing Model:<br />
Some Empirical Tests”, in M. Jensen, ed., Studies in the Theory <strong>of</strong> Capital Markets,<br />
30
Praeger Publisher Inc<br />
C<strong>as</strong>ey, C., and N. Bartczak, 1985, “Using Operating C<strong>as</strong>h Flow Data to Predict <strong>Financial</strong><br />
Distress: Some Extensions”, Journal <strong>of</strong> Accounting Research, Vol. 23, No. 1, p384-401<br />
C<strong>as</strong>tagna, A. D., and Z. P. Matolcsy, 1981, “The Prediction <strong>of</strong> Corporate <strong>Failure</strong>: Testing<br />
the Australian Experience”, Australian Journal <strong>of</strong> Management 6, p23-28<br />
Chava S., and A. Purnanandam, 2008, “Is Default-Risk Negatively Related to Stock<br />
Returns?”, unpublished paper<br />
Deakin, E., 1972, “A discriminant analysis <strong>of</strong> predictors <strong>of</strong> business failure”, Journal <strong>of</strong><br />
Accounting Research<br />
Fama, E., 1986, “Term premiums and default premiums in money markets”, Journal <strong>of</strong><br />
<strong>Financial</strong> Economics 17, p175-196<br />
<strong>Financial</strong> Accounting Standards Board, 1981, “Reporting Income, C<strong>as</strong>h Flows and<br />
<strong>Financial</strong> Position <strong>of</strong> Business Enterprises, Stamford<br />
Geary, R. C., 1963, “Some Results about Relations between Stoch<strong>as</strong>tic Variables: A<br />
Discussion Document”, Review <strong>of</strong> International Statistical Institute, Vol. 31, p163-181<br />
Gentry, J. A., P. Newbold, and D. T. Whitford, 1985, “Cl<strong>as</strong>sifying bankrupt firms with<br />
funds flow components”, Journal <strong>of</strong> Accounting Research 23, p146-159<br />
Gombola, M. J. M. E. H<strong>as</strong>kins, J. E. Ketz, and D. D. Williams, 1987, “C<strong>as</strong>h Flow in<br />
Bankruptcy Prediction”, <strong>Financial</strong> Management p55-65<br />
Gujarati, D. N., 2003, “B<strong>as</strong>ic Econometrics”, 4 th Edition, The McGraw Hill Companies<br />
Hackbarth, D., J. Miao, and E. Morellec, 2006, “Capital structure, credit risk, and<br />
macroeconomic conditions”, Journal <strong>of</strong> <strong>Financial</strong> Economics 82, p519-550<br />
Ho, S. S. M., 2003, “Corporate Governance in Hong Kong: Key Problems and Prospects”,<br />
CUHK Centre for Accounting Disclosure and Corporate Governance Research Paper<br />
No. 1<br />
Hol, S., S. Westgaard, and N. van der Wijst, 2002, “Capital Structure and the Prediction<br />
<strong>of</strong> Bankruptcy”, unpublished paper<br />
31
Hong Kong Society <strong>of</strong> Accountants, 1996, Hong Kong Accountants “Special Issue on<br />
Corporate Governance”<br />
Hong Kong Society <strong>of</strong> Accountants, 1997, Second Report <strong>of</strong> the Corporate Governance<br />
Working Group<br />
Izan, H. Y., 1984, “Corporate Distress in Australia”, Journal <strong>of</strong> Banking and Finance 8,<br />
p303-320<br />
Jensen, M., 1986, “Agency Costs <strong>of</strong> Free C<strong>as</strong>h Flow, Corporate Finance, and Takeovers”,<br />
American Economic Review 76, p323-329<br />
Kim, E. H., 1978, “A Mean-Variance Theory <strong>of</strong> Optimal Capital Structure and Corporate<br />
Debt Capacity”, Journal <strong>of</strong> Finance, Vol. 33, No. 1, p45-63<br />
Kraus, A., and R. H. Litzenberger, 1973, “State Preference Model <strong>of</strong> Optimal <strong>Financial</strong><br />
Leverage”, Journal <strong>of</strong> Finance 28, p911-922<br />
Lintner, J., 1965, “The valuation <strong>of</strong> risk <strong>as</strong>sets and the selection <strong>of</strong> risky investments in<br />
stock portfolios and capital budgets”, Review <strong>of</strong> Economics and Statistics 47, p13-37<br />
Manzoni, K., 2004, “Modeling Eurobond Credit Ratings and Forec<strong>as</strong>ting Downgrade<br />
Probability”, International Review <strong>of</strong> <strong>Financial</strong> Analysis 13, p277-300<br />
Marais, D. A. J., 1979, “A Method <strong>of</strong> Quantifying Companies Relative <strong>Financial</strong><br />
Strength”, Discussion Paper No.4, Bank <strong>of</strong> England, London<br />
Martin, D., 1977, “Early Warning <strong>of</strong> Bank <strong>Failure</strong>”, Journal <strong>of</strong> Banking and Finance 1,<br />
p249-276<br />
Modigliani, F., and M. H. Miller, 1958, “The cost <strong>of</strong> capital, corporation finance and the<br />
theory <strong>of</strong> investment”, The American Economic Review 48, p261-297<br />
Modigliani, F., and M. H. Miller, 1963, “Corporate income taxes and the cost <strong>of</strong> capital: a<br />
correction”, The American Economic Review 53, p433-443<br />
Mossin, J., 1966, “Equilibrium in a Capital Asset Market”, Econometrica, Vol. 34, No. 4,<br />
p768-783<br />
Myers, S. C., 1984, “The Capital Structure Puzzle”, Journal <strong>of</strong> Finance 39<br />
32
Ohlson, J. A., 1980, “<strong>Financial</strong> <strong>Ratios</strong> and the Probabilistic Prediction <strong>of</strong> Bankruptcy”,<br />
Journal <strong>of</strong> Accounting Research, Vol.18, No.1<br />
Scott, J., 1981, “The probability <strong>of</strong> bankruptcy: A comparison <strong>of</strong> empirical predictions<br />
and theoretical models”, Journal <strong>of</strong> Banking and Finance 5, p317-344<br />
Sharpe, W. F., 1964, “Capital <strong>as</strong>set prices: A theory <strong>of</strong> market equilibrium under<br />
conditions <strong>of</strong> risk”, Journal <strong>of</strong> Finance 19, p425-442<br />
Sinkey, J., 1975, “A multivariate statistical analysis <strong>of</strong> the characteristics <strong>of</strong> problem<br />
banks”, Journal <strong>of</strong> Finance<br />
Studenmund, A. H., 2000, “Using Econometrics: A Practical Guide”, 4 th Edition, Addison<br />
Wesley<br />
Treynor, J. L., 1962, “Toward a Theory <strong>of</strong> Market Value <strong>of</strong> Risky Assets”, unpublished<br />
manuscript<br />
Westgaard, S., and N. Wijst, 2001, “Default probabilities in a corporate bank portfolio: A<br />
logistic model approach”, European Journal <strong>of</strong> Operational Research 135, p338-349<br />
Zeitun, R., G. Tian, and S. Keen, 2007, “Default Probability for the Jordanian Companies:<br />
A Test <strong>of</strong> C<strong>as</strong>h Flow Theory”, International Research Journal <strong>of</strong> Finance and<br />
Economics 8<br />
33
MDA<br />
Appendix One<br />
Table 1 Literature Summary<br />
Author Year <strong>Ratios</strong><br />
Beaver 1966<br />
Altman 1968<br />
Deakin 1972<br />
Sinkey 1975<br />
Altman et al 1977<br />
c<strong>as</strong>h flow/total <strong>as</strong>sets, net income/total <strong>as</strong>sets, total debt/total <strong>as</strong>sets,<br />
and c<strong>as</strong>h flow/total debt<br />
working capital/total <strong>as</strong>sets, retained earnings/total <strong>as</strong>sets, earning<br />
before interest and taxes/total <strong>as</strong>sets, market value equity/book<br />
value <strong>of</strong> total debt, and sales/total <strong>as</strong>sets<br />
Working capital/Total <strong>as</strong>sets, current <strong>as</strong>sets/current liabilities, total<br />
debt/total <strong>as</strong>sets, quick <strong>as</strong>sets/sales, quick <strong>as</strong>sets/total <strong>as</strong>sets,<br />
c<strong>as</strong>h/total <strong>as</strong>sets, c<strong>as</strong>h/sales, current <strong>as</strong>sets/total <strong>as</strong>sets, c<strong>as</strong>h/current<br />
liabilities, net income/total <strong>as</strong>sets, current <strong>as</strong>sets/sales, c<strong>as</strong>h<br />
flow/total debt<br />
Other expenses <strong>as</strong> % <strong>of</strong> revenue, loans <strong>as</strong> % <strong>of</strong> revenue, operating<br />
expense/operating income, loans/(capital + reserve), state and local<br />
obligations <strong>as</strong> % <strong>of</strong> revenue, (c<strong>as</strong>h + U.S. tre<strong>as</strong>ury securities)/total<br />
<strong>as</strong>sets, loans/total <strong>as</strong>sets, provision for loan losses/operating<br />
expense, U.S. tre<strong>as</strong>ury securities <strong>as</strong> % <strong>of</strong> revenue, interest paid on<br />
deposits <strong>as</strong> % in revenue<br />
Return on <strong>as</strong>sets, stability <strong>of</strong> earnings (me<strong>as</strong>ured by a normalized<br />
me<strong>as</strong>ure <strong>of</strong> the standard error <strong>of</strong> estimate around a ten-year trend,<br />
debt service (me<strong>as</strong>ured by the familiar interest coverage ratio,<br />
cumulative pr<strong>of</strong>itability (me<strong>as</strong>ured by the firm’s retained earnings),<br />
liquidity, capitalization, size<br />
34
Logistic<br />
regression<br />
Appendix One (continued)<br />
Author Year <strong>Ratios</strong><br />
Martin 1977<br />
Ohlson 1980<br />
Westgaard and<br />
Wijst<br />
2001<br />
Hol et al 2002<br />
Zeitun et al 2007<br />
Net income/total <strong>as</strong>sets, gross<br />
charge-<strong>of</strong>fs/net operating income,<br />
expenses/operating revenues,<br />
loans/total <strong>as</strong>sets, commercial<br />
loans/total loans, loss<br />
provision/loans+securities, net liquid<br />
<strong>as</strong>sets/total <strong>as</strong>sets, gross capital/risk<br />
<strong>as</strong>sets<br />
Size, total liabilities to total <strong>as</strong>sets,<br />
working capital to total <strong>as</strong>sets,<br />
current liabilities to current <strong>as</strong>sets,<br />
OENEG (one if total liabilities<br />
exceeds total <strong>as</strong>sets, zero otherwise),<br />
net income to total <strong>as</strong>sets, funds<br />
provided by operations to total<br />
liabilities, INTWO (one if net income<br />
w<strong>as</strong> negative for the l<strong>as</strong>t two years,<br />
zero otherwise)<br />
c<strong>as</strong>h flow to debt, financial coverage,<br />
liquidity, and equity ratio<br />
total debt/total <strong>as</strong>sets, tax/earnings<br />
before interest and tax, c<strong>as</strong>h flow (net<br />
income+depreciation/total <strong>as</strong>sets),<br />
standard deviation <strong>of</strong> c<strong>as</strong>h flow,<br />
bankruptcy cost (ln(sales))<br />
Net income to total liabilities, c<strong>as</strong>h<br />
flow to total debt, sales to total<br />
<strong>as</strong>sets, current <strong>as</strong>sets minus current<br />
liabilities to total <strong>as</strong>sets, , long-term<br />
liabilities to total <strong>as</strong>sets, total debt to<br />
total equity, firms age in years, log<br />
the <strong>as</strong>sets <strong>of</strong> the firm, retained<br />
earning to total <strong>as</strong>sets<br />
Significant &<br />
Positive<br />
expenses/operating<br />
revenues,<br />
loans/total <strong>as</strong>sets<br />
current liabilities<br />
to current <strong>as</strong>sets,<br />
INTWO<br />
total debt/total<br />
<strong>as</strong>sets, standard<br />
deviation <strong>of</strong> c<strong>as</strong>h<br />
flow, and<br />
bankruptcy cost<br />
retained earning to<br />
total <strong>as</strong>sets<br />
Significant &<br />
Negative<br />
gross<br />
capital/risk<br />
<strong>as</strong>sets<br />
working capital<br />
to total <strong>as</strong>sets<br />
all<br />
c<strong>as</strong>h flow<br />
sales to total<br />
<strong>as</strong>sets, net<br />
income to total<br />
liabilities<br />
35
Appendix Two<br />
Table 4 Descriptive Statistics (Sample One, 2 nd and 3 rd year)<br />
Default Companies Non-Default Companies<br />
Minimum Maximum Mean STDV Variance Minimum Maximum Mean STDV Variance<br />
CFTD2 -513.12 125.90 -12.35 97.35 9476.50 -11.80 19.23 1.64 5.36 28.77<br />
CFTD3 -4.57 9.29 0.36 2.09 4.39 -10.68 36.35 2.28 8.23 67.73<br />
RETA2 -24.60 0.55 -0.95 4.50 20.29 -38.82 0.67 -1.38 7.15 51.08<br />
RETA3 -8.89 0.51 -0.44 1.83 3.34 -29.47 0.78 -0.98 5.44 29.55<br />
WCTA2 -1.21 0.54 -0.10 0.43 0.18 -0.43 0.61 0.12 0.23 0.05<br />
WCTA3 -0.94 0.99 0.06 0.38 0.14 -0.44 0.73 0.17 0.25 0.06<br />
CR2 0.03 3.89 1.20 0.88 0.77 0.15 3.47 1.56 0.85 0.71<br />
CR3 0.16 67.21 4.37 12.76 162.69 0.16 6.52 1.75 1.19 1.41<br />
NITA2 -257.04 31.96 -17.25 62.04 3848.38 -85.28 41.94 -0.06 24.72 610.83<br />
NITA3 -205.59 28.30 -10.87 45.93 2109.58 -124.05 27.01 -3.19 28.17 793.38<br />
TDTA2 0.01 113.25 33.34 28.42 807.88 0.34 56.01 16.40 13.42 180.00<br />
TDTA3 0.22 277.39 37.82 49.67 2467.28 0.00 71.25 17.43 15.82 250.40<br />
SATA2 0.02 2.84 0.89 0.77 0.59 0.04 3.11 1.00 0.78 0.61<br />
SATA3 0.02 2.84 0.88 0.68 0.46 0.03 4.55 0.96 0.86 0.73<br />
Size2 1.60 4.07 2.93 0.61 0.38 1.14 5.69 2.97 0.89 0.79<br />
Size3 -1.08 3.98 2.86 0.94 0.88 1.34 5.60 2.93 0.86 0.74<br />
EQTC2 30.79 100.00 77.24 22.48 505.56 37.35 100.00 83.18 16.85 283.81<br />
EQTC3 18.89 100.00 74.56 22.36 499.77 -652.16 100.00 56.89 135.77 18434.32<br />
ROE2 -610.38 84.34 -31.73 127.36 16220.59 -1593.75 68.05 -52.14 295.40 87261.91<br />
ROE3 -2537.76 58.16 -110.31 476.83 227364.26 -424.07 93.25 -11.49 91.22 8321.36<br />
36
Appendix Three<br />
Table 5 Descriptive Statistics (Sample Two, 2 nd and 3 rd year)<br />
Default Companies Non-Default Companies<br />
Minimum Maximum Mean STDV Variance Minimum Maximum Mean STDV Variance<br />
CFTD2 -513.12 125.90 -12.35 97.35 9476.50 -4.55 158.32 6.50 24.00 575.98<br />
CFTD3 -4.57 9.29 0.36 2.09 4.39 -10.68 64.07 4.51 13.14 172.57<br />
RETA2 -24.60 0.55 -0.95 4.50 20.29 -3.94 0.73 -0.02 0.91 0.82<br />
RETA3 -8.89 0.51 -0.44 1.83 3.34 -3.87 0.78 -0.02 0.83 0.69<br />
WCTA2 -1.21 0.54 -0.10 0.43 0.18 -0.43 0.71 0.17 0.25 0.06<br />
WCTA3 -0.94 0.99 0.06 0.38 0.14 -0.42 0.66 0.16 0.23 0.05<br />
CR2 0.03 3.89 1.20 0.88 0.77 0.15 23.32 2.42 3.18 10.10<br />
CR3 0.16 67.21 4.37 12.76 162.69 0.01 11.26 2.16 2.12 4.47<br />
NITA2 -257.04 31.96 -17.25 62.04 3848.38 -85.28 41.94 3.96 16.72 279.46<br />
NITA3 -205.59 28.30 -10.87 45.93 2109.58 -124.05 41.34 4.42 20.76 431.18<br />
TDTA2 0.01 113.25 33.34 28.42 807.88 0.08 66.50 20.85 16.12 259.76<br />
TDTA3 0.22 277.39 37.82 49.67 2467.28 0.00 60.24 21.30 16.04 257.37<br />
SATA2 0.02 2.84 0.89 0.77 0.59 0.01 3.18 0.87 0.72 0.52<br />
SATA3 0.02 2.84 0.88 0.68 0.46 0.00 3.55 0.86 0.72 0.51<br />
Size2 1.60 4.07 2.93 0.61 0.38 1.14 5.69 3.34 0.84 0.71<br />
Size3 -1.08 3.98 2.86 0.94 0.88 1.34 5.60 3.29 0.82 0.67<br />
EQTC2 30.79 100.00 77.24 22.48 505.56 23.55 100.00 80.55 18.17 330.29<br />
EQTC3 18.89 100.00 74.56 22.36 499.77 10.39 100.00 80.10 19.98 399.03<br />
ROE2 -610.38 84.34 -31.73 127.36 16220.59 -202.77 68.05 5.64 39.61 1568.70<br />
ROE3 -2537.76 58.16 -110.31 476.83 227364.26 -196.74 93.25 11.46 39.46 1556.94<br />
37
Appendix Four<br />
Table 9 Coefficients two or three years before default (Sample One)<br />
Variables Two years before default Three years before default<br />
RETA 0.447 1.214**<br />
(0.206) (0.006)<br />
NITA -0.074 0.156*<br />
(0.339) (0.019)<br />
TDTA 0.097** 0.084**<br />
(0.007) (0.001)<br />
ROE 0.023 -0.089*<br />
(0.509) (0.011)<br />
FBT -1.558 dropped<br />
(0.274)<br />
TPT 1.540 dropped<br />
(0.293)<br />
MT dropped -2.267<br />
(0.159)<br />
CD dropped -0.583<br />
(0.469)<br />
CG dropped -0.451<br />
(0.683)<br />
TS dropped -1.128<br />
(0.422)<br />
2001 -3.371* -2.458*<br />
(0.041) (0.043)<br />
2002 -1.651 -1.183<br />
(0.170) (0.334)<br />
2003 -1.501 -1.521<br />
(0.060) (0.083)<br />
2004 dropped dropped<br />
2005 -1.577 -0.962<br />
(0.108) (0.302)<br />
2006 -2.275 -0.834<br />
(0.052) (0.406)<br />
2007 -2.475* -1.810<br />
(0.050) (0.099)<br />
38
Appendix Five<br />
Table 9 (continued) Model Summary<br />
Percentage Correct 73.333 73.333<br />
-2 Log likelihood 62.294 58.940<br />
Cox & Snell R Square 0.294 0.332<br />
Nagelkerke R Square 0.392 0.443<br />
Omnibus Tests <strong>of</strong> Model Coefficients<br />
Chi-square 20.883 24.237<br />
df 12.000 14.000<br />
sig 0.050* 0.043*<br />
Hosmer and Lemeshow Test<br />
Chi-square 3.654 9.892<br />
df 8.000 8.000<br />
sig 0.887 0.273<br />
39
Appendix Six<br />
Table 10 Coefficients two or three years before default (Sample Two)<br />
Variables Two years before default Three years before default<br />
NITA -0.068 0.036<br />
-0.077 -0.316<br />
Size -0.604* -0.609<br />
(0.026) -0.067<br />
ROE 0.018 -0.029<br />
-0.147 -0.122<br />
TDTA 0.037** 0.043**<br />
(0.006) (0.010)<br />
SATA -0.367 -0.67<br />
-0.349 -0.183<br />
EQTC 0.004 -0.001<br />
-0.741 -0.956<br />
RETA 0.247 0.464<br />
-0.344 -0.382<br />
CD 1.391 1.745*<br />
-0.055 (0.049)<br />
MT -0.199 -0.094<br />
-0.825 -0.924<br />
RE -0.35 0.146<br />
-0.77 -0.915<br />
TH -0.016 dropped<br />
-0.984<br />
DF -0.057 dropped<br />
-0.96<br />
CG dropped 1.099<br />
-0.252<br />
FBT dropped 0.669<br />
-0.513<br />
SS dropped -0.15<br />
-0.898<br />
TS dropped 0.314<br />
-0.779<br />
TPT dropped 0.117<br />
-0.916<br />
40
Appendix Seven<br />
Table 10 (continued) Model Summary<br />
Percentage Correct 78.218 79.208<br />
-2 Log likelihood 101.122 97.363<br />
Cox & Snell R Square 0.320 0.344<br />
Nagelkerke R Square 0.426 0.459<br />
Omnibus Tests <strong>of</strong> Model Coefficients<br />
Chi-square 38.894 42.653<br />
df 12.000 15.000<br />
sig 0.000** 0.000**<br />
Hosmer and Lemeshow Test<br />
Chi-square 4.774 4.556<br />
df 8.000 8.000<br />
sig 0.781 0.804<br />
41
Appendix Eight<br />
Table 12 Cl<strong>as</strong>sification (Sample Two, 1 st year before default)<br />
Predicted<br />
Default<br />
Observed 0 1 Percentage Correct<br />
Default 0 68 3 95.8<br />
The cut value is .500<br />
1 11 19 63.3<br />
Overall Percentage 86.1<br />
42
C<strong>as</strong>e Selected<br />
Status a<br />
Appendix Nine<br />
Table 16 C<strong>as</strong>ewise List b (Sample Two, 1 st year, outliers)<br />
Observed Predicted Predicted Temporary Variable<br />
Default<br />
Group<br />
Resid ZResid<br />
67 S 1** 0.020 0 0.980 6.992<br />
99 S 1** 0.013 0 0.987 8.757<br />
a. S = Selected, U = Unselected c<strong>as</strong>es, and ** = Miscl<strong>as</strong>sified c<strong>as</strong>es.<br />
b. C<strong>as</strong>es with studentized residuals greater than 2.000 are listed.<br />
Table 17 Cl<strong>as</strong>sification (Sample Two, 1 st year, excluding outliers)<br />
Predicted<br />
Default<br />
Observed 0 1 Percentage Correct<br />
Default 0 68 3 95.8<br />
The cut value is .500<br />
1 6 22 78.6<br />
Overall Percentage 90.9<br />
Table 18 Variables in the Equation (Sample Two, 1 st year, excluding outliers)<br />
B S.E. Wald df Sig. Exp(B)<br />
NITA1 -0.488** 0.164 8.866 1.000 0.003 0.614**<br />
Size1 -1.227* 0.484 6.433 1.000 0.011 0.293*<br />
RETA1 2.130 1.208 3.107 1.000 0.078 8.412<br />
TDTA1 0.095** 0.032 8.650 1.000 0.003 1.099**<br />
SATA1 -3.280* 1.530 4.594 1.000 0.032 0.038*<br />
EQTC1 0.033 0.019 3.118 1.000 0.077 1.033<br />
ROE1 0.008 0.005 2.424 1.000 0.119 1.008<br />
CD 3.654* 1.583 5.330 1.000 0.021 38.613*<br />
DF 2.086 1.604 1.692 1.000 0.193 8.057<br />
MT -1.440 1.388 1.076 1.000 0.300 0.237<br />
SS -2.411 1.891 1.625 1.000 0.202 0.090<br />
TPT 3.198* 1.612 3.937 1.000 0.047 24.479*<br />
TH -1.324 2.330 0.323 1.000 0.570 0.266<br />
43