Financial Ratios as Predictors of Failure: Evidence from Hong Kong using Logit Regression

Transcription

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

2 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

3 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 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

4 Table of Contents 1. Introduction Probability of Default and Bankruptcy Literature Review Theories Multi factors in predicting PD and the methodologies Multiple Discriminant Analysis Logistic Regression Data and Methodology Methodology Data and Sample Explanatory Variables and Hypotheses Empirical Results Descriptive Results Estimation results of the Logit model Predictive power of the model Robustness Test Conclusion Reference Appendix One Appendix Two Appendix Three Appendix Four Appendix Five Appendix Six Appendix Seven Appendix Eight Appendix Nine

5 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

6 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

7 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. 6

8 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

9 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

10 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 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)=R f +β*(r m - R f ), E(R) is the expected return of the capital asset, R f is the risk-free rate of interest, β is the sensitivity of the asset returns to market returns, R m is the expected return of the market, (R m - R f ) 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

11 ratios 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)) 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 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

12 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 ( ). 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

13 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 L i =ln[p i /(1-p i )]=βx i +u i, 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 Data and Sample The companies in this study are publicly traded and listed on the Hong Kong Stock Exchange (HKEx) 13 over the period 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 Although inactive companies are usually default. 12

14 to the definition of default (see section two) in this study, 30 default companies with complete financial data have been found over 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 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

15 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 L i = ln [p i /(1-p i )] = β 1 TDTA i - β 2 EQTC i + β 3 RETA i + β 4 ROE i - β 5 CFTD i β 6 NITA i β 7 SATA i β 8 WCTA i β 9 CR i β 10 Size i + dummy (year) + dummy (industry) + u i. 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

16 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

17 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

18 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. Variance Minimum Maximum Mean Std. Variance Deviation Deviation CFTD RETA WCTA CR NITA TDTA SATA Size EQTC ROE Table 3(b) Descriptive Statistics (Sample Two, 1 st year before default) CFTD RETA WCTA CR NITA TDTA SATA Size EQTC ROE 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

19 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 CFTD ** RETA ** ** ** ** 0.284* 0.299* WCTA ** ** ** * 0.311* 0.354** CR ** NITA ** 0.965** ** 0.262* 0.262* TDTA ** ** * * * SATA Size ** 0.322* ** * * EQTC * 0.311* * * * ROE ** ** ** * 0.318* 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

20 Table 6(b) Correlations (Sample Two, 1 st year before default) CFTD1 RETA1 WCTA1 CR1 NITA1 TDTA1 SATA1 Size1 EQTC1 ROE1 CFTD * * RETA ** ** ** ** 0.257** WCTA ** ** 0.944** ** ** 0.287** CR * ** * NITA ** 0.944** ** 0.238* 0.249* TDTA ** ** ** ** SATA * Size ** 0.281** ** ** * EQTC * 0.257** 0.287** 0.215* 0.238* ** ROE *. 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 L i =ln[p i /(1-p i )], after taking the antilog of the estimated logit, we get p i /(1-p i ) (that is, the odds ratio). In this case, since p represents probability of default, p i /(1-p i ) 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

21 Table 7 Variables in the Equation (Sample One, 1 st year before default) B S.E. Wald df Sig. Exp(B) RETA NITA ** ** TDTA * * ROE * * RE TH MT CD DF CG TS Omnibus Tests of Model Hosmer and Lemeshow Coefficients Test Model Summary Chi-square Chi-square Log Likelihood df df Cox & Snell R significance 0.007** significance Nagelkerke R Notes: *, and ** significant at 5, and 1 percent level respectively. The sample includes 60 companies over period 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 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

22 ROE increases the odds of default 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% (( )*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

23 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 log 10 (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 (e ) and 22

24 (e ) 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) NITA ** ** Size * * RETA TDTA * * SATA EQTC ROE CD DF MT SS TPT TH Omnibus Tests of Model Hosmer and Lemeshow Coefficients Test Model Summary Chi-square Chi-square Log Likelihood df df Cox & Snell R significance 0.000*** significance Nagelkerke R Notes: *, **, and *** significant at 10, 5, and 1 percent level respectively. The sample includes 101 companies over period 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 default company is misclassified as non-default, and when a non-default company is 23

25 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 Overall Percentage 81.7 The cut value is.500 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=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

26 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

27 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). Table 13 Casewise List b (Sample One, 1 st year, outliers) Case Selected Observed Predicted Predicted Temporary Variable Status a Default Group Resid ZResid 34 S 0** S 1** S 1** S 1** a. S = Selected, U = Unselected cases, and ** = Misclassified cases. b. Cases with studentized residuals greater than are listed. Table 14 Classification (Sample One, 1 st year, excluding outliers) Predicted Default Observed 0 1 Percentage Correct Default Overall Percentage 89.3 The cut value is.500 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

28 Table 15 Variables in the Equation (Sample One, 1 st year, excluding outliers) B S.E. Wald df Sig. Exp(B) RETA NITA *** TDTA ** ROE ** RE TH MT CD DF CG TS ** 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

29 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 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: : 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