An empirical evaluation of bankruptcy prediction models for small firms: an over-the-counter (OTC) market experience.

He, Yihong ; Kamath, Ravindra ; Meier, Heidi Hylton 等

ABSTRACT

The focus of this paper is on the bankruptcy prediction of small firms. Specifically, two successful bankruptcy prediction models, Ohlson's model (1980) and Shumway's model (2001), are re-estimated with the data of a sample of firms traded on the over-the-counter (OTC) market in a recent period in the 1990s. While Ohlson's model relies strictly on accounting ratios, Shumway's model combines market measures with the accounting ratios. Both models are then validated by a classification test and a more rigorous prediction test to predict the bankruptcy probability of the holdout samples. The results indicate that both the classification accuracy and the prediction accuracy are impressive with these two models for predicting bankruptcy up to three years before their actual demise, while Shumway's model performs marginally better than Ohlson's model.

INTRODUCTION

Business failures are considered both unfortunate and costly at least by the owners, creditors, employees, suppliers and customers of the failed firms. Even the ardent admirers of the market mechanisms' ability to increase efficiency through its "survival of the fittest" principle find the social and economic consequences of business failures rather unpleasant in the short run. Accordingly, for over thirty years, academic researchers and practitioners in the fields of accounting, economics and finance have shown a strong and determined interest in developing and testing business failure prediction models.

The literature on bankruptcy prediction models is rich and it demonstrates numerous strides made over the years since the pioneering research by Beaver (1966) and Altman (1968). For the most part however, prior research has concentrated on firm samples made up of the largest of the corporations traded on the New York Stock Exchange (NYSE) and/or the American Stock Exchange (AMSE). (1) Yet in reality, the small firms are more vulnerable to business failure than their larger counterparts. (2) According to the Small Business Administration (SBA, 1999), over 99 percent of business closures are small firms. Moreover, small businesses are the backbone of the U.S. economy. They produce 39 percent of the GNP and make 47 percent of all sales within the U.S. (SBA, 1999). Small firms also account for about half of the private sector employment and create two of every three new jobs. The crucial importance of small firms in the American business frontier provides partial impetus for this study. The relative paucity of studies focusing on small business failure provides additional motivation for the present study.

The objective of the empirical investigation in this study is to examine the effectiveness of two highly successful bankruptcy prediction models, namely, Ohlson's model (1980) and Shumway's model (2001) in predicting bankruptcy of small firms. Specifically, this study applies the two models for predicting bankruptcy of a sample of over-the-counter (OTC) traded firms during a period of the 1990s. While Ohlson's model relies strictly on accounting data, Shumway's model combines market information with the accounting data.

The distinguishing features of this study, which are summarized next, make strong attempts to overcome some of the glaring voids in the literature. First, this study addresses the issue of business failures specifically to the OTC traded small firms. Only firms with assets less than $130 million are considered in this investigation. About 75 percent of the sample firms had assets of less than $50 million one year prior to bankruptcy. Second, this paper analyzes the data from a large sample of 316 OTC firms, consisting of 158 bankrupt firms during the 1990s and 158 matched nonbankrupt firms by size, industry and the timing of the financial reports during the same period. Third, by using all the data, the financial as well as the market data, from the most recent decade, the problem of pooling the data from 2 or 3 decades in the previous studies is mitigated. Fourth, the estimated models are externally validated by a prediction test up to 3 years prior to bankruptcy with the help of a holdout sample. Specifically, the bankruptcy prediction models estimated by using the data of 246 matched firms over the 1990-1996 period are utilized to predict failure for a group of 70 matched firms during 1997 and 1998.

The rest of the paper is organized as follows. A brief review of the literature is the subject of the second section. The methodology and the data adopted in this study are explained in the third section. The empirical results are presented and analyzed in the fourth section. A summary of the paper makes up the final section.

LITERATURE REVIEW

Since the seminal work of Beaver (1966) and Altman (1968), financial ratio analysis has become the favorite approach to investigating the bankruptcy problem (Altman, 1993). Numerous studies have been published through the development of various statistical techniques into ratio analysis to predict bankruptcy over the past thirty years. Table 1 presents the summary of the major studies using financial ratios in discriminating between bankrupt and nonbankrupt firms.

Empirical research for predicting bankruptcy started with univariate analysis (e.g., Beaver, 1966). Under this method, each individual ratio is examined at a time and the ratios which provide the most accurate prediction are recognized. Multivariate discriminant analysis (MDA) later replaced univariate analysis to develop bankruptcy prediction models (e.g., Altman, 1968; Deakin, 1972; Edmister, 1972; Blum, 1974) because the MDA method can measure a firm's risk of bankruptcy by analyzing several ratios simultaneously. A composite number, such as Z score, from the MDA is used to classify a firm as bankrupt or nonbankrupt. More recent prediction models have been developed using logit analysis, which is in response to the limits of the MDA method (e.g., Ohlson, 1980; Zavgren, 1985; Platt & Platt, 1990) to improve the predictive reliability and accuracy. The most distinctive advantage of the logit analysis over the MDA method, according to Eisenbeis (1977), is that the coefficient of an individual variable in a logit model is interpretable and the significance of a variable can be tested statistically. Thus, each financial ratio in a logit model is examined so that the predictive accuracy of the model can be improved.

Ohlson (1980) is among the first to use logit analysis to develop a bankruptcy prediction model to assess the probability of corporate failure. The variables include financial ratios which measure liquidity, profitability, leverage and solvency. The sample was made up of 105 publicly traded industrial firms that went bankruptcy during the period of 1970 to 1976. The model found that leverage ratio and profitability ratio were consistently significant in discriminating between bankrupt and nonbankrupt firms up to three years prior to bankruptcy. Ohlson also concluded that smaller firms were more prone to bankruptcy. Due to lack of new data beyond 1976, Ohlson examined the validity of his model only by classifying the same sample which was used to estimate the model. The classification test showed that Ohlson's model was able to identify about 88 percent of 105 bankrupt firms accurately one year before bankruptcy.

Table 1 reflects how the research has evolved in conjunction with stock market behavior and further effort to pursue a successful bankruptcy prediction model can be beyond financial ratio analysis. This is because a model relying solely on financial ratios might not capture some firm-specific attributes in time. These idiosyncratic characteristics for bankrupt firms include "unmeasured quality of assets, the creative ability of management, random event, and the courts of law" (Zavgren, 1985). Recently, researchers began to investigate the relationship between market behavior and bankruptcy (e.g., Aharony et al., 1980; Clark & Weinstein, 1983; Katz et al., 1985; Queen & Roll, 1987; Simons & Cross, 1991). Given a semi-strong efficient market, if a firm is experiencing deteriorating solvency, the capital market will assimilate such unfavorable information immediately and promptly impound on the stock price to reflect the increasing insolvency risk well before eventual bankruptcy. A number of studies confirmed that certain market measures had information content related to bankruptcy and had reported strong support for the efficient market paradigm. For example, Aharony et al. (1980) and Clark & Weinstein (1983) found evidence in an event study that a significant negative return for bankrupt firms started about three years before bankruptcy.

Finally, the most recent work of Shumway (2001) shed new light on developing a more dynamic bankruptcy prediction model by combining both financial ratios and market-driven measures. Shumway's sample consisted of 239 bankrupt firms which were traded on the NYSE and the AMSE over the 1962-1992 period. The results indicated that both financial ratios and market measures possessed strong discriminating ability and had lower correlations with each other. When applied to a holdout sample, Shumway's model provided impressive prediction accuracy and outperformed other benchmark models (Altman's model (1968) and Zmijewski's model (1984)), which were based solely on financial ratios. The results support the assertion that financial ratios and market-driven measures should not be regarded as competing predictors. On the contrary, combining both in a multivariate context can help improve prediction ability.

Further efforts are still needed to overcome certain limitations in the past studies in order to improve the usefulness of bankruptcy prediction models. One criticism concerns sample selection bias. As can be seen from Table 1, all research except Edmister's study (1972) collected the bankrupt firms and data primarily from Moody's Industrial Manual, in earlier studies, or the Compustat, in recent work. Since these data sources mainly provide information for the largest firms, any sampling frame drawn from the above sources is weighted heavily toward large firms. Another criticism has to do with the pooling problem. Since only a few large firms declare bankruptcy each year, researchers usually pooled observations over different years to obtain an adequate sample size to permit statistical testing. The majority of studies shown on Table 1 covered a sample period over 10 years, and some (e.g., Altman, 1968; Queen & Roll, 1987; Shumway, 2001) stretched over 20 years. Considering the dramatic change of business environment over the last decades, such pooling data results in nonstationary statistical inferences of the predictive variables (i.e., means, variances and covariances) for the sample firms during the test periods. Consequently, pooling data from different periods would have confounded empirical results significantly.

Last, due to the limited sample size of large firms, validation of the developed models encounters difficulty. Table 1 shows that different procedures of validating the predictive reliability of the models have been used. Many studies adopted a classification test (e.g., Beaver, 1968; Edmister, 1972; Aharony et al., 1980; Ohlson, 1980; Queen & Roll, 1987), in which the model is evaluated merely according to the accuracy to classify the same sample from which the model was estimated. Some studies used a more powerful cross-validation test (e.g., Beaver, 1966; Altman, 1968; Deakin, 1972; Blum, 1972; Zmijewski, 1984), which splits the sample into two subsamples. One subsample is used to estimate the model, and then the other subsample in the same time period is used to evaluate the predictive accuracy of the model. The most rigorous validation is the prediction test, which is on the ex ante basis, but performed by few studies due to small sample sizes. Under this test, the model is estimated by one sample in an earlier period and then is used to predict another holdout sample in a later period. Only three studies (i.e., Zavgren, 1985; Platt & Platt, 1990; Shumway, 2001) performed the prediction test. Platt & Platt (1990) and Shumway (2001) reported the prediction results for only one year before bankruptcy. Zavgren (1985) reported the results up to five years prior to bankruptcy, though not with much success. In general, the value of a bankruptcy prediction model in decision-making would be much greater if such a model displays superior ability to predict bankruptcy several years prior to actual declaration of bankruptcy.

METHODOLOGY

The objective of this study is to determine whether models that have been used successfully to predict bankruptcy for very large firms can be used effectively to predict bankruptcy for small firms, as well. In this section, we first describe the models used in this research, then discuss the variables in those models, and the data used in our sample.

Models and Variables

To evaluate the effectiveness of bankruptcy prediction models, we have chosen to utilize two successful models: Ohlson's model (1980) and Shumway's model (2001).

Ohlson constructed a logit model in which the dependent variable was a score to determine the probability of bankruptcy. This model was estimated based on a set of independent variables which were financial statement ratios and is defined as follows:

Z = 1/ [1 + exp - (a + [b.sub.1] TLTA + [b.sub.2] WCTA + [b.sub.3] CLCA + [b.sub.4] OENEG + [b.sub.5] NITA + [b.sub.6] FUTL + [b.sub.7] INTWO + [b.sub.8] CHIN)]

Where:

Z = the probability of bankruptcy for a firm

TLTA = Total liabilities/total assets

WCTA = Working capital/total assets

CLCA = Current liabilities/current assets

OENEG = 1, if total liabilities exceeds total assets; zero otherwise

NITA = Net income/total assets

FUTL = Fund provided by operations/total liabilities

INTWO = 1, if net income was negative for the last two years; zero otherwise

CHIN = ([NI.sub.t] [NI.sub.t-1]) / ([NI.sub.t] + [NI.sub.t-1]), Where [NI.sub.t] is net income for the most recent period. The denominator acts as a level indicator. The variable is thus intended to measure changes in net income

Examining these financial ratios more closely, the expected relationship of the ratios with the probability of bankruptcy can be noted. Two of the ratios, TLTA and CLCA, are indicators of increasing liabilities and the signs of the coefficients are predicted to be positive. Whereas, WCTA, NITA, and FUTL, which measure the relationship of working capital, net income and funds provided by operations, respectively, are all expected to decrease as the firm approaches bankruptcy. Therefore, the coefficients for these variables are expected to have negative signs. The variables OENEG and INTWO are indicator variables which are expected to be positively related to the increasing probability of bankruptcy.

Ohlson (1980) applied logit analysis to develop a prediction model using a group of bankrupt firms that were traded on the NYSE and AMSE during the 1970s. Logit analysis weights the independent variables and creates an overall score which can be interpreted as the probability of a firm's bankruptcy. The coefficients measure the effect on the probability of bankruptcy in terms of a unit change in the corresponding variables (Jones, 1987).

It can be argued that Shumway (2001) improved on the basic bankruptcy models by combining market ratios along with the traditional financial ratios. This model is defined as follows:

Z = 1/ [1 + exp - (a + [b.sub.1] NITA + [b.sub.2] TLTA + [b.sub.3] ERR + [b.sub.4] SDR)]

Where:

Z = the probability of bankruptcy for a firm

NITA = Net income/total assets

TLTA = Total liabilities/total assets

ERR = Excess rate of return (i.e., a firm's rate of return minus the market's rate of return)

SDR = Standard deviation of residual returns (Residual return = a firm's realized rate of return - its expected rate of return)

The two accounting ratios measures the return on assets and financial leverage which proxy for the firm's profitability and financial leverage risk, respectively. It is expected that a firm will experience deteriorating profits and increased reliance on borrowed funds as it approaches bankruptcy. Therefore, we predict a negative coefficient for the variable NITA and a positive coefficient for the variable TLTA. The two market variables in the model include the excess rate of return (ERR) which is an indication of the firm's rate of return and the standard deviation of residual returns (SDR) which reflects the market risk of publicly traded firms. It is expected that as a firm approaches bankruptcy, it is riskier than a healthy firm and the risk-averse market will react by downgrading the firm's stock price and thus, we expect that the coefficient for the variable ERR will be negative. Meanwhile, as a firm approaches bankruptcy, it is also expected to be more unstable than other firms and its returns will produce a larger standard deviation. Therefore, the coefficient of the variable SDR is expected to be positive.

Both models originally included a variable to control for firm size. In this study an elaborate pair-matching procedure has been used to control for the size effect and therefore, a variable is not used in the model. This will be discussed further in the following sections.

Sample and Data

The bankrupt sample firms consist of a group of industrial OTC companies that went bankrupt during the period from 1990 to 1998. The list of bankrupt OTC firms and bankruptcy filing dates is initially searched from Moody's OTC Industrial Manual and Moody's OTC Unlisted Manual. Additional bankrupt OTC firms and petition dates are supplemented from the National Stock Summary. Firms falling within the SIC code from 6000 to 6999 (financial firms) are not included. The original sample contained 553 bankrupt OTC industrial firms.

The financial data in Ohlson's and Shumway's models are retrieved from the Compustat Research File, Moody's OTC Industrial Manual and Moody's OTC unlisted Manual. A firm is excluded from the sample whenever required data are missing for the computation of ratios in a given year. The market data in Shumway's model are obtained from Compustat and OTC Daily Stock Prices Record by Standard & Poor. For some firms which were delisted before filing bankruptcy, the latest available trading data are used. The market index for OTC firms is surrogated by the Industrial Index of OTC Market Indicator (before 1993) and the Industrial Index of Nasdaq Market Indicator (after 1993). The Market Index is collected from OTC Daily Stock Prices Record by Standard & Poor and Nasdaq Daily Stock Prices Record by Standard & Poor, respectively. Of the initial 553 bankrupt industrial firms, many firms are deleted due to incomplete financial and market data, resulting in 222 bankrupt OTC firms with complete financial and market data during the period 1990-1998.

To avoid using adjusted financial statements to exaggerate the predictive accuracy of models, financial data from the last year's financial statements for a bankrupt firm is considered only if the firm filed the petition six months after the last fiscal year end. For example, if a firm with a fiscal year end on December 31 filed bankruptcy in April 1993, the data of one year before bankruptcy should be retrieved from the financial statements ended on December 31 1991. Likewise, for a firm that filed bankruptcy in September 1993, financial data for the December 1992 year end will be used as one year before. Thus, one year before bankruptcy in this study is defined as a firm's most recent fiscal year end at least six months prior to the date of its bankruptcy filing. The second year and third year before bankruptcy are defined accordingly. Similarly, data for market variables are also lagged at least six months before the bankruptcy filing. Although such a lag might lower the predictive power of the models, it adds practical value of prediction for decision makers because predicting bankruptcy within a few months prior to bankruptcy provides little protection to prevent losses.

Matching of Nonbankrupt Firms

Firms are paired by industry according to the SIC code with the same first two-digit number. Each nonbankrupt firm is matched as closely to a bankrupt one in size on the basis of the book value of total assets one year prior to bankruptcy. Size is further controlled by limiting a sample firm to one with total assets less than $130 million one year prior to bankruptcy in order to keep the study focused on relatively small firms. It was also made sure that the fiscal year of a selected nonbankrupt firm falls within three months of the fiscal year of a bankrupt firm to have matched firms report financial statements in the same period. Sources of sample selection and the requirements of data collection for nonbankrupt firms are the same as those for bankrupt firms. To be considered nonbankrupt, a firm must not have filed bankruptcy before the matched period, or have filed for bankruptcy in the following three years after the matching data.

The final paired sample consisted of 158 bankrupt firms and 158 nonbankrupt firms with complete financial and market data from 1990 to 1998. Compared with previous studies summarized earlier, only Begly et al. (1996) collected a slightly larger sample with 165 bankrupt firms which covered a period of 1980 to 1989. Shumway's study (2001) had an impressive 300 bankrupt firms, but those samples extended over a thirty-year period. Table 2 Panel A provides descriptive statistics of bankrupt and nonbankrupt firms matched in total assets at one year before bankruptcy.

About 75 percent of 316 matched firms have assets less than $50 million at one year preceding bankruptcy. There are only nine paired firms with assets over $100 million but below $130 million, accounting for less than 6 percent of the total sample. The selected sample represents a group of small-sized firms in the capital market. The results of the t-test further show no significant size difference in terms of total assets between bankrupt and nonbankrupt firms when matched one year before bankruptcy. The sample is drawn from a variety of industries in the period of 1990 to 1998. The distributions of the sample across industries and years are presented in Panel B and C of Table 2.

Division of the Matched Sample

To examine the classification and prediction ability of a bankruptcy prediction model, the whole matched sample of 316 firms is split into two subsamples. One subsample consists of 246 matched firms from 1990 to 1996, and another consists of 70 matched firms from 1997 to 1998. The 246 matched firms in the earlier period are used to re-estimate Ohlson' model and Shumway's model, respectively. The classification test of the model is conducted on the subsample of these 246 firms. The second subsample of 70 matched firms in the subsequent period is used as a holdout sample to evaluate external prediction validity of the model on an ex ante basis. Both Ohlson's and Shumway's models are evaluated and compared in terms of classification and prediction accuracy at one, two and three years prior to bankruptcy.

RESULTS AND ANALYSIS

Re-estimation of the Models

Unlike most of the previous studies that performed an empirical comparison of the models, we first re-estimate Ohlson's and Shumway's original models with the updated coefficients by using our new data on small firms. Two hundred-forty-six matched OTC firms from 1990 to 1996 are used to re-estimate the models, and Table 3 and 4 present the results for each model in each of the three years prior to bankruptcy.

The statistical test for the significance of Ohlson's model indicates that all three models are significant at the 0.01 level and exhibit strong discriminating ability to account for the probability of bankruptcy. Further analysis of individual predictive variables in Ohlson's model, however, raises several concerns. First, the signs of the coefficients of several predictors, WCTA, FUTL, CLCA and INTWO, change over the study period. The inconsistency of relationship between these variables and probability of bankruptcy makes the interpretation of results difficult. Of the eight predictive variables in Ohlson's model, only NITA, TLTA, CHIN and OENEG exhibited consistent relationships with the probability of bankruptcy in all three periods. Second, most variables are not statistically significant, which are underlined in Table 3. NITA and TLTA are the only two variables statistically significant at the 0.01 level for all three years. The lack of significance of the explanatory abilities for the other six variables in Ohlson's model suggests that multicollinearity may exist among variables. The backward stepwise procedure is conducted to test if certain variables can be eliminated without significantly losing the proportion of variance explained by the model at the 0.10 level. The results, which are not presented in the study, indicate that TLTA and NITA are the only two variables remaining in the models for all three years, while other variables can be eliminated from the models without significant loss of variance explanation.

The re-estimated Shumway's model in Table 4 shows statistical significance in distinguishing bankrupt firms from nonbankrupt firms at less than a 0.01 level in each of the three years. Unlike Ohlson's model, the signs of coefficients for each variable in Shumway's model exhibit the expected relationships with the probability of bankruptcy in a consistent fashion during the test period. The chi-square statistics also indicate that each variable in Shumway's model has a statistically significant effect on predicting bankruptcy at the 0.01 level in each of the three years.

Furthermore, to interpret the marginal effect of the coefficients of the predictive variables on the probability of bankruptcy in the logit model, elasticity is computed by the following equation:

Elasticity = B (1 - P) X

Where:

Elasticity = percent change in probability/percent change in predictive variables

B = the coefficient of the variable

P = the mean of the probability estimated in the sample

X = the mean of the predictive variable in the sample

Table 5 presents the results of the elasticity for Shumway's model to measure the marginal effect of each variable on the probability of bankruptcy. An elasticity value of greater than 1 is known as elastic, which means that the predictive variable has a larger impact on the probability of bankruptcy. An elasticity value of less than 1 is called inelastic and indicates less impact of the predictive variable on the probability of bankruptcy. Table 5 shows that TLTA has the most impact on the probability of bankruptcy, given that its elasticity value is greater than 1 for each of three years. This finding is not surprising because bankruptcy is largely caused by failing to meet creditors' obligation in time, and TLTA measures the level of debt risk. The variable SDR has the second most influence, followed by the variable NITA and ERR, respectively.

Classification Test

The 246 matched firms, which are used to re-estimate the models, are classified by each model. Since both Ohlson's model and Shumway's model are estimated for each of the three years before bankruptcy, consequently, the one-year prior model is used to classify the 246 matched firms with one-year prior data, while the two-year prior model is used to classify the 246 firms with two-year prior data and so on. Table 6 and 7 present the results of accuracy for the classification test for each model for one, two and three years before bankruptcy, in terms of number of firms and classification accuracy rate.

The overall accuracy of classification supports a strong internal validity of both Ohlson's model and Shumway's model. Of 246 firms, Ohlson's model is able to classify 90%, 81% and 78% correctly for one, two and three years prior to bankruptcy, respectively. Shumway's model, on the other hand, achieves 92% of overall classification accuracy one year before bankruptcy, and 83% and 80% in two years and three years before bankruptcy, respectively. The results also indicate that as the lead-time from bankruptcy increases, the classification accuracy of the model is decreased. The lower Type I error rates indicate that Shumway's model is able to classify more accurately than Ohlson's model in the classification test for each of three years, although the differences of classification accuracy between the two models are not significant.

Prediction Test

A bankruptcy prediction model becomes more rigorous and practical when the model is successful in classifying a group of holdout firms, which are not used to develop the model, in a subsequent period. Such a validation procedure is the prediction test because it is conducted on the ex ante basis. To do so, the re-estimated Ohlson's model and Shumway's model are applied to a group of 70 matched firms in the subsequent period of 1997 and 1998 when the bankruptcies were filed. In addition, only the models estimated with one-year prior data are used to classify those 70 firms one, two and three years before bankruptcy. Such a consideration is critical in a practical sense since the timing for a firm to file bankruptcy petition is likely unknown in advance. Thus, it is impossible for decision makers to select an appropriate model estimated from different periods before bankruptcy. Instead, applying a model which captures the most discriminatory ability with the best accuracy in the classification test is more intuitive and practical in performing a prediction test. The results of the prediction test for Ohlson's and Shumway's model are exhibited in Table 8 and 9.

Ohlson's model classifies 83% of total 70 holdout samples correctly one year prior to bankruptcy, while the overall prediction accuracy are 76% for both year two and year three prior. When compared to its own results from the classification test in Table 7, Ohlson's model loses the largest margin of accuracy in the prediction test by 7% one year before, and 5% and 2%, respectively, two and three years before bankruptcy. Shumway's model, however, achieves very impressive prediction accuracy one year prior to bankruptcy. Of the total 70 holdout sample firms, Shumway's model is able to classify 67 firms correctly, and to predict 96% of the firms accurately one year preceding bankruptcy. The predictive ability of the model drops as the lead-time before bankruptcy is lengthened. The overall rates of prediction accuracy are 77% at two years before, and 74% at three years before bankruptcy, in comparison to 83% and 80% under classification test in the corresponding periods, respectively. The results of the prediction test display relative stability in the discriminatory ability of Ohlson's model and Shumway's model, and both models maintain strong external validity when applied to a holdout sample in the subsequent period.

SUMMARY

The primary objective of this paper was to estimate and ascertain the ability of two successful models from the bankruptcy prediction literature to predict bankruptcy of small firms. To fulfill this task, this paper utilized the accounting information based model by Ohlson (1980) and the accounting and market information based model by Shumway (2001). The sample was made up of 316 OTC traded small firms from the 1990s. This sample had 158 bankrupt firms and 158 matching but nonbankrupt firms. The matching of the firms was based on the size, industry, as well as, the timing of their financial reports. While the asset size in this investigation was limited to $130 million, about 75 percent of the firms had assets of $50 million or less one year prior to bankruptcy.

Considering the well documented vulnerability of small firms to business failure and yet, ignored for the most part in the bankruptcy prediction literature, this paper has made some important inroads. With the proliferation of OTC traded firms in the 1990s and the accompanying five fold increase in the market values of these firms, the OTC firm sample used in this paper is timely as well. This paper has also contributed in terms of having all the data from the 1990-1998 period. This relatively short period of study has thus avoided the use of data pooled from distinctly different time periods. Moreover, this study has used a holdout sample of 70 OTC traded firms consisting of 35 matching pairs of bankrupt and nonbankrupt firms. The models estimated from the 1990-1996 information of 246 firms are used to predict bankruptcy experience of the holdout sample in later years.

The results indicate that for the sample at hand, Shumway's model (2001) marginally outperforms Ohlson's model (1980) in terms of predicting business failure of small firms. The overall accuracy of classification with Shumway's model was 92 percent, 83 percent, and 80 percent with 1, 2 and 3 years prior to bankruptcy, respectively. The comparable figures with Ohlson's model were 90, 81 and 78 percent. With respect to the holdout sample, Shumway's model achieved overall prediction accuracy levels of 96, 77 and 74 percent with 1, 2 and 3 years prior to bankruptcy, respectively. The comparable figures with Ohlson's model were 83, 76, and 76 percent. It is believed that this empirical investigation has extended the contributions of Shumway (2001), Ohlson (1980) and others, and particularly the efforts of Edmister (1972) in terms of bankruptcy prediction of small firms.

REFERENCES

Aharony, H. J., P. Charles & I. Swary. (1980). An analysis of risk and return characteristics of corporate bankruptcy using capital market data. Journal of Finance, 35, 1001-1016.

Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance, 23, 589-609.

Altman, E. I. (1993). Corporate financial distress and bankruptcy: a complete guide to predicting and avoiding distress and profiting from bankruptcy (Second Edition). New York: John Wiley & Sons, Inc.

Beaver, W. H. (1966). Financial ratios as predictors of failure. Journal of Accounting Research, 4 (supplement), 71111.

Beaver, W. H. (1968). Market prices, financial ratios, and the prediction of failure. Journal of Accounting Research, 6, 179-192.

Begley, J., M. Jin & S. Watts. (1996). Bankruptcy classification errors in the 1980s: An empirical analysis of Altman's and Ohlson's Models. Review of Accounting Studies, 1, 267-284.

Blum, M. (1974). Failing company discriminant analysis. Journal of Accounting Research, 12, 1-25.

Clark, T. A. & M. I. Weinstein. (1983). The behavior of the common stock of bankrupt firms. Journal of Finance, 38, 489-504.

Deakin, E. B. (1972). A discriminant analysis of predictors of business failure. Journal of Accounting Research, 10, 167-179.

Dimistras, A. I., S. H. Zanakis & C. Zopoundis (1996). Theory and methodology: A survey of business failures with an emphasis on prediction methods and industrial applications. European Journal of Operational Research, 90, 487-513.

Dietrich, J. R. (1984). Discussion of methodological issues related to the estimation of financial distress prediction models. Journal of Accounting Research, 22 (Supplement), 83-99.

Edmister, R. O. (1972). An empirical test of financial ratio analysis for small business failure prediction. Journal of Financial and Quantitative Analysis, 7, 1477-1493.

Eisenbeis, R. A. (1977). Pitfalls in the application of discriminant analysis in business, finance, and economics. Journal of Finance, 32, 875-900.

Gilbert, L. R., K. Menon & K. B. Schwartz (1990). Predicting bankruptcy for firms in financial distress. Journal of Business, Finance and Accounting, 17(1), 161-171.

Johnsen, T. & R. W. Melicher (1994). Predicting corporate bankruptcy and financial distress: information value added by multinomial logit models. Journal of Economics and Business, 46, 269-286.

Jones, F. L. (1987). Current techniques in bankruptcy prediction. Journal of Accounting Literature, 6, 131-164

Katz, S., S. Lilien & B. Nelson (1985). Stock market behavior around bankruptcy model distress and recovery predictions. Financial Analysts Journal, 41, 70-74

McGurr, P. T. & S. A. DeVaney (1998). Predicting business failure of retail firms: an analysis using mixed industry models. Journal of Business Research, 43, 169-176.

Mossman, C. E., G. G. Bell, L. M. Swartz & H. Turtle (1998). An empirical comparison of bankruptcy models. Financial Review, 33, 35-54.

Ohlson, J. A. (1980) Financial ratios and the probabilistic prediction of bankruptcy. Journal of Accounting Research, 18, 109-131.

Platt, H. D. & M. B. Platt (1990). Development of a class of stable predictive variables: The case of bankruptcy prediction. Journal of Business, Finance and Accounting, 17 (1), 31-51.

Queen, M. & R. Roll (1987). Firm mortality: using market indicators to predict survival. Financial Analysts Journal, 43, 9-26.

SBA. (1999). The facts about small business. Retrieved May 2001 from http://www.sba.gov/lib/library.html.

Shumway, T. (2001). Forecasting bankruptcy more accurately: a simple hazard model. Journal of Business, 74, 101-124.

Simons, K. & S. Cross (1991). Do capital markets predict problems in large commercial banks? New England Economic Review, 51-56.

Zavgren, C. V. (1985). Assessing the vulnerability of failure of American industrial firms: a logistic analysis. Journal of Business, Finance and Accounting, 12, 19-45.

Zavgren, C, V., M. T. Dugan & J. M. Reeve (1988). The association between probabilities of bankruptcy and market responses--a test of market anticipation. Journal of Business, Finance and Accounting, 15 (1), 27-45.

Zmijewski, M. E. (1984). Methodological Issues related to the estimation of financial distress prediction models. Journal of Accounting Research, 22 (Supplement), 59-82.

Yihong He, Monmouth University

Ravindra Kamath, Cleveland State University

Heidi Hylton Meier, Cleveland State University

ENDNOTES

(1.) A study by Edmister (1972) is a notable exception, which solely focused on small firms.

(2.) Some empirical studies concurred that a firm with smaller size was more likely to fail. For example, in the studies of Ohlson (1980) and Shumway (2001), when size was added as a predictor in logit analysis, the smaller firms were found to have a higher probability of failure than the larger firms.

Table 1. Summary of Selected Bankruptcy Prediction Studies

No. Author (Year) Primary Sample Sample Size
 (Note 1) & Data Sources of Failed
 (Note 2) Firms

 Financial-Ratio Based

 1 Beaver (1966) MI 79
 2 Altman (1968) MI 33
 3 Deakin (1972) MI 32
 4 Edmister (1972) SBA 21
 5 Blum (1974) MI 115
 6 Ohlson (1980) WSJ & COMP 105
 7 Zmijewski (1984) WSJ & COMP 81
 8 Zavgren (1985) COMP 45
 9 Platt & Platt (1990) COMP 57
 10 Gilbert (1990) COMP 76
 11 Begley et al. (1996) COMP 165
 12 McGurr & DeVaney (1998) COMP 56

 Market-Measure Based

 13 Beaver (1968) MI 79
 14 Aharony et al. (1980) COMP & CRSP 45
 15 Clark & Weinstein (1983) CRSP 36
 16 Katz et al. (1985) COMP & CRSP 101
 17 Queen & Roll (1987) CRSP Unknown
 18 Zavgren et al. (1988) CRSP 45
 19 Simon & Cross (1991) CRSP 22
 20 Mossman et al. (1998) COMP & CRSP 72
 21 Shumway (2001) WSJ, COMP & 300
 CRSP

No. Author (Year) Sample Independent
 (Note 1) Period Variables Type

 Financial-Ratio Based

 1 Beaver (1966) 1954-1964 Financial Ratios
 2 Altman (1968) 1946-1965 Financial Ratios
 3 Deakin (1972) 1964-1970 Financial Ratios
 4 Edmister (1972) 1954-1969 Financial Ratios
 5 Blum (1974) 1954-1968 Financial Ratios
 6 Ohlson (1980) 1970-1976 Financial Ratios
 7 Zmijewski (1984) 1972-1978 Financial Ratio
 8 Zavgren (1985) 1972-1978 Financial Ratios
 9 Platt & Platt (1990) 1972-1986 Financial Ratios
 10 Gilbert (1990) 1974-1983 Financial Ratios
 11 Begley et al. (1996) 1980-1989 Financial Ratios
 12 McGurr & DeVaney (1998) 1983-1993 Financial Ratios

 Market-Measure Based

 13 Beaver (1968) 1954-1964 Market Data
 14 Aharony et al. (1980) 1970-1978 Market Data
 15 Clark & Weinstein (1983) 1962-1979 Market Data
 16 Katz et al. (1985) 1968-1976 Market Data
 17 Queen & Roll (1987) 1962-1985 Market Data
 18 Zavgren et al. (1988) 1972-1978 Market Data
 19 Simon & Cross (1991) 1981-1987 Market Data
 20 Mossman et al. (1998) 1980-1991 Market & Financial
 21 Shumway (2001) 1962-1992 Market & Financial

No. Author (Year) Statistical Method Validation Type

 Financial-Ratio Based

 1 Beaver (1966) Univariate Cross Validation
 2 Altman (1968) Discriminant Classification
 & Cross validation
 3 Deakin (1972) Discriminant Classification
 & Cross validation
 4 Edmister (1972) Discriminant Classification
 5 Blum (1974) Discriminant Cross validation
 6 Ohlson (1980) Logit Classification
 7 Zmijewski (1984) Probit Classification
 & Cross validation
 8 Zavgren (1985) Logit Classification
 & Prediction
 9 Platt & Platt (1990) Logit Classification &
 Prediction
 10 Gilbert (1990) Logit Classification
 & Cross validation
 11 Begley et al. (1996) Discriminant & Logit Classification
 12 McGurr & DeVaney (1998) Discriminant & Logit Classification

 Market-Measure Based

 13 Beaver (1968) Univariate Classification
 14 Aharony et al. (1980) Univariate Classification
 15 Clark & Weinstein (1983) Univariate No
 16 Katz et al. (1985) Univariate No
 17 Queen & Roll (1987) Univariate & Logit No
 18 Zavgren et al. (1988) Univariate No
 19 Simon & Cross (1991) Univariate No
 20 Mossman et al. (1998) Logit Classification
 21 Shumway (2001) Multi-Period Logit Prediction

No. Author (Year) Years of Validation

 Financial-Ratio Based

 1 Beaver (1966) Five years before
 2 Altman (1968) Five years before
 & One year before
 3 Deakin (1972) Five years before
 & Five years before
 4 Edmister (1972) One year before
 5 Blum (1974) Five years before
 6 Ohlson (1980) One year before
 7 Zmijewski (1984) One year before
 8 Zavgren (1985) Five years before
 & Five years before
 9 Platt & Platt (1990) One year before
 &One year before
 10 Gilbert (1990) One year before
 & One year before
 11 Begley et al. (1996) One year before
 12 McGurr & DeVaney (1998) One year before

 Market-Measure Based

 13 Beaver (1968) Five Years Before
 14 Aharony et al. (1980) Four Years Before
 15 Clark & Weinstein (1983) No
 16 Katz et al. (1985) No
 17 Queen & Roll (1987) No
 18 Zavgren et al. (1988) No
 19 Simon & Cross (1991) No
 20 Mossman et al. (1998) Two Years Before
 21 Shumway (2001) One Year Before

Notes of Table 1:

(1.) The studies of Begley et al. (1996) and Mossman et al. (1998)
applied previous models to new data in a later period. McGurr &
DeVaney (1998) compared prediction performance of several previous
bankruptcy models which were applied to the retailing industry. The
studies of Clark & Weinstein (1983), Katz et al. (1985), Zavgren et
al. (1988), and Simon & Cross (1991) are not considered as the
development of bankruptcy prediction models because these works
only examined the relationship between stock market behavior and
bankruptcy by an event study. Market measures were not used to
predict bankruptcy.

(2.) MI-Moody Industrial Manual; SBA-Small Business Administration;
WSJ-Wall Street Journal; COMP-Compustat Files; CRSP-Center for
Research into Securities Prices Database.

Table 2

Panel A - Descriptive Statistics of Assets
for the Matched Sample ($000)

 N Min Max Mean Std. p-value

Bankrupt firms 158 1278 126926 34230.76 31907.40
Nonbankrupt firms 158 2463 127295 33320.16 29771.99
t-test of size
 difference 0.793

Pane B - Distribution of Matched OTC Firms by Industry

SIC Code (Note) Frequency Percent

1000-1999 18 5.7
2000-2999 42 13.3
3000-3999 134 42.4
4000-4999 16 5.1
5000-5999 54 17.1
7000-7999 26 8.2
8000-8999 20 6.3
9000-9999 6 1.9

Total 316 100

Note: Financial service firms with SIC code of 6000-6999
are excluded from this study.

Panel C - Distribution of Matched OTC Firms by Year of Bankruptcy

Year Frequency Percentage

1990 44 13.9
1991 48 15.2
1992 40 12.7
1993 38 12.0
1994 28 8.7
1995 22 7.1
1996 26 8.2
1997 34 10.8
1998 36 11.4

Total 316 100.0

Table 3. Re-estimation of Ohlson's Model and Variable
Coefficients (N=246; Period: 1990-1996)

 Standard Chi-square
 Coefficient Error Statistics p-value

 1 Year prior to bankruptcy

Constant -4.45 1.14 15.35 .000
NITA -7.62 3.15 5.84 .016
TLTA 7.19 1.63 19.45 .000
WCTA -1.17 1.31 0.80 .371
CLCA -0.22 0.17 1.64 .200
FUTL 0.18 0.41 0.21 .648
CHIN 0.07 0.43 0.02 .880
OENEG 3.42 21.26 0.03 .872
INTWO 2.11 0.71 8.93 .003

Model 222.95 .000

 2 Years prior to bankruptcy

Constant -1.99 1.10 3.28 .070
NITA -7.98 2.28 12.26 .000
TLTA 4.85 1.07 20.41 .000
WCTA -1.75 1.49 1.38 .240
CLCA -0.39 0.63 0.39 .531
FUTL -0.08 0.18 0.21 .651
CHIN 0.44 0.31 2.12 .145
OENEG 3.94 19.59 0.04 .841
INTWO -0.13 0.59 0.05 .827

Model 141.59 .000

 Standard Chi-square
 Coefficient Error Statistics p-value

 3 Years prior to bankruptcy

Constant -3.16 1.01 9.89 .002
NITA -9.92 2.53 15.4 .000
TLTA 4.42 1.07 17.23 .000
WCTA 1.18 1.25 0.89 .345
CLCA 0.73 0.45 2.68 .101
FUTL -0.02 0.15 0.01 .906
CHIN 0.12 0.29 0.17 .682
OENEG 4.50 18.11 0.06 .804
INTWO -0.28 0.54 0.28 .598

Model 124.97 0

Table 4. Re-estimation of Shumway's Model and Variable
Coefficients (N=246; Period: 1990-1996)

 Chi-square
 Coefficient Standard Statistics p-value

 1 Year prior to bankruptcy

Constant -5.67 0.96 35.05 .000
NITA -7.47 2.35 10.09 .001
TLTA 5.05 1.30 15.06 .000
ERR -2.28 0.58 15.37 .000
SDR 12.42 3.17 15.39 .000

Model 237.02 .000

 2 Years prior to bankruptcy

Constant -3.87 0.63 38.29 .000
NITA -5.74 1.42 16.4 .000
TLTA 5.17 0.95 29.74 .000
ERR -1.21 0.36 11.14 .001
SDR 5.76 1.92 8.96 .003

Model 152.25 .000

 Standard Chi-square
 Coefficient Error Statistics p-value

 3 Years prior to bankruptcy

Constant -3.06 0.58 28.21 .000
NITA -7.29 1.68 18.82 .001
TLTA 4.02 0.81 24.73 .000
ERR -0.97 0.34 7.98 .005
SDR 5.83 2.21 6.99 .008

Model 125.84 .000

Table 5. Elasticity of Predictive Variables from
the Shumway Model (N=246; Period: 1990-1996)

 Mean of
 Coefficient Mean Probability Elasticity

 1 year prior to bankruptcy

NITA -7.47 -0.17 0.5 0.63
TLTA 5.05 0.63 0.5 1.51
ERR -2.28 -0.08 0.5 0.10
SDR 12.42 0.19 0.5 1.18

 Coefficient Mean Mean of Elasticity
 Probability

 2 years prior to bankruptcy

NITA -5.74 -0.16 0.5 0.45
TLTA 5.17 0.57 0.5 1.47
ERR -1.21 0.02 0.5 -0.01
SDR 5.76 0.18 0.5 0.51

 3 years prior to bankruptcy

NITA -7.29 -0.06 0.5 0.22
TLTA 4.02 0.51 0.5 1.03
ERR -0.97 0.34 0.5 -0.04
SDR 5.83 2.21 0.5 0.52

Table 6. Results of Classification (N=246; Period: 1990-1996)

1. Ohlson's Model

 Actual Status Total No. Classified Status
 (Note) of Samples.
 B NB

Year 1 B 123 108 15
 NB 123 9 114
Year 2 B 123 98 25
 NB 123 22 101
Year 3 B 123 94 29
 NB 123 25 98

2. Shumway's Model

 Actual Status Total No. Classified Status
 of Samples.
 B NB

Year 1 B 123 113 10
 NB 123 10 113
Year 2 B 123 102 21
 NB 123 21 102
Year 3 B 123 98 25
 NB 123 24 99

Note:

1) B-bankrupt firms; NB-nonbankrupt firms

2) Cutoff value = 0.5

Table 7. Classification Rates of Errors and Overall Accuracy
(N=246; Period: 1990-1996)

1. Ohlson's Model

(Note) Year 1 Year 2 Year 3

Type I error 12% 20% 24%
Type II error 7% 18% 20%
Total error 10% 19% 22%
Overall accuracy of classification 90% 81% 78%

2. Shumway's Model

 Year 1 Year 2 Year 3

Type I error 8% 17% 20%
Type II error 8% 17% 20%
Total error 8% 17% 20%
Overall accuracy of classification 92% 83% 80%

Note: 1) Type I error = misclassification of bankrupt firms

2) Type II error= misclassification of nonbankrupt firms.

3) Cutoff value = 0.5

Table 8. Results of Prediction (N=70; Period: 1997-1998)

1. Ohlson's Model

 Actual Status Total No. of Classified Status
 (Note) the Sample
 B NB

Year 1 B 35 29 6
 NB 35 6 29
Year 2 B 35 25 10
 NB 35 7 28
Year 3 B 35 24 11
 NB 35 6 29

2. Shumway's Model

 Actual Status Total No. of Classified Status
 (Note) the Sample
 B NB

Year 1 B 35 34 1
 NB 35 2 33
Year 2 B 35 22 13
 NB 35 3 32
Year 3 B 35 24 11
 NB 35 7 28

Note:

1) B-bankrupt firms; NB-nonbankrupt firms

2) Cutoff value = 0.5

Table 9. Prediction Rates of Errors and Overall Accuracy
(N=70; Period: 1997-1998)

1. Ohlson's Model

(Note) Year 1 Year 2 Year 3

Type I error 17% 19% 31%
Type II error 17% 20% 17%
Total error 17% 24% 24%
Overall accuracy of prediction 83% 76% 76%

2. Shumway's Model

 Year 1 Year 2 Year 3

Type I error 3% 37% 31%
Type II error 6% 9% 20%
Total error 4% 23% 26%
Overall accuracy of prediction 96% 77% 74%

Note: 1) Type I error = misclassification of bankrupt firms

2) Type II error= misclassification of nonbankrupt firms.

3) Cutoff value = 0.5