A hybrid bankruptcy prediction model with dynamic ...

Journal of Empirical Finance 17 (2010) 818–833

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Journal of Empirical Finance j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j e m p f i n

A hybrid bankruptcy prediction model with dynamic loadings on accounting-ratio-based and market-based information: A binary quantile regression approach Ming-Yuan Leon Li a,1, Peter Miu b,⁎ a Department of Accountancy and Graduate Institute of Finance and Banking, College of Management, National Cheng Kung University, No. 1, University Rd., Tainan, Taiwan b DeGroote School of Business, McMaster University, 1280 Main Street West, Hamilton, ON, Canada L8S 4M4

a r t i c l e

i n f o

Article history: Received 23 April 2009 Received in revised form 24 March 2010 Accepted 2 April 2010 Available online 18 April 2010 JEL classification: G33 C51

Keywords: Binary quantile regression z-score Distance-to-default Bankruptcy

a b s t r a c t While using the binary quantile regression (BQR) model, we establish a hybrid bankruptcy prediction model with dynamic loadings for both the accounting-ratio-based and marketbased information. Using the proposed model, we conduct an empirical study on a dataset comprising of default events during the period from 1996 to 2006. In this study, those firms experienced bankruptcy/liquidation events as defined by the Compustat database are classified as “defaulted” firms, whereas all other firms listed in the Fortune 500 with over a B-rating during the same time period are identified as “survived” firms. The empirical findings of this study are consistent with the following notions. The distance-to-default (DD) variable derived from the market-based model is statistically significant in explaining the observed default events, particularly of those firms with relatively poor credit quality (i.e., high credit risk). Conversely, the z-score obtained with the accounting-ratio-based approach is statistically significant in predicting bankruptcies of firms of relatively good credit quality (i.e., low credit risk). In-sample and out-of-sample bankruptcy prediction tests demonstrated the superior performance of utilizing dynamic loadings rather than constant loadings derived by the conventional logit model. © 2010 Elsevier B.V. All rights reserved.

1. Introduction The difficulty in predicting corporate failure has posed a long standing problem in credit risk research. The most famous credit risk model is Altman's (1968) z-score model, which employs accounting-ratio-based information in determining and quantifying how the probability of default and a set of financial ratios are related. The Altman's z-score model relies mostly on information obtained from companies' financial statements; whereas a different approach is based on the work by Merton (1974) which suggests that one can use a company's debt ratio together with its asset value volatility to predict its default probability.2 This market-based approach serves as the building block of a number of credit risk models commonly used in practice (e.g. that of Moody's KMV). This study differs from previous related works by offering a new perspective on the link between Altman's and Merton's models. In particular, this study explores the effectiveness of a hybrid model, in which information from both accounting-ratio-

⁎ Corresponding author. Tel.: +1 905 525 9140x23981. E-mail addresses: [email protected] (M.-Y.L. Li), [email protected] (P. Miu). 1 Tel.: +886 6 2757575x53421; fax: +886 6 2744104. 2 In particular, Merton (1974) considers that holding the debt of a risky company is equivalent to holding the debt of a risk-free company plus being short a put option on the assets of the company. The put option arises because if the value of the assets falls below the value of the debt, the shareholders can put the assets to debt holders, and in return, receive the right not to repay the full amount of the debt. In this analogy, the underlying for the put option is the company assets, and the strike price is the amount of debt. 0927-5398/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jempfin.2010.04.004

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based and market-based approaches is incorporated. This approach merits detailed study. In combining the two sets of information in a hybrid model, we may enhance the predictive power of a company's default event if both the accounting-ratio variables involved in Altman's model and the equity-based information obtained with Merton's model convey company-specific credit risk information that is not subsumed by each other.3 In establishing a hybrid model, one key issue is the determination of the optimal “loading” for each of the two types of information when they are incorporated in the model. In this study, we examine a bankruptcy prediction model utilizing dynamic loadings established by the binary quantile regression (BQR). It can be considered as a generalized version of those hybrid models with static loadings, which have been examined in previous studies. Our ideas are presented below. Typically, in developing a credit risk model, financial institutions conduct statistical analyses with the historical data of various characteristics of both the defaulted and survived borrowers and their loans. The loading for each borrower/loan characteristic is estimated by ensuring the observed default events could be best explained. Using the vector of calibrated loadings, financial institutions can therefore decide on whether to approve or reject a loan application by knowing the borrower's characteristics which can in turn be used in assessing her credit quality and default probability. A key question addressed in this study is whether the optimal loading of each borrower/loan characteristics is different between good and poor credit quality companies. If they are different, should banks attach more weight to accounting-ratio-based content or marketbased information when poor credit quality companies are concerned? Such dynamic assignment of loadings may enhance the overall predictive power of the credit risk model over loan portfolios of different credit qualities. A number of studies have pointed out that investors and financial institutions rarely opt for only one approach, but rather combine different sources of information in arriving at their own credit risk assessments. In particular, most closely related is the research by Miller (1998), Kealhofer and Kurbat (2001), Kealhofer (2003), Löffler (2007) and Mitchell and Roy (2008). Except for the findings of Kealhofer and Kurbat (2001), these studies conclude that combining various failure prediction models improves the prediction of default over the use of a single measure.4 However, in determining the weights to be assigned to the various default prediction techniques, these studies either employ the straightforward logit regression or use some subjective combination rules.5 The predictive power of these hybrid models is potentially limited owing to the use of a constant or an exogenously imposed loading for each credit score or specific ranges of each credit score. In practice, financial institutions recognize the benefits of adopting a risk rating system which allows for different weighting schemes for different credit portfolios. For example, given that market-based information is more readily available and thus more reliable for large corporate borrowers than mid-market ones, banks tend to attach a heavier weight to market-based information when they assess the credit risks of the former than the latter. However, any such segmentations are likely to be exogenously imposed (e.g. by size, geography, etc.) rather than driven by statistical analyses with the objective of ensuring minimal default prediction errors. Unlike previous studies, we are one of the first to employ dynamic loadings in a bankruptcy prediction model of which not only the magnitudes of the loadings but also their applicability over the population of interest are endogenously determined. By utilizing dynamic loadings established by BQR, we allow the data to reveal to us the implicit segmentations that can ensure the least prediction errors over the whole dataset. In this setup, the segmentations and the optimal loadings on the credit-related explanatory variables are jointly determined. Specifically, we consider a BQR model in which these loadings vary with the quantile levels of credit risks of the borrowers.6 We also conduct an empirical study to demonstrate the benefit of our proposed dynamic model in explaining the observed default events in comparison with an alternative hybrid model utilizing constant loadings.7 The rest of this paper is organized as follows. Section 2 presents the literature review. In Section 3, we describe the hybrid credit risk models used in this study, including (1) the setting with constant loadings generated by the conventional logit regression, and (2) the setting with dynamic loadings under the BQR model. The model evaluation methods are defined in Section 4. Section 5 presents the data sources and empirical results. Finally, a few concluding remarks are made in Section 6.

2. Literature review Under the regulatory capital requirements of Basel II, banks are allowed to develop their own credit risk models in adopting the internal ratings-based approach in determining the capital charges with respect to the credit risks of their portfolios. Research in this area has generated considerable interest. In this study, we examine how accounting-ratio-based and market-based information may be used in a joint fashion in implementing such models.

3

In practice, financial institutions typically use both types of information in assessing the credit quality of their corporate clients in their risk raking systems. Kealhofer and Kurbat (2001) examine the default prediction power of Merton's approach relative to expert debt ratings and accounting variables and show that agency credit ratings have no incremental value for default prediction. 5 For example, a subjective combination rule is specified under the standardized approach of Basel II. It specifies that banks working with two credit ratings must assign the higher (i.e., maximum) risk assessments to its borrowers; whereas banks working with three credit ratings or more must use the highest of the two lowest risk assessments (see Basel Committee, 2006). 6 In this study, the credit risk quantile of a borrower is defined as the percentage of borrowers which are expected to have a lower credit risk (based on the credit model) than the borrower being considered. 7 Unlike Löffler (2007) in which separate loadings are estimated for companies with low vs. high credit score being subjectively defined based on, for example, their Moody's ratings, we let the data reveal the optimal segmentation based on the interaction of all the explanatory variables and the observed default events utilizing BQR. We believe our approach is more flexible and thus can ensure our conclusions to be more robust to any potential misclassification errors. 4

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Accounting-ratio-based models are typically built by using a set of accounting-ratio variables. The most famous of such models is Altman's z-score. Following Altman's (1968) study, Mensah (1984) indicates that the past performance involved in a firm's accounting statements may not be informative in predicting the future, and thus suggests that it is necessary to regenerate the accounting-ratio-based models periodically. Hillegeist et al. (2004) argue that the ability of accounting information in predicting bankruptcy is likely to be limited given the fact that they are formulated to describe the financial condition of the company under the “going-concern” principle (i.e., assuming it will not go bankrupt). Based on the criticisms of accounting-ratio-based models, market-based models are proposed by Black and Scholes (1973) and Merton (1974). It is claimed that market prices reflect future expected cash flows, and thus should be more useful in predicting bankruptcy. Market-based models are further examined by a number of studies, including Hillegeist et al. (2004), Reisz and Perlich (2004), Vassalou and Xing (2004) and Campbell et al. (2006), in assessing default probability. Research comparing market-based and accounting-ratio-based bankruptcy prediction models has also been conducted. Although Altman's (1968) z-score model may suffer from a lack of theoretical underpinning, the validity of Merton's model is also limited by a number of stringent assumptions (see for example Saunders and Allen, 2002). It is therefore not surprising that the empirical evidence on the relative performance of market-based against accounting-ratio-based models is mixed (see Kealhofer, 2003; Oderda et al., 2003; Hillegeist et al., 2004; Reisz and Perlich, 2004; Stein, 2005; Campbell et al., 2006; Blochlinger and Leippold, 2006 and Agarwal and Taffler, 2008). Even if one model is superior to the other, it does not imply that the inferior model should be neglected altogether. It may be possible to combine the two models to form an even better one (see Miller, 1998; Kealhofer and Kurbat, 2001; Kealhofer, 2003; Löffler, 2007; Mitchell and Roy, 2008). This study claims that both accounting-ratio-based and market-based information should be valuable for bankruptcy prediction. Both types of information are considered as credit risk indicators and are utilized simultaneously in explaining the probability of default. Notably, the weights assigned to the two types of credit risk information could change according to the level of credit risk. Specifically, by using BQR, we establish a hybrid credit risk model with dynamics loadings. We judge the performance of the proposed model by comparing it with that of the conventional logit model with uniform loadings. There is a rapidly expanding empirical literature on quantile regression (QR) in both economics and finance. For example: Chamberlain (1994) and Buchinsky (1994, 1997) on wage effects; Conley and Galenson (1998) and Gosling et al. (2000) dealing with earnings inequality and mobility; Taylor (1999), Engle and Manganelli (1999), Chernozhukov and Umantsev (2001), and Bassett and Chen (2001) on value at risk. Kordas (2006) extends the maximum score estimation method introduced by Manski (1975, 1985) to establish the BQR model for binary data. In this study, we borrow the BQR technique in developing a dynamic hybrid model of credit risk. It is flexible enough to capture any non-uniform relation between the probability of default and the explanatory variables. Besides, unlike conventional hybrid credit risk model, it allows for the segmentation of the data together with the corresponding factor loadings to be endogenously determined. Specifically, we implement a BQR model in which the optimal loadings vary with the inherent default risks of the borrowers. 3. Model specifications 3.1. Accounting-ratio-based and market-based information 3.1.1. Altman's z-score (accounting-ratio-based information) To capture the accounting-ratio-based information, the widely used z-score variable derived by Altman (1968) is adopted in this study. Specifically, a firm's z-score is calculated as follows: z = 1:2x1 + 1:4x2 + 3:3x3 + 0:6x4 + 1:0x5

x1 x2 x3 x4 x5

ð1Þ

= working capital / total assets = retained earnings / total assets = earnings before interest and taxes / total assets = market value of equity / total assets = sales / total assets

We adopt the z-score equation exactly as it was proposed by Altman (1968). Specifically, we use the same numerical values of the weights of the financial ratios as obtained by Altman.8 One might argue that banks adopting Altman's approach should recalibrate the equation against the default experiences of their own credit portfolios to achieve the highest goodness-of-fit.9 Given the fact that the focus of this study is to compare the importance of the accounting-ratio-based and market-based information rather than to pursue the best credit risk model, we do not recalibrate the weights in this analysis. 8

In practice, some banks also use the z-score equation exactly as it was proposed by Altman in their risk rating systems. For example, an optimal set of weights can be obtained by maximizing the difference between the average score of those borrowers that later default and the average score of those that do not. 9

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3.1.2. Distance-to-default (market-based information) The distance-to-default (DD) variable derived from Merton's model is employed to capture the market-based information. The DD of a firm can be computed by knowing both the current level and volatility of its market equity value. The calculation of DD is detailed below. If we assume a company's asset value (A1) at the end of the year follows a normal distribution with a mean equals to the current asset value (A0) and a standard deviation equals to σA, the probability of default (i.e., its equity value, E1, becomes equal to or less than zero) is simply:

 A −D E PrðE1 ≤0Þ = Φ − 0 =Φ − 0 ð2Þ σA σA where E0 and D are respectively the current equity value and the constant level of debt; whereas Φ(•) is the cumulative normal probability function.10 The ratio E0/σA is referred as the distance-to-default (DD). From Eq. (2), the higher (lower) the level of the current equity value (the volatility of asset value), the larger the value of DD, and thus the lower the probability of default. Given that a company's asset value is difficult to be observed directly, we use the volatility of equity value (σE) as a proxy of the volatility of asset value (σA) in this study.11 Equity value is readily available for publicly traded companies, and it reflects the market's collective opinion of the prospect of its business. We estimate E0 by computing the mean value of equity over a quarterly period. The standard deviation (σE) of equity values are also estimated using daily data observed during that quarter. The DD is therefore a function of both the mean and standard deviation of the equity value over that quarter. At the end of each quarter, the two parameters are updated with the most recent market information. 3.2. Hybrid model with constant loadings Intuitively, information for both accounting-ratio-based z-score and market-based DD could be captured by conducting a regression in which both the z-score and DD are used as explanatory variables. Similar to many other studies (e.g. that of Löffler, 2007), we first consider the conventional logit regression model in establishing the hybrid bankruptcy prediction model with constant loadings. In particular, we first denote the credit risk of company i by a single number y⁎i (i.e., a credit score), which can be expressed as a weighted sum of a number of observable variables of the loan applicant. 0 * yi = xi ⋅β + ui ð3Þ where xi is the a (K × 1) vector of explanatory variables of y⁎i and β is an (K × 1) unknown vector of parameters (i.e. “loadings”) to be estimated. Notably, y⁎i is an unobservable latent variable. What we observe is a dummy variable yi which is defined as: yi = 1 if y⁎i N 0 (i.e., company i defaults); otherwise, yi = 0 (i.e., company i does not default). The default probability for company i is thus defined as: 0

Pi = Pðyi = 1 jxi Þ = Pðxi ⋅β + ui N 0Þ = Pðui N −xi ⋅βÞ

ð4Þ

Assuming the distribution of ui is symmetric, we can write: Pi = Fðxi ⋅βÞ

ð5Þ

where F is the cumulative distribution function of ui. Subsequently, if the cumulative distribution of ui is logistic, we have what is known as the logit model and default probability becomes12: Pi = pðyi = 1jxi Þ =

1 0

1 + e−xi ⋅β

ð6Þ

To create the best model, we want to find the set of weights that produces the best fit between Pi and the observed default events. Specifically, we would like Pi to be close to 100% for those companies that eventually default, whereas close to 0% for those who do not. In the subsequent analysis, we estimate the optimal weights by using maximum likelihood estimation (MLE).13 To capture both the accounting-ratio-based and market-based information, this study adopts a regression model in which both the z-score and DD variables are used as the explanatory variables for y⁎i. We use the model specification of Eq. (3) to denote a 10

The second equality of Eq. (2) is based on the assumption that the value of assets equals to the value of debt plus that of equity. In the literature, different formulations of the distance-to-default have been proposed and implemented. Since the objective of this study is to compare the significances of the accounting-ratio-based and market-based information rather than to pursue the best credit risk model, we adopt a basic formulation based on the original Merton's model which can be implemented relatively easily. Besides, we simply consider the volatility of equity value as a direct substitute for the volatility of asset value. One could have theoretically established the relation between the two volatilities based on certain assumptions. For example, in deriving DD for computing a company's expected default frequency, Moody's KMV derives the volatility of asset value from the observed volatility of equity value via a transformation utilizing information like the debt value of the company. 12 If ui follows a normal distribution, we have the probit model. 13 The MLE method is well documented in the literature, and therefore this study omits any detailed discussion of it. 11

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hybrid model with constant weights, which has been commonly used in previous related research. Such a specification is potentially restrictive owing to the use of constant loadings for the explanatory variables. For example, in adopting this model, we assume that the sensitivities (i.e., β) of default risk to the explanatory variables are identical for all companies, disregarding whether they are of good or poor credit quality. 3.3. Hybrid model with dynamic loadings To resolve the potential shortcoming of the restriction of constant loadings on the z-score and DD variables, this study adopts the BQR technique in establishing the following hybrid model with dynamic loadings. 0 * yi = xi ⋅βθ + uθi

ð7Þ

0 * Quantθ ðyi jxi Þ≡inf fy* : Fi ðy* jxÞθg = xi ⋅βθ

ð8Þ

Quantθ ðuθi jxi Þ = 0

ð9Þ

where Quantθ(y⁎i |xi) denotes the θth conditional quantile of y⁎i on the regressor vector xi; βθ is the unknown vector of parameters to be estimated for different values of θ in (0,1); uθi is the error term which follows a continuously differentiable cumulative density function Fuθ(.|x) and a density function fuθ(.|x).14 The value Fi(.|x) denotes the conditional distribution of y⁎ given x. Varying the value of θ from 0 to 1 reveals the entire distribution of y⁎ conditional on x. Using the score function method proposed by Manski (1975, 1985), the estimator for βθ is obtained from: argmin

N

βθ

−1

N

0

∑ ρθ ðyi −Ifxi ⋅βθ ≥0gÞ

ð10Þ

i=1

where yi is the observable status of company i (yi = 1 if default; yi = 0 if not default), N is the number of observations, I{·} is the indicator function, and ρθ(v) ≡ [θ− I{v b 0}]·v is the asymmetric absolute loss function of Koenker and Bassett (1978). We estimate the BQR model using the simulated annealing algorithm of Corana et al. (1987) and Goffe et al. (1994). The standard errors of estimates are obtained via bootstrapping method.15 One feature of the BQR model used in this study is the ability to trace the entire distribution of the dependent variable (y⁎) conditional on the independent variable (x). In particular, comparing Eq. (7) with Eq. (3) reveals a key feature of BQR technique: the estimator vector of βθ varies with θ. We can therefore examine the variation of the dynamic loading vector (βθ), at different quantile levels of credit risk (y⁎). In the following discussion, the model specifications of Eq. (7) are applied to a hybrid credit risk model with dynamic loadings. The default probability generated by the BQR model is detailed below. First, according to the definition of the binary response model, the probability of the event {yi = 1} is presented as: 0

Pi = pðyi = 1jxi Þ = ∫Ifxi β + ui ≥0gdFui j xi

ð11Þ

where Fui|xi is the distribution of ui conditional on xi. Subsequently, we rewrite Eq. (11) as: 1

0

Pi = ∫0 Ifxi βθ ≥0gdθ

ð12Þ

which gives the probability of success as a function of the quantile process βθ, θ 2 (0, 1). In this study, we establish the bankruptcy prediction model with dynamic loadings over nineteen quantile levels: 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90 and 0.95, and thus nineteen sets of loadings are estimated. In this setup, we can simplify Eq. (12) as: 1 0:95 0 ∑ Ifx β = jjβθ jj≥0g 19 θ = 0:05 i θ where ||.|| denotes the Euclidean norm and βθ/||βθ|| are the normalized coefficients. Pi =

ð13Þ

4. Model evaluation approaches To compare the performances of alternative bankruptcy prediction models, we draw the cumulative accuracy profiles (CAP) and operating characteristic (ROC) curves, together with computing the respective accuracy ratios.16 14 Following Kordas (2006), the conditional errors in the BQR model are assumed to be independently and identically distributed (i.i.d.). Under i.i.d. errors, Kordas (2006) have defined the BQR estimator and proved its consistency and asymptotic normality. 15 In Appendix A, we outline the methodology of estimating the standard errors via bootstrapping. The program codes (in version 6.1 of S-plus) used in the computations are available (upon request) from the authors. 16 The CAP and ROC curves are commonly-used techniques for assessing the discriminatory power of risk rating methodologies.

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4.1. CAP curve To plot the CAP curve, we first rank companies by their default probabilities (i.e., credit scores) as predicted by the model, from highest to lowest. Then, out of those companies with a score higher than a value such that altogether they represent x% of the total number of companies, we record the corresponding number of defaulted companies being captured as a percentage (y%) of total number of defaulted companies. The CAP curve can then be traced out by varying x from 0 to 100 and plotting the corresponding values of x and y along and the x-axis and y-axis, respectively. Fig. 1 shows an example of a CAP plot. Using a good model will result in a majority of the defaulters having relatively high default probability estimates and so the percentage of defaulters being captured (the y values in Fig. 1) increases quickly as one moves down the sorted sample of all companies (the x values in Fig. 1). If the model were totally uninformative, for example, by assigning default probabilities randomly, we would expect to capture a proportional fraction (i.e., x% of the defaulters with about x% of the observations), resulting in a CAP curve along the 45-degree line (i.e., the “Random CAP” curve of Fig. 1). A perfect model would produce the “Ideal CAP” curve, which consists of a straight line capturing 100% of the defaults within a fraction of the population equal to the default rate of the sample. While CAP plots are a convenient way to visualize the model performance, it will be even more convenient if we can summarize the predictive accuracy of the model in a single statistic. One such statistic is the accuracy ratio derived from the CAP curve: Accuracy ratio by CAP curve = ðthe area under a model’s CAP Þ = ðthe area under the ideal CAP Þ The higher the accuracy ratio, the better the predictive power of the model. 4.2. ROC curve The ROC curve is constructed by varying the cutoff probability. In particular, for every cutoff probability, the ROC curve defines the “true positive rate” (percentage of defaults that the model correctly classifies as defaults) on the y-axis as a function of the corresponding “false positive rate” (percentage of non-defaults that are mistakenly classified as defaults) on the x-axis.17 As shown in Fig. 2, the ROC curve of a constant or entirely random prediction model corresponds to the 45-degree line, whereas a perfect model will have a ROC curve that goes straight up from (0, 0) to (0, 1) and then across to (1, 1). Given two models, the one with better performance will display a ROC curve that is further to the top left of Fig. 2 than the other. The accuracy ratio of a model obtained with the ROC curve is defined as the area under its ROC curve, i.e.: Accuracy ratio by ROC curve = 2 × ðarea under a model’s ROC curve−0:5Þ It must be noted that a model with perfect performance has an accuracy ratio of one (all defaulting firms are assigned a larger probability of bankruptcy than any surviving firms), whereas a model with constant or random predictions has an accuracy ratio of 0. In general, models with higher accuracy ratios exhibit better performance on bankruptcy prediction. 5. Empirical results 5.1. Data Our sample of failed (i.e., defaulted) firms consists of the firms encountering bankruptcy or liquidation events as defined by the Compustat database over the period from 1996 Q2 to 2006 Q4.18 It consists of a total of 73 failed firms.19 To ensure our sample of non-failed firms is of comparable size, we only consider a relatively small fraction of all the non-failed firms in Compustat database.20 Specifically, we select those non-failed firms in the Compustat database which are also Fortune 500 firms with a Brating or higher during the same time period as our sample of non-failed firms.21 This gives us a total of 138 firms in our sample of

17 For example, if the cutoff is equal to 10%, a firm of which the expected probability of default exceeds 10% is predicted to be a defaulted firm by the model, whereas a firm of which the expected probability of default is less than 10% is predicted to be a non-defaulted firm. The “true positive rate” and “false positive rate” are then computed by expressing the number of correctly and incorrectly predicted defaulters respectively as percentages of the total numbers of defaulted and non-defaulted firms being realized. 18 We do not consider a very long sample period because we are assuming the loadings of z-score and DD are constant throughout the sample period. This assumption will become less valid if we consider a sample which spans over an extended time period. We do not want our findings to be affected by the potential violation of this assumption of time consistency. 19 The list of all 73 failed companies selected for this study is given in Appendix B. 20 Some previous studies (e.g. Altman, 1968) also consider balanced samples of failed and non-failed firms. Using samples of comparable sizes in this study ensures that similar weights are assigned to these two types of firms in examining the explanatory powers of z-score and DD. It therefore enhances our ability in detecting any difference in the predictive power of alternative default risk models. 21 Using firms listed in the Fortune 500, which are arguably of relatively better credit quality, as our non-failed firms ensures our samples of failed and nonfailed firms are very different from each other in terms of their credit qualities. Fortune 500 firms with B-rating or higher are deemed to be of good financial health and far from experiencing any distressed conditions. The discriminatory power of the models examined in this study could therefore be enhanced, thus enabling us to achieve a more refined comparison of the performances of alternative models. Focusing on Fortune 500 firms also ensures the qualities of the stock price and financial statement information used in computing z-score and DD in this study.

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Fig. 1. Illustrations of CAP curves.

non-failed firms. Financial firms are excluded from both samples. During the sample period, we collected a total of 1329 and 4959 observations of quarterly financial data of the above samples of failed and non-failed firms respectively. Equity values and financial statement information are obtained from the CRSP and Compustat databases. Table 1 presents the average values of the z-score and DD. Comparing the values of failed firms against non-failed firms, the z-score and DD values of the latter are considerably higher than those of the former.

5.2. Model estimation results: Constant loadings versus dynamic loadings Table 2 presents the estimation results of the hybrid model with constant loadings derived by the logit regression model. Using the 5% significance level as a criterion, the coefficients of both the z-score and DD are significantly negative.22 This result indicates that as a company's z-score and DD increases, it is less likely to go bankrupt. Although the two estimates are significant and have the expected sign, this hybrid model derived by the conventional logit regression approach does not allow for the impact of z-score and DD variables to differ between good and poor quality companies. In Table 3, we report the estimation results of the hybrid model with dynamic loadings derived by the BQR model. The negative values of the point estimates together with their respective 95% confidence intervals are plotted in Figs. 3 and 4. This model allows for the loadings of the z-score and DD to assume different values based on the quantile levels of credit risk. Specifically, we estimate the loadings at nineteen different quantile levels: 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90 and 0.95. First, let us examine the conditional quantile estimates for the loadings of the z-score in credit risk prediction. As expected, the z-score variable has a negative loading at each quantile level being considered. The coefficients are however of different magnitude and degree of statistical significance. In particular, except for the 0.25 quantile, the loadings on the z-score are found to be statistically significant at the 5% level for all of the low quantile levels below or equal to 0.60. The loadings however become insignificant at higher quantile levels from 0.65 to 0.95. Moreover, as shown in Fig. 3, the magnitudes of the z-score loading estimates change dramatically across the quantiles.23 In particular, when moving up the quantile levels, the magnitude decreases considerably and eventually approaches zero at the quantile levels of 0.85, 0.90 and 0.95. These results suggest that the accounting-ratio-based information, such as the z-score, is more useful in predicting bankruptcy of those companies of relatively better credit quality (i.e., low quantile level). The ability of the z-score in predicting bankruptcy of poor quality companies (i.e., high quantile level) is however neither statistically nor economically significant.24 The above findings require some intuitive elucidation. First, accounting fraud is potentially involved in poor quality companies and hence their z-scores (computed based on their financial statements) are more likely to be unreliable. Second, we actually do not expect the sensitivity of default probability to accounting ratios is uniform across companies of different 22

One-period lag z-score and DD variables are employed as explanatory variables for firm bankruptcy prediction. As expected, the point estimates of the loadings of z-score and DD variables are negative at each quantile level being considered. In Fig. 3, for illustrative purpose, we present the negative of these negative values. That is, Fig. 3 presents the magnitudes of the point estimates of these loadings. 24 The estimated loadings of the z-score variable become insignificant in the higher quantiles from 0.65 to 0.95 (i.e., their 95% confidence intervals overlap the value of zero in Fig. 3). 23

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Fig. 2. Illustrations of ROC curves.

credit qualities.25 Let us take EBIT/Assets ratio (which is one of the five accounting ratios used in formulating the z-score) as an example. Theoretically, it is negatively related to the company's default probability. Whereas Company X having a EBIT/Assets ratio of 5% could have a much lower probability of default than Company Y having a − 5% EBIT/Assets ratio, the difference between the probability of default of the above Company Y and another Company Z having a ratio of − 15% might not be as significant. Given their negative EBIT/Assets ratios, the default risks of both Company Y and Z are likely to be high, thus belonging to the high quantiles of the BQR regression. The fact that Company Y has a less negative EBIT/Assets ratio than Company Z does not necessarily suggest that it is in a much better financial position to avoid a potential bankruptcy event. Consequently, the negative relation between EBIT/Assets and default probability could be disappearing for the high quantile levels (as illustrated in Fig. 3). Next, the coefficients of the DD variables, as shown in Table 3, are significantly negative at the 5% level for most of the higher quantile levels (the loading of the 0.80 quantile is statistically significant at 10% level); whereas they become insignificant at the three lower quantiles, namely 0.05, 0.10 and 0.25 (i.e., as shown in Fig. 4, their 95% confidence intervals overlap the value of zero). The magnitudes of the DD loadings tend to be increasing with the quantile levels. The average magnitude of the DD loadings of the lowest 6 quantiles is 0.12; whereas that of the highest 6 quantiles being 0.16. This increasing trend of the magnitude of the DD loadings is consistent with the implications of the Merton's model. In particular, under the assumption of normally distributed asset value, the probability of default is equal to Φ(−DD), as presented in Eq. (2). Given this functional relation, the magnitude of the rate of change of probability of default with respect to DD increases as DD decreases. We therefore expect the magnitude of the DD loading increases with the quantile level. In Fig. 5, we plot the negative values of the rates of changes of probabilities of default implied by Merton's model over the range of probabilities of default from 2% to 20%. The magnitudes of the point estimates of the DD loadings, which are also plotted on Fig. 5, tend to vary with the quantile levels in a similar increasing trend. The constant loading model as depicted in Eq. (3) is likely to be too restrictive in capturing this non-uniform relation between DD and the probability of default. To summarize, two hybrid models using both the z-score and DD variables have been examined. In the first model (defined by Eq. (3)), we impose constant weights on the two variables and thus disregard the possibility that credit risk prediction might be more reliable with market-based variables than with accounting-ratio-based information in certain conditions, and vice versa. In the second hybrid model (defined by Eq. (7)), we adopt the BQR technique to allow the loadings of the z-score and DD variables to differ among companies of different credit risks. Our empirical findings suggest that creditors should decrease (increase) the loading of the accounting-ratio-based z-score while increase (decrease) the loading of the market-based DD when they appraise companies which are perceived to be of higher (lower) credit risk.26

25

The relation between default probability and accounting ratios might not even be monotonic. Our findings suggest that the magnitude of the loading |βz,θ| (|βDD,θ|) decreases (increases) when the quantile level θ increases. However, the products |βz,θ| × z-scoreθ and |βDD,θ| × DDθ should both be decreasing when we move up the quantile level. Note that, the lower the values of the z-score and DD, the higher is the default risk of the firm (i.e. belonging to a higher quantile). Our findings therefore suggest the diminishing effect of DD as a default risk indicator when DDθ decreases in value is partially offset by an increasing value of |βDD,θ| as we move up the quantile level. Our BQR approach enriches the modeling of default risk by allowing for the capturing of this non-linear effect which cannot be modeled under a constant loading model. The authors acknowledge the anonymous reviewer for this comment. 26

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Table 1 Average values of z-score and DD: failed firms versus non-failed firms.

Altman's z-score DD (distance-to-default)

Failed firms

Non-failed firms

− 9.46 3.08

7.25 22.90

Failed firms are those which experienced bankruptcy/liquidation events as defined by the Compustat database over the period from 1996 Q2 to 2006 Q4. Firms listed in the Fortune 500 with at least a B-rating during the same time period are classified as non-failed. Financial firms are excluded from the sample. The overall sample consists of a total of 74 failed and 138 non-failed firms. During the sample period, we collected a total of 1329 and 4959 observations of quarterly financial data of the above samples of failed and non-failed firms respectively. The average values of the z-score and DD of non-failed firms are considerably higher than those of failed firms.

5.3. Bankruptcy prediction tests of alternative risk models The above empirical results have showed how the loadings of accounting-ratio-based and market-based information change according to the credit quality of companies. Specifically, our results indicate that creditors should pay more attention to the market-based information when assessing a firm with higher credit risk. In contrast, for a firm with lower credit risk, the accounting-ratio-based z-score deserves more attention as a bankruptcy prediction variable. The loading of each bankruptcy forecasting variable varies according to the credit risk level of the company. The remaining inquiry is whether the hybrid model with dynamic loadings offers banks better bankruptcy prediction performance. To compare the bankruptcy forecasting performances of the two models, we conduct two commonly used tests: CAP and ROC curves, and the corresponding accuracy ratios. Fig. 6 shows the CAP curves for the two bankruptcy prediction models established in this study. The 45 degree line represents the naïve case (which is equivalent to a random assignment of scores). Apparently, the two models perform better than a random model; however, the relative performance of the two competing models is not clear. In particular, the model with dynamic loadings derived by the BQR model performs better than the logit model with constant loadings in the bottom 50% of the population in terms of credit quality. Notably, the model with dynamic loadings performs slightly worse than the model with constant loadings in the case of good quality firms (that is, the top 50% of the population). In Fig. 7, we present the ROC curves for the two competing models. It shows two things: (i) the two credit models selected in this study are considerably better than the naïve model, and (ii) the dynamic BQR model outperforms the logit model with constant loadings, resulting in a larger area under the ROC curve. In Table 4, we summarize the results of the accuracy ratio (AR) as a performance measure of bankruptcy prediction. The model with dynamic loadings derived by the BQR technique is consistently associated with higher AR values in comparison with the setting with constant loadings generated by the traditional logit model. The conclusion is clear: adopting a hybrid model with dynamic loadings does enhance bankruptcy prediction performance. 5.4. Out-of-sample tests The above results demonstrate that the model with dynamic loadings would provide better prediction in firm bankruptcy in an in-sample analysis. Specifically, the tests are conducted on the same historical sample of default data on which the two models were calibrated against. It is not surprising that, by providing more degree of freedom, we achieve a better in-sample goodness-offit when adopting the dynamic BQR model. Undeniably, banks would be more concerned with how well the alternative forecasting techniques will perform in the future (i.e., in an out-of-sample setting). For that purpose, we conduct an out-of-sample test by randomly withholding 500 observations (150/350 of them are failed/non-failed firms), which are defined as the “test set”. The residual observations are defined as the “model set” and are used in calibrating the models and calculating the loadings. The calibrated models are then used to predict the default events in the previously withheld “test set”.

Table 2 Estimates of bankruptcy prediction model with constant loadings derived by logit regression model. Variables

Expected sign

Estimate (standard error)

Intercept z-score DD

− ve − ve

1.9576 (0.0856)* − 0.0313 (0.0055)* − 0.2560 (0.0077)*

This table presents estimation results of the hybrid bankruptcy prediction model with constant loadings derived by the logit model (see Eqs. (3)–(6) for the details of model specifications). The value in the parenthesis is the standard error of the point estimate and the * denotes statistical significance at 5% level. As shown in this table, the coefficients of z-score and DD are significantly negative. This result indicates that as a company's z-score and DD increases, it is less likely to go bankrupt. Although the two estimates are significant and have the expected sign, this credit risk model derived by the conventional logit regression approach does not allow for the loadings of z-score and DD variables to differ between good and poor quality companies.

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Table 3 Estimates of bankruptcy prediction model with dynamic loadings derived by BQR model. Quantile

Intercept

z-score

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95

0.8821 1.1032 1.7920 2.677 1.1110 2.4856 1.8971 2.6936 2.2890 2.1434 2.4698 2.5100 1.9440 2.7941 1.3532 1.0193 1.4426 2.9101 2.7336

− 1.4214 − 1.282 − 1.6957 − 1.763 − 0.7124 − 1.5610 − 1.1482 − 1.5920 − 1.0936 − 1.0463 − 1.2055 − 1.2249 − 0.2848 − 0.0797 − 0.0413 − 0.0309 − 0.0054 − 0.0075 − 0.0097

(0.5523) (0.5195)* (0.5783)* (0.5374)* (0.6821) (0.4448)* (0.4520)* (0.2992)* (0.4349)* (0.5775)* (0.4435)* (0.4872)* (0.6554)* (0.4582)* (0.6277) (0.8050) (0.4839)* (0.3801)* (0.5119)*

DD (0.7077)* (0.5849)* (0.5446)* (0.4607)* (0.4865) (0.2519)* (0.2875)* (0.1965)* (0.2095)* (0.2971)* (0.2859)* (0.3300)* (0.4183) (0.2531) (0.0915) (0.0355) (0.0547) (0.0056) (0.0058)

− 0.0519 − 0.0725 − 0.1309 − 0.2255 − 0.0801 − 0.1807 − 0.1415 − 0.1934 − 0.1782 − 0.1347 − 0.1552 − 0.1577 − 0.1674 − 0.2778 − 0.1201 − 0.0905 − 0.1165 − 0.1948 − 0.1417

(0.0365) (0.0454) (0.0536)* (0.0505)* (0.0554) (0.0381)* (0.0368)* (0.0245)* (0.0379)* (0.0431)* (0.0292)* (0.0434)* (0.0500)* (0.0604)* (0.0625)* (0.0545) (0.0430)* (0.0270)* (0.0289)*

This table presents the estimation results of the hybrid bankruptcy prediction model with dynamic loadings derived by BQR model (see Eqs. (7)–(13) for the details of the model specifications). In this model, the loadings of the z-score and DD are allowed to change according to the quantile level of credit risk. In particular, the loadings are estimated at nineteen different quantile levels: 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60, 0.65, 0.70, 0.75, 0.85, 0.90 and 0.95. The value in the parenthesis is the standard error of the point estimate and the * denotes statistical significance at the 5% level. The z-score variable has a statistically significant loading at the lower quantile levels, from 0.05 to 0.60 (except for the 0.25 quantile); it becomes insignificant at higher quantile levels from 0.65 to 0.95. The coefficients of the DD variable are significantly negative at the 5% level for most of the higher quantile levels (the loading of the 0.80 quantile is statistically significant at 10% level); nevertheless, they become insignificant at the three lower quantiles, such as 0.05, 0.10 and 0.25.

The estimates of bankruptcy prediction model with dynamic loadings derived by BQR model using the 5788 (=6288 − 500) residual observations from the “model set” are listed at Table 5. Importantly, using the 5% significance level as a criterion, the zscore variable is insignificant at the six higher quantile levels, from 0.70 to 0.95 whereas it is significant under the lower quantile levels, from 0.05 to 0.65 with two exceptions: 0.30 and 0.50 quantiles. By contrast, although the DD variable is significant for most quantile levels, it becomes insignificant at the two lower quantiles: 0.05 and 0.30. Our previous finding of the loadings of z-score (DD) variables becoming less significant for companies with worse (better) credit quality is therefore robust in this subsample of the dataset. Table 6 presents the results of the out-of-sample bankruptcy prediction performances of the two models. First, in

Fig. 3. The negative value of z-score loading estimate and its confidence intervals across various quantile levels.

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Fig. 4. The negative value of DD loading estimate and its confidence intervals across various quantile levels.

Fig. 5. The negative values of DD loadings implied by Merton's model versus the DD loading estimates by the BQR model.

having positive AR values, the two hybrid models still outperform a naïve (random) model. Second, by having higher AR values, the dynamic BQR model still outperforms the logit model with constant loadings.27 6. Conclusions and future research While adopting the BQR technique, we propose a bankruptcy prediction model with dynamic loadings for both the accountingratio-based z-score and the market-based DD variable. With this proposed model, we conduct an empirical study on a dataset of default events observed during the period from 1996 to 2006. Our sample of “defaulted” firms consists of those firms which

27 We also re-run the tests using the probit model (to conserve space, we do not present these results here). The AR results are qualitatively similar when the probit model is used instead of the logit model. This result indicates that bankruptcy prediction enhancement heavily depends on allowing for dynamic loadings on accounting-ratio-based and market-based information, rather than on the distribution assumption of the errors ui in Eq. (3).

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Fig. 6. CAP curves for the two hybrid models.

Fig. 7. ROC curves for the two hybrid models.

experienced bankruptcy or liquidation events as recorded in the Compustat database. Our sample of “survived” firms is made up of the Fortune 500 companies with over a B-rating over the same time period. The empirical results of this study are consistent with the following notions. First, in predicting the bankruptcy of those companies with relatively poor (good) credit quality, we can improve the accuracy by putting more (less) emphasis on the market-based DD variable while reducing (increasing) the emphasis on the accounting-ratio-based z-score. Second, the proposed

Table 4 Accuracy ratios comparison: in-sample tests. The setting with constant loadings derived by the Logit Model The setting with dynamic loadings derived by the BQR Model Accuracy ratio by CAP curve 80.38% Accuracy ratio by ROC curve 79.47%

85.72% 84.60%

This table summarizes the results of accuracy ratio (AR) as performance measure of bankruptcy prediction. See Section 4 in the text for detail discussions on the two AR measures. The AR of a naïve (random) model is zero.

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Table 5 Estimates of bankruptcy prediction model with dynamic loadings derived by BQR model using observations from the “model set”. Quantile

Intercept

z-score

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95

1.5778 2.0386 2.7618 2.1054 2.7445 1.0549 1.5218 2.8376 2.6112 0.7964 2.3000 2.9256 2.2818 1.6895 2.7199 1.9171 1.5979 2.8552 1.8947

− 2.5297 − 1.8370 − 2.4807 − 1.3898 − 1.6605 − 0.6116 − 0.9080 − 1.6926 − 1.4354 − 0.3888 − 1.1244 − 0.9433 − 0.7371 − 0.1934 − 0.0821 − 0.0587 − 0.0060 − 0.0173 −0.0051

(0.4936)* (0.4579)* (0.5559)* (0.3666)* (0.5666)* (0.7683) (0.5919)* (0.4342)* (0.5058)* (0.8296)* (0.5029)* (0.5002)* (0.5947)* (0.4000)* (0.4675)* (0.4545)* (0.4680)* (0.5490)* (0.5362)*

DD (0.6080)* (0.5670)* (0.5435)* (0.3189)* (0.3508)* (0.4666) (0.3237)* (0.2977)* (0.3415)* (0.4564) (0.3169)* (0.3826)* (0.4101)* (0.1193) (0.0912) (0.0591) (0.0607) (0.0120) (0.0066)

− 0.0942 − 0.1531 − 0.2085 − 0.1773 − 0.2048 − 0.0805 − 0.1087 − 0.2027 − 0.1889 − 0.0500 − 0.1444 − 0.1941 − 0.1512 − 0.1345 − 0.2416 − 0.1700 − 0.1290 − 0.1839 − 0.0950

(0.0604) (0.0393)* (0.0420)* (0.0310)* (0.0497)* (0.0606) (0.0465)* (0.0342)* (0.0418)* (0.0669)* (0.0429)* (0.0345)* (0.0368)* (0.0421)* (0.0475)* (0.0408)* (0.0336)* (0.0354)* (0.0265)*

This table presents the estimation results of the hybrid bankruptcy prediction model with dynamic loadings derived by BQR model (see Eqs. (7)–(13) for the details of the model specifications). To conduct the out-of-sample test, 500 observations (127/373 of them are failed/non-failed firms) are randomly withheld and defined as the “test set”. The residual 5788 (= 6288 − 500) observations are defined as the “model set” and are used in calibrating the models and calculating the loadings. Other notions are consistent with Table 3.

Table 6 Accuracy ratios comparison: out-of-sample tests. The setting with constant loadings derived by the Logit Model The setting with dynamic loadings derived by the BQR Model Accuracy ratio by CAP curve 81.75% Accuracy ratio by ROC curve 81.69%

88.00% 85.72%

To conduct the out-of-sample test, 500 observations (127/373 of them are failed/non-failed firms) are randomly withheld and defined as the “test set”. The residual observations are defined as the “model set” and are used in calibrating the models and calculating the loadings. We then test the performances of the calibrated models in predicting the default events within the “test set”. The AR of a naïve (random) model is zero.

model performs better than a hybrid model with constant loadings in predicting default events in both the in-sample and out-ofsample settings. This study provides both the theoretical and empirical underpinnings of a dynamic hybrid model which is more able to explain and predict the default events of companies of diverse credit qualities than conventional logit model. We therefore provide an alternative modeling approach for banks to consider in developing their internal risk rating systems. One important caveat should be noted in interpreting the results of this study. In practice, default dependencies among firms play an important role in the quantification of a portfolio's credit risk exposure. Moreover, growing linkages in financial markets also have led to a greater degree of joint default propensity. Some of the systematic changes in credit risk, which govern the probability of the occurrence of multiple default events, might not be able to be fully captured by either the z-score or the DD variable. The conditional distribution of the error term in the BQR model therefore might not be i.i.d. Dealing with default dependencies across firms and over times by relaxing the assumption of i.i.d. errors is a valuable direction for future research. Acknowledgment The authors gratefully acknowledge funding from the National Science Council of Taiwan (NSC96-2416-H-006-023-MY3). Appendix A. The bootstrap estimate of the standard error Assume we have a real-valued estimator β̂(X1, X2,…, Xn), which is a function of n independently and identically distributed observations: iid

X1 ; X2 ; :::; Xn ∼ F;

ðA1Þ

F being an unknown probability distribution on a space κ. Having observed X1 = x1, X2 = x2,…, Xn = xn, we wish to obtain an estimate of the standard error of β̂.

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The true standard error of β̂ is a function of F, n, and the form of the estimator β̂, say ˆ ð:; :; :::; :ÞÞ = σðFÞ: σðF; n;β

ðA2Þ

This last notation emphasizes that, knowing n and the form of β̂, the true standard error is only a function of the unknown distribution F. The bootstrap estimate of the standard error, σ̂B, is simply ˆ Þ; ˆ = σðF σ B

ðA3Þ

where F ̂ is the empirical probability distribution 1 Fˆ : mass on xi ; n

i = 1; 2; …; n:

ðA4Þ

In practice, the function σ(F) is usually impossible to express in simple form, and σ̂B must be evaluated using a Monte Carlo algorithm: Step 1. Construct F ̂ as at Eq. (A4). Step 2. Draw a bootstrap sample from F ̂, iid ˆ X1⁎ ; X2⁎ ; :::; Xn⁎ ∼ F;

ðA5Þ

̂ = β̂(X1⁎, X2⁎,..., Xn⁎). and calculate β⁎ Step 3. Independently repeat Step 2 some number B times, obtaining bootstrap replications β̂⁎(1), β̂⁎(2),…, β̂⁎(B), and calculate " #1 = 2 ˆ ˆ B ½β* ðbÞ− β* ð⋅Þ ˆB = ∑ σ ; ðA6Þ B−1 b=1 where B

ˆ ðbÞ = B: ˆ ð⋅Þ = ∑ β* β*

ðA7Þ

b=1

As B → ∞, the right-hand side of Eq. (A6) converges to σ(F ̂). Appendix B. Alphabetical list of the failed companies selected for this study No.

Firm name

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

A3DO Co Acclaim Entertainment Inc Accrue Software Inc All American Semiconductor Allied Holdings Inc Aphton Corp Armstrong Holdings Inc Biotransplant Inc Boundless Corp Calpine Corp Ceyoniq AG Cinemastar Luxury Theaters Collins & Aikman Corp Composite Technology Corp Congoleum Corp Corporacion Durango SA D G Jewelry Inc Dairy Mart Convenience Strs Dana Corp Delphi Corp Donnkenny Inc DT Industries Inc Dura Automotive Sys Earthshell Corp (continued on next page)

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Appndix B (continued) No.

Firm name

25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73.

Enernorth Industries Inc Enesco Group Inc Engage Inc Environmental Elements Corp Fantom Technologies Inc Federal Mogul Corp Florsheim Group Inc Frisby Technologies Inc Frontline Capital Group Global Power Equipment Group Glycogenesys Inc Grace W R & Co Hancock Fabrics Inc Home Products Intl Inc Interstate Bakeries CP Intl Fibercom Inc KPNQWest NV Movie Gallery Inc National Steel Corp Newpower Holdings Inc NQL Inc NX Networks Inc Onetravel Holdings Inc PCD Inc Polymer Research Corp of AM President Casinos Inc Ramp Corp Robotic Vision Systems Inc Rowe Companies Sea Containers Ltd Solutia Inc Storage Engine Inc Talisman Enterprises Inc Televideo Inc Thermoview Industries Inc Three Five Systems Inc Tower Automotive Inc Trans Industries Inc Trinsic Inc Tweeter Home Entmt Group Inc Uniroyal Technology Corp Universal Access Global Hldg Universal Automotive Inds V One Corp Verilink Corp Waterlink Inc Westpoint Stevens Inc Women First Healthcare World Health Alternatives

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