Impact of reorganization announcements on distressed-stock returns

Economic Modelling 24 (2007) 749 – 767 www.elsevier.com/locate/econbase

Impact of reorganization announcements on distressed-stock returns Li-Chiu Chi a,⁎, Tseng-Chung Tang b a

Department of Finance, National Formosa University, 64 Wenhwa Road, Huwei, Yunlin 632, Taiwan, ROC b Department of Business Administration, National Formosa University, Taiwan, ROC Accepted 22 February 2007

Abstract In this study, we show the potential substantial gains from identifying the attributes of firms whose stock prices are likely to rise as a consequence of reorganization. Our study indicates that an ex ante trading strategy of investing in distressed stocks with a respective 30.65% and 46.77% likelihood of being a winner on the dates of reorganization filing and filing confirmation and holding the stocks for a month can generate average cumulative abnormal returns of + 25.438% and +27.956%, respectively. We further compare the performance of three input selection techniques relative to the rank of input importance as well as demonstrate the predictability of distressed-stocks investment using hybrid GABPNs. We find that the generalization ability of the GA-BPNs can be harnessed in creating an effective and efficient tool for distressed-stock selection to a high degree of accuracy and investors can, then, translate the often-confusing lexicon of the reorganization process into a lucrative investment vehicle. © 2007 Elsevier B.V. All rights reserved. JEL classification: G33; G34 Keywords: Corporate reorganization; Distressed-stock investing; Hybrid genetic algorithm and backpropagation network

1. Introduction In today's vulnerable and volatile business climate, corporate bankruptcy and Chapter 11 reorganization is a common occurrence among U.S. corporations of all sizes and in all sectors (Altman, 1999). Distressed stocks are stocks of firms in bankruptcy or financial distress; many of ⁎ Corresponding author. Tel.: +886 5 6315757; fax: +886 5 6315751. E-mail address: [email protected] (L.-C. Chi). 0264-9993/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2007.02.007

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them are of poor quality and have low recovery values, as well as having more varied rates of return. A financially distressed firm normally experiences stock price declines before it files for Chapter 11. The stock price inevitably drops even more because of the dampening effect on stock price reactions to Chapter 11 filing. As often as not the prices of distressed stocks fall in anticipation of the financial distress when their holders choose to sell rather than remain invested in a financially distressed firm. In most cases these sellers may be overreacting to the stigma of current or potential bankruptcy, causing them to overlook or ignore the firm's true worth. Distressed-stock investment is inherently riskier than non-distressed-stock investment. A firm that is on the edge of bankruptcy does not sound like a very good investment opportunity, but in many instances bad news can be good news for distressed-stock arbitrageurs. By investing in distressed stocks, these contrarian investors attempt to capture value as the companies reorganize. Their strategy is to take advantage of the knowledge, flexibility, and patience that distressed investors have which the creditors of a firm often do not have. Investing in troubled economic times can mean creating opportunity out of misfortune; however, it carries a high risk and remains a niche field. According to Altman's (1998) research, distressed securities during the period 1980–1993 outperformed the relevant market indices by over 20% during their first 200 days of trading. In other contexts, this finding is similar to results presented by Hotchkiss and Mooradian (1997), Indro et al. (1999), and Chi and Tang (2005), who conclude that distressed securities returns can be positive and significantly higher than non-distressed securities returns for various holding periods after bankruptcy reorganization filing. It is no surprise that the market for distressed securities continues to capture the interest and imagination of the investment community and that the numbers of distressed securities investors in the world have multiplied. During the past few years, stock return or stock market prediction has been an important financial subject that has attracted researchers' attention, and the large body of this research provides evidence that stock market returns are to some extent predictable (see for example Lo and MacKinlay, 1988; Renshaw, 1993; Callen et al., 1996; Kim and Chun, 1998; Leung et al., 2000; Thawornwong and Enke, 2004). To date, however, little attention has been paid to distressed securities investment returns (see for example Altman, 1991; Harpel, 1992; Moulton and Thomas, 1993; Lakonishok et al., 1994), and furthermore the existing distressed-securitiesinvestment studies have focused primarily on distressed debt securities (see for example Morse and Shaw, 1988; Howe, 1990; Putnam III, 1991; John, 1993; Altman, 1998). Only very few studies (Gilson et al., 1990; Datta and Iskandar-Datta, 1995; Tashjian et al., 1996; Hotchkiss and Mooradian, 1997; Indro et al., 1999; Chi and Tang, 2005) have directly examined the impact of reorganization announcements on the distressed-stock returns. In this regard, the first objective of this study is to investigate the impact of the information released by both reorganization filing and final resolution announcement on distressed-stock return forecasts. Kim and Chun (1998) assert that the central issue in investment analysis and risk management lies in the prediction of input variables, a process of determining a set of inputs. In a similar vein, other researchers have supported their view that identifying key predictive variables is the crucial part of the prediction process (see for example Bhargava et al., 1998; Ooghe and Balcaen, 2002; Thawornwong and Enke, 2004; Tang and Chi, 2005). Studies related to the predictability of stock return and its determinant factors are ample and one can easily find such studies in the literature (a good summary of the literature is provided by Leung et al., 2000). However, the relevant key variables determined by traditional stock return or stock market prediction may be ineffectual or redundant for the predictive task of distressed securities return and could produce misleading results in that distressed securities investment has little stock market dependence or correlation to

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the performance of the stock market. As far as stock selection is concerned, firm-specific factors constitute an important consideration. Distressed stocks are likely to move when firm-specific events are significant and sustained enough to catch the eye of investors. Succeeding or failing can only be based on the effectiveness of the investor's capability of uncovering the attributes and trading strategies associated with the distressed firms (Chi and Tang, 2005). Ideally, theory would suggest a causal link between a battery of selected predictors and the predictive function; the proposed linkage could then be tested by an appropriately constructed prediction model. Unfortunately, the lack of such a theory of predictor selection in distressedstock return forecasts has prevented the comprehensive use of this scientific approach. Although there have been some limited efforts in the selection and measurement of input variables for distressed-stock return forecasts in recent years, no specific set of input variables or feature selection methods have managed to achieve a predominant position in this area. Given this notion, a second objective of this study is to propose and compare different methods for selecting inputs and ranking input importance in the distressed-stock return forecast context. It is our hope that the input selection process can identify which variables must always be retained and which can safely be ignored in the predictive task. To shed some light on the intricacies involved in distressed-stock investing, the overall intent of the study is twofold. First, the study investigates the impact of both the reorganization filing announcement and the reorganization resolution announcement on the distressed-stock return forecasting over a long horizon, from 180 trading days preceding the filing date to 180 trading days after the confirmation date of the reorganization plan. From this we are able to separate the investment winners (i.e., distressed firms whose investors experience at least +25% excess returns over a 30-day holding-period) from the losers, and to identify the characteristics of winners and therefore develop effective ex ante trading strategies. In this study, we show the potential substantial gains from identifying the attributes of firms whose stock prices are likely to rise as a consequence of reorganization. Our study indicates that an ex ante trading strategy of investing in distressed stocks with a respective 30.65% and 46.77% likelihood of being a winner on the dates of reorganization filing and filing confirmation and holding the stocks for a month can generate average cumulative abnormal returns of + 25.438% and +27.956%, respectively. The second intent of this study is to analyze three different methods — sensitivity analysis (SA), principal components analysis (PCA), and genetic algorithm (GA) — of ranking the importance of input parameters, and to compare their effectiveness on a hybrid GAbackpropagation network (BPN) approach (i.e., hybrid GA-BPNs) for discrimination that combines the population-based parallel search technique of GA and point-based gradient descent search of BPNs. More specifically, three input importance-ranking techniques — SA, PCA, and GA — are employed with a view to identifying the relevant and useful factors that play important roles in input variables. The resulting variables are then provided to construct hybrid GA-BPN models to classify and predict the investment winners. To the best of our knowledge, we are among the first to use artificial intelligence techniques in rating the importance of input variables as well as in constructing models for distressed-stock return forecasts. This forecasting involves a complicated process of cognition and decisionmaking relating to human value systems and is more suitable for analysis by artificial intelligence algorithms. Since the effect of the information released by a reorganization announcement on distressed-stock investment returns is poorly understood, as are the characteristics of the winners, the results of this study can contribute to the research of distressed-stock return forecasts and may be very relevant for investors interested in investing in distressed stocks, helping them to make

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better tactical decisions about which firms promise to benefit from the reorganization process, and to evaluate the expected gains from such investments. Our six-variable hybrid GA-BPN models perform quite well in both classification and prediction tasks. The classification accuracies are 85.00% for Model 1 and 84.78% for Model 2. These results are significantly much higher than a proportionate two-group random classification of 54.88% and 50.62%, respectively. The prediction accuracies for Models 1 and 2 are 82.61% and 86.54%, respectively, significantly better than the proportionate chance predictions of 53.92% and 52.30%. Hybrid GA-BPNs appear to have the potential to have sound generalization capability. The remainder of this paper is organized as follows. In Section 2, we present the data, sample, and variable selection and empirical design. Empirical results are described in Section 3, followed by a summary and conclusions in Section 4. 2. Data and methodology In this section, we discuss our data sources and sample selection criteria, calculation of abnormal returns, variable selection, and our empirical methodology. 2.1. Data and sample selection A preliminary sample of distressed firms is compiled from the Taiwan Stock Exchange Corporation (TSEC) listing of firms that filed petitions for reorganization from 1980 to 2005. We also search the descriptions of company characteristics, the dates associated with reorganization and confirmation plan filing, and the filing resolutions, from an in-depth check of Extemporary Newspaper Headline & Index Database. We exclude firms in financial institutions, foreign-based entities, and firms for which data required for our empirical analyses are missing or where discrepancies cannot be resolved. In addition, in order to examine the dollar value effect associated with the reorganization filing, we restrict our sample by requiring that the firm has stock price data (financial statement data) available in the Taiwan Economic Journal (TEJ) or the Compustat Global Data for 180 trading days (one year) before and 180 days after the reorganization filing and final resolution dates. After applying these selection criteria, 62 firms are available for our empirical test. This full sample is used to classify the winner/loser resolution at the first day after the filing. The firms are further split into training and testing sets. The training subset includes 40 firms that filed for reorganization from 1980 to 2000. The testing subset includes 22 firms that filed for reorganization from 2001 to 2005. 2.2. Calculation of abnormal returns The daily abnormal returns (ARs) from investing in distressed-firm stocks are calculated using the market model given by: ARjt ¼ Rjt −ðaĵ þ bĵ Rmt Þ where ARjt is the abnormal return for stock j on day t relative to the event date, Rjt is stock j's return on day t, and Rmt is the return on an equally weighted market portfolio drawn from the TSEC and TEJ daily returns file on each day t in the estimation period. Market model coefficients

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are designated over a 281-day estimation period starting 135 days prior to the two major event periods, the reorganization filing date (F0) and the final resolution date (R0), and concluding 135 days after the events (see Cochran et al., 1995). Daily ARs are then aggregated over various event windows to obtain the cumulative abnormal returns (CARs) and are subsequently tested for statistical significance. The expected value of the AR or CAR is zero in the absence of abnormal performance. To test whether the AR or CAR is significantly different from zero, the t-test recommended by Brown and Warner (1985) in the presence of event clustering to take into account cross-sectional correlation is used. In addition, a majority of the returns for distressed firms are expected to be generated by infrequent trading data, which will lead to biased and inconsistent estimates of α and β. This study employs the Scholes-Williams (1977) procedure to adjust for the nonsynchronous trading problem. Following Chi and Tang (2005), the generalized sign test is used, which differs from the simple sign test in that the fractions of negative and positive ARs (CARs) under the null hypothesis are determined by the fractions observed in the estimation period rather than fixed at 50%. Furthermore, Brown and Warner (1985) and Corrado and Zivney (1992) indicate that non−parametric rank tests are much less influenced by event-induced heteroskedasticity (i.e., variance changes) than their parametric counterparts. Chandra et al. (1995) further assert that rank tests perform on average the best across all tests, i.e. they are approximately independent of the underlying and unknown model for the true change in the median of abnormal returns. Thus, we also proceed with two-sample Wilcoxon ranksum non−parametric test which is especially well suited for cases with small sample sizes to examine whether abnormal returns significantly differ between winners and losers. Since the exact significance is always sufficiently reliable — regardless of the size, distribution, sparseness, or balance of the data — to enable us to make reliable inferences, we compute the asymptotic p value, exact p value, and the Monte Carlo estimate of the exact p value. 2.3. Variable selection In a survey profiling investors in financially troubled firms, Altman (1998) finds that the majority invest in debt securities and require a minimum return on investment of between 20% and 25%. The acceptable minimum return on distressed-firm stocks should be no less than it is on debt because they are inherently riskier than debt. We use the CARs over the event windows (F0, F + 30) and (R0, R + 30) as the dependent variables to reflect an investment strategy under which investors decide on the distressed-firm stock to invest in by distinguishing the features that make the stock a likely winner. Accordingly, a firm is classified as a winner if its holding-period CAR is at least 25%. This produces 19 winners and 43 losers on day F0 and 29 winners and 33 losers on day R0. Fama and French (1992) argue that size is the main determinant of the cross-section of stock returns. They observe the evidence that the larger drop in NASDAQ-listed stock is consistent with the assertion that for smaller stocks there may be a larger surprise. Dissanaike (2002) also finds a long-term winner–loser effect in the UK, within a sample of large firms. Thus, it is reasonable to hypothesize that the likelihood that a distressed firm's stock will be a winner can be related to its size. We use the natural logarithm of the firm's total assets as an alternative measure of firm size. Leverage magnifies the negative market reactions but not the positive reactions. Iqbal (2002) asserts that firms with low leverage enjoy larger stock returns. Lang and Stulz (1992) also propose that negative valuation effect is highly correlated with leverage because of elasticity. Hence, we would expect the equity value of highly leveraged firms to fall more in percentage terms than the

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equity value of distressed firms with low leverage. This study uses total liabilities to total assets to measure financial leverage. We include liquidity in our analysis because Platt (1985) argues that the liquidity to be the driving forces behind returns. O'Hara (2003) also finds a cross-sectional association between changes in liquidity and expected stock returns — illiquid firms earn lesser returns than liquid stocks. More recently Sadka (2006) investigates the relationship between expected return and exposure to aggregate liquidity risk and find that liquidity risk is a priced factor. In this study, the ratio of cash and cash equivalents to total assets that provides an indication of a firm's liquidity is used as a control. Profitability is an important determinant of investor's perceptions of a firm. Firms with less profitability are viewed most negatively by investors as prime candidates for negative valuation effect. Thus, past profitability is usually regarded as a useful indicator of future profitability, and can be a prospectus to comparing firm's financial quality. An often-used measure of profitability is net income to total assets, referred to as return on assets (ROA). Holding other things constant, it is expected that the more profitable a firm, the more competitive it is. One common method used to construct an estimate of expected return on an investment is to average the historical stock returns. In fact, over the long-run, historical returns are just as good as forward estimates in predicting stock returns (Indro et al., 1999). In this study, we look at a sixmonth holding-period return prior to the respective event days. The last explanatory variable of industry competition is a hybrid suggested by the studies of Guadagni and Little (1983) and Chi and Tang (2005). Erwin and Miller (1998) state that any positive market reactions would be more pronounced in industries that are characterized by low levels of competition. It is therefore expected that the lower the level of competition within an industry, the more likely the firms operating in the industry will be able to exploit new profitable opportunities. We use Herfindahl–Hirschman Index as the proxy for degree of competition. 2.4. Hybrid GA-BPNs There is considerable evidence that many macro series including stock returns are non-linear. Renshaw (1993) and Refenes and Bolland (1996) document that the relation between financial variables and stock returns is non-linear even though conventional regression analysis fails to discern any obvious non-linearities. Refenes and Bolland (1996) also state that applications of artificial neural networks (ANNs) to financial and investment decision-making problems have been fairly successful. The novelty of ANNs lies in their ability to model non-linear processes from historical data without a priori assumptions about the nature of the data-generating process. This is particularly useful in stock investment and other financial studies, where much is assumed and little is known about the nature of the processes driving changes in asset prices (see for example, Burrell and Folarin, 1997; Chi and Tang, 2005). BPN is currently the most widely used search technique and is more mature than other networks for learning functions of interest. Unlike conventional mathematic methods, a BPN can mathematically replicate the neural connections of the human brain and approximate any nonlinear continuous function for specific input and output relationship without a certain model (Turban, 1992). Wong et al. (1995) find that an overwhelming majority of studies using ANNs rely on gradient techniques for network training, typically a variation of backpropagation (BP) developed by Werbos (1993) and popularized by Rumelhart and McClelland (1986). However, Rumelhart et al. (1986) make two important observations concerning the limitations of the BP gradient descent nature, namely, its slowness in convergence and its inability to escape local optima.

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Unlike BP, the genetic algorithm (GA) is a heuristic population-based search procedure that searches from one population of solutions to another, focusing on the area of the best solution so far, while continuously sampling the total parameter space. The GA has been shown to perform exceedingly well in obtaining global solution when optimizing difficult non-linear functions (Dorsey and Mayer, 1995). An extension of this research has also shown the GA to perform well for optimizing the ANN, another complex non-linear function (Dorsey et al., 1994). In this study, we use the hybrid GA and BPNs (hybrid GA-BPNs) methodology proposed by Pendharkar (2001), which employs the principles of Darwin-type natural evolution and local gradient descent to train the ANNs. Also, we combine the GAs with the BP algorithm in order to optimize the connection weights of the ANNs, i.e., we use GAs to perform a global search and obtain a higher probability of convergence and a heuristic near-optimal solution. After a heuristic solution is obtained, we use the local gradient descent BP algorithm to improve the heuristic nearoptimal solution and possibly obtain the global optimum solution. 3. Results and analysis 3.1. Market reactions surrounding the reorganization filing Tables 1 and 2 report the average ARs and CARs for the full sample of 62 distressed stocks and for the subsamples of 19 winner and 43 loser stocks surrounding the reorganization filing. More importantly, Figs. 1 and 2 clearly suggests that, overall, investments in the stocks of a distressed firm surrounding the filing seem to be a losing proposition. This may be due to substantial uncertainty resolution and/or investor overreaction to the filing announcement. We find significantly large negative filing day ARs of − 1.768% and − 3.855%, respectively, for our full sample and loser stocks and the adverse effect of filings spill into the following days till day F + 10. The winner stocks, surprisingly, do not experience negative reactions except days F + 4 and F + 5. We also find that the CARs for the winner subsample are significantly positive for selected event windows ranging from +1.076% to + 25.438%. Over the traditional two- and three-day event windows, (F0, F + 1) and (F − 1, F + 1), the full sample (loser stocks) decline by over − 3.423% (− 4.349%) and − 5.678% (− 7.019%), respectively. Over the window (F0, F + 30), the decrease in values is − 36.133% and − 63.338%, respectively. The proportion of losers in the full sample is 70%, which significantly outnumbers winners by 2.3 to 1. Furthermore, the gains and losses between winners and losers differ in magnitude over all selected event days (windows), ranging from + 0.022% to + 5.449% (+ 5.065% to +88.777%), and the differences in the ARs and CARs are statistically significant according to the non-parametric Wilcoxon rank-sum test. Mean ARs (CARs) for our full sample and losers are also statistically different from zero, but not for all those in the winner subsample. The non−parametric generalized sign test confirms the evidence that significant shifts occur both in the ratio of positive to negative AR observations and in the ratio of positive to negative CAR observations in the period surrounding the reorganization filing. The null hypothesis is that the proportion of positive to negative returns is equal to the ratio in the estimation period. 3.2. Market reactions surrounding the final resolution The average ARs and CARs for the distressed stocks surrounding the final resolution date are presented in Tables 3 and 4. The ratio of positive to negative reactions is 26 to 36 and 29 to 33,

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Table 1 ARs surrounding the reorganization filing date (day F0)

F − 10 F−9 F−8 F−7 F−6 F−5 F−4 F−3 F−2 F−1 F0 F+1 F+2 F+3 F+4 F+5 F+6 F+7 F+8 F+9 F + 10

Full sample

Winners

Losers

ARt (%)

t (ARt)

+/−

G. sign test

ARt (%)

t (ARt)

− 0.166 − 1.516 − 0.944 − 1.204 − 0.404 − 1.581 − 1.593 − 1.735 −0.908 − 1.084 − 1.768 − 2.280 − 2.213 − 2.284 − 3.452 − 3.438 − 1.614 − 2.747 − 2.252 − 2.542 − 1.250

− 0.287 − 2.602b − 1.156 − 2.002b − 0.669 − 2.252b − 2.503b − 2.490b −1.376 − 1.520 − 2.575b − 3.486c − 3.275b − 3.334b − 4.837c − 4.926c − 2.248b − 3.784c − 3.747c − 3.763c − 1.686a

25/37 21/41 28/34 23/39 24/38 17/45 17/45 20/42 24/38 23/39 18/44 13/49 18/44 15/47 13/49 10/52 18/44 15/47 12/50 16/46 21/41

− 4.372c − 4.015c − 4.541c − 4.197c − 4.286c − 3.621c − 3.621c − 3.920c −4.286c − 4.197c − 3.724c − 3.180c − 3.724c − 3.408c − 3.180c − 2.803b − 3.724c − 3.408c − 3.059b − 3.516c − 4.015c

− 0.149 − 0.457 − 0.110 − 1.225 0.867 − 1.030 − 0.715 − 1.150 0.423 0.020 1.683 0.976 0.276 0.298 − 0.455 − 1.671 1.578 0.939 1.757 1.573 2.784

0.787 7/12 1.088 7/12 0.526 8/11 0.385 7/12 1.929a 7/12 − 0.083 3/16 0.356 5/14 − 0.377 5/14 1.354 8/11 1.178 6/13 1.542 8/11 1.980a 7/12 1.001 8/11 0.991 7/12 − 0.240 6/13 − 0.872 4/15 1.056 7/12 0.550 6/13 1.220 7/12 1.440 9/10 3.890b 10/9

a, b, c Significant at the 0.1, 0.05, and 0.001 levels, respectively.

+/−

Difference Wilcoxon rank-sum test (%) Z Asymp. Monte Exact P Carlo P P

G. sign test ARt (%)

t (ARt)

+/−

G. sign test

− 2.366b − 2.366b − 2.201b − 2.366b − 2.201b − 1.604a − 2.023b − 2.023b −1.826a − 2.201b − 1.826a − 2.023b − 1.826a − 2.023b − 2.201b − 1.826a − 2.023b − 2.201b − 2.023b − 1.604a − 1.342

− 0.260 − 2.951b − 1.191 − 1.678a − 1.108 − 2.171b − 2.734b − 2.383b −1.740b − 1.673a − 3.855c − 4.591c − 3.810c − 4.008c − 5.547c − 4.932c − 3.228b − 5.029c − 6.279c − 5.620c − 3.060b

18/25 14/29 20/23 16/27 17/26 14/29 12/31 15/28 16/27 17/26 10/33 6/37 10/33 8/35 7/36 6/37 11/32 9/34 5/38 7/36 11/32

−3.724c 0.022 −3.296c 1.420 −3.920c 1.119 −3.516c − 0.028 −3.621c 1.665 −3.296c 0.708 −3.059c 1.135 −3.408c 0.756 −3.516c 1.720 −3.621c 1.426 −2.803c 4.461 −2.201b 4.233 −2.803b 3.236 −2.521b 3.357 −2.366b 3.896 −2.201b 2.310 −2.934b 4.174 −2.666b 4.849 −2.023b 5.275 −2.366b 5.449 −2.934b 5.342

− 0.171 − 1.877 − 1.229 − 1.197 − 0.798 − 1.738 − 1.850 − 1.906 −1.297 − 1.407 − 2.777 − 3.257 − 2.960 − 3.059 − 4.351 − 3.981 − 2.596 − 3.911 − 3.518 − 3.876 − 2.558

− 4.372 − 4.015 − 4.541 − 4.197 − 4.286 − 3.621 − 3.621 − 3.920 −4.286 − 4.197 − 3.724 − 3.180 − 3.724 − 3.408 − 3.180 − 2.803 − 3.724 − 3.408 − 3.059 − 3.516 − 4.015

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.001 0.001 0.005 0.000 0.001 0.002 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.000 0.000 0.000 0.000 0.000

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Event day

Event Full sample window t (ARt) ARt (%)

+/−

G. sign test

ARt (%)

t (ARt)

+/−

G. sign test

ARt (%)

t (ARt)

+/−

G. sign test

Difference Wilcoxon rank-sum test (%) Z Asymp. Monte Exact P Carlo P P

−10, 10 −5, +5 −1, +1 −1, 0 0, +1 0, +30 0, +60 0, +90 0, +120 0, +150 0, +180

12/50 10/52 16/46 18/44 13/49 11/51 11/51 13/49 16/46 18/44 17/45

− 3.059b − 2.803b − 3.516c − 3.724c − 3.180c − 2.934b − 2.934b − 3.408c − 3.724c −4.015c −4.015c

3.765 − 0.849 1.692 1.076 1.679 25.438 24.648 19.199 19.374 7.893 8.137

− 0.332 − 0.152 0.957 0.872 1.395 − 2.146b − 2.146b − 1.867 − 2.163b − 1.603 − 1.883a

6/13 5/14 7/12 6/13 7/12 3/16 3/16 3/16 3/16 5/14 4/15

− 2.201b − 2.023b − 2.023b − 2.201b − 2.023b − 1.604a − 1.604a − 1.826a − 1.826a − 2.366b − 2.201b

− 46.320 − 26.792 −7.019 −3.989 −5.678 − 63.338 − 63.082 − 63.086 − 60.122 − 61.298 − 59.533

− 7.516c − 6.246c − 4.208c − 3.050b − 5.062c − 2.037b − 2.037b − 3.062b − 2.905b − 2.623b − 2.535b

6/37 5/38 9/34 12/31 6/37 8/35 8/35 10/33 13/30 13/30 13/30

− 2.201b − 2.023b − 2.666b − 3.059b − 2.201b − 1.183 − 1.183 − 1.988b − 2.411b − 2.481b − 2.982b

50.085 25.942 8.711 5.065 7.357 88.777 87.731 82.285 79.495 69.191 67.670

− 30.972 − 18.842 − 4.349 − 2.437 − 3.423 − 36.133 − 36.197 − 37.870 − 35.760 − 40.094 − 38.796

− 5.560c − 5.269c − 3.217b − 2.393b − 3.625c − 2.775b − 2.775b − 3.606c − 3.644c − 3.050b − 3.180b

Winners

Losers

a, b, c Significant at the 0.1, 0.05, and 0.001 levels, respectively.

−3.724 −3.724 −4.372 −4.541 −4.107 −3.621 −3.823 −4.107 −4.286 −4.197 −4.107

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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Table 2 CARs surrounding the reorganization filing date (day F0)

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Fig. 1. ARs surrounding day FO.

indicating 41.94% and 46.77% firms have positive ARs on day R0 and R + 1, respectively. Also, 26 of the 62 firms (41.94%) have positive CARs on window (R0, R + 1) and 30 of 62 firms (48.39%) have positive CARs on window (R − 1, R + 1). The proportion of winners in the full sample is 58.06%, which is significantly more than half. The results shown in Figs. 3 and 4 clearly reveal that investments in distressed stocks surrounding the date of final resolution are profitable. Confirmation of the reorganization filing by the court appears to be unambiguously good news — the ARs on the final resolution date are +0.826%. However this increase is not

Fig. 2. CARs surrounding day FO.

Table 3 ARs surrounding the final resolution date (day R0)

+/−

G. sign test

ARt (%)

t (ARt)

+/−

G. sign test

ARt

t (ARt)

+/−

G. sign test

Difference Wilcoxon rank-sum test (%) Z Asymp. Monte Exact P Carlo P P

R − 10 R−9 R−8 R−7 R−6 R−5 R−4 R−3 R−2 R−1 R0 R+1 R+2 R+3 R+4 R+5 R+6 R+7 R+8 R+9 R + 10

21/41 24/38 21/41 18/44 16/46 15/47 20/42 24/38 26/36 25/37 26/36 29/33 28/34 27/35 22/40 25/37 22/40 24/38 18/44 26/36 27/35

− 4.015c − 4.107c − 4.015c − 3.724c − 3.516c − 3.408c − 3.920c − 4.197c − 3.920c − 4.015c − 3.823c − 3.621c − 3.724c − 3.823c − 4.107c − 4.015c − 4.107c − 4.107c − 3.724c − 3.920c − 3.823c

− 1.174 1.034 0.403 − 1.188 − 2.574 − 2.533 − 1.430 0.914 0.153 − 0.247 3.163 3.408 3.235 3.569 3.436 1.599 0.496 0.846 1.374 2.793 2.160

4.364c 0.714 0.210 − 1.208 0.589 0.654 − 1.579 − 0.502 − 0.622 − 1.438 1.553 1.818b 2.791b 4.617c 5.006c 4.374c 2.179b 1.997a 1.228 1.683a 1.077

10/26 16/20 11/25 9/27 6/30 5/31 11/25 14/22 15/21 12/24 21/15 19/17 20/16 20/16 19/17 15/21 14/22 15/21 12/24 16/20 16/20

− 2.803b − 2.521b − 2.934b − 2.666b − 2.201b − 2.023b − 2.934b − 2.934b − 2.803b − 3.059b − 1.826a − 2.201b − 2.023b − 2.023b − 2.201b − 2.803b − 2.934b − 2.803b − 2.803b − 2.201b − 2.201b

0.750 − 0.957 0.078 − 0.779 − 0.532 0.292 − 1.384 − 0.361 0.171 1.782 − 2.096 − 0.722 − 1.394 − 2.020 − 4.152 − 1.620 − 1.726 − 1.086 − 1.488 − 0.227 0.422

0.572 − 0.901 0.070 − 0.706 − 0.500 0.319 − 1.672a − 0.327 0.175 1.510 − 2.658b − 0.803 − 1.249 − 1.791a − 4.463c − 1.601 − 1.563 − 1.015 − 1.438 − 0.187 0.394

11/15 8 :/8 10/16 9/17 10/16 10/16 9/17 10/16 11/15 13/13 5/21 10/16 8/18 7/19 3/23 10/16 8/18 9/17 6/20 10/16 11/15

− 2.934b − 2.521b − 2.803b − 2.666b − 2.803b − 2.803b − 2.666b − 2.803b − 2.803b − 2.521b − 2.023b − 2.803b − 2.521b − 2.366b − 1.604a − 2.803b − 2.521b − 2.666b − 2.201b − 2.803b − 2.803b

−1.924 1.991 0.324 −0.409 −2.041 −2.825 −0.045 1.275 −0.018 −2.029 5.260 4.131 4.628 5.589 7.587 3.219 2.222 1.932 2.862 3.020 1.738

− 0.254 0.082 0.248 − 0.992 − 1.597 − 1.211 − 1.408 0.318 0.161 0.679 0.826 1.523 1.122 1.017 − 0.028 0.129 − 0.518 − 0.036 0.068 1.414 1.366

1.925a − 0.241 − 0.136 − 0.610 0.690 − 1.938a − 1.151 − 0.950 − 0.811 − 1.112 0.336 0.811 2.330b 4.076c 1.814a 2.185b 0.566 0.103 − 1.723a − 1.103 − 0.388

Winners

Losers

−4.015 −4.107 −4.015 −3.724 −3.516 −3.408 −3.920 −4.197 −3.920 −4.015 −3.823 −3.621 −3.724 −3.823 −4.107 −4.015 −4.107 −4.107 −3.724 −3.920 −3.823

0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

L.-C. Chi, T.-C. Tang / Economic Modelling 24 (2007) 749–767

Event Full sample day ARt t (ARt) (%)

a, b, c Significant at the 0.1, 0.05, and 0.001 levels, respectively.

759

760

Event Full sample window t (ARt) ARt (%)

+/−

G. sign test

ARt (%)

t (ARt) +/−

G. sign test

ARt (%)

t (ARt)

+/−

G. sign test

Difference Wilcoxon rank-sum test (%) Z Asymp. Monte Exact P Carlo P P

− 10, 10 − 5, +5 − 1, +1 − 1, 0 0, +1 0, +30 0, +60 0, +90 0, +120 0, +150 0, +180

26/36 27/35 30/32 27/35 26/36 27/35 17/45 11/51 15/47 13/49 13/49

− 4.015c − 3.920c − 3.516c − 3.823c − 3.920c − 3.921c − 4.015c − 3.621c − 4.016c − 3.922c − 3.920c

16.878 13.162 5.453 2.514 5.665 27.956 18.969 11.388 19.081 17.331 13.955

2.097b 3.100b 3.270b 2.114b 3.727c 3.482b 1.580 0.104 0.845 0.926 0.512

− 2.666b − 2.521b − 2.366b − 3.059b − 2.666b − 2.366b − 3.516c − 3.296c − 3.724c − 3.621c − 3.516c

− 10.873 −11.645 − 0.596 − 0.137 − 1.730 − 21.617 − 22.784 − 31.834 − 35.954 − 40.947 − 36.725

− 2.200b − 2.647b − 0.627 − 0.296 − 2.146b − 4.160c 3.633b − 2.583b − 3.151b − 1.843b − 2.577b

5/21 5/21 7/19 9/17 5/21 3/23 2/24 3/23 3/23 2/24 3/23

−2.023b −2.023b −2.366b −2.366b −2.023b −1.604a −1.342 −1.604a −1.604a −1.604a −1.826a

27.751 24.807 6.049 2.651 7.396 49.573 41.753 43.222 55.035 58.278 50.680

2.107 2.270 2.233 1.103 1.729 1.570 −3.254 − 11.617 −10.212 −13.688 −13.020

0.412 0.560 2.149 1.388 1.982a 0.626 0.099 − 1.502 − 1.196 − 1.374 − 1.504

Winners

Losers

a, b, c Significant at the 0.1, 0.05, and 0.001 levels, respectively.

21/15 22/14 23/13 18/18 21/15 23/13 14/22 8/28 12/24 11/25 10/26

−4.015 −3.920 −3.516 −3.823 −3.920 −3.920 −4.782 −4.458 −4.782 −4.623 −4.623

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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Table 4 CARs surrounding the final resolution date (day R0)

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761

Fig. 3. CARs surrounding by RO.

significant, since the t-statistic is only 0.336. A possible explanation for this might lie in the lack of uniform industry response, with a considerable subset of distressed firms recording negative AR changes and thus offsetting the positive results of the majority of firms. Winners (losers) experience an additional gain (loss) during the restructuring period when their final resolution is revealed. The gains and losses between winners and losers differ in magnitude ranging from +2.651% to + 58.278%, and the differences are statistically significant except in the

Fig. 4. CARs surrounding by RO.

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(R − 1, R0), (R0, R + 90), and (R0, R + 180) intervals. For winners, the overall mean CARs over windows (R0, R + 1), (R − 1, R + 1), and (R0, R + 30) are + 5.665%, + 5.453%, and + 27.956%, respectively. However, the losers exhibit a significantly negative and greater decline in CARs over all selected event intervals, ranging from − 0.137% to − 40.947%. The mean ARs for winners on 9 of the 21 event days are statistically different from zero, but only 4 of 21 event days are statistically significant for losers. The mean CARs for winners (losers) on 6 (9) of the 11 event windows are statistically different from zero. The non−parametric generalized sign test confirms the evidence that significant shifts occur both in the ratio of positive to negative AR observations and in the ratio of positive to negative CAR observations in the period surrounding the final resolution. The results allow us to reject the null hypothesis that the proportion of positive to negative returns is equal to the ratio in the estimation period. 3.3. Input feature selection In this section we analyze three different methods — sensitivity analysis (SA), principal components analysis (PCA), and genetic algorithm (GA) — of ranking the importance of input parameters, and of comparing their effectiveness on a hybrid GA-backpropagation network (BPN) approach (i.e., hybrid GA-BPNs) for discrimination that combines the population-based parallel search technique of GA and point-based gradient descent search of BPNs. More specifically, three input importance-ranking techniques — SA, PCA, and GA — are employed with a view to identifying the relevant and useful factors that play important roles in input variables. The resulting variables are then provided to construct hybrid GA-BPN models to classify and predict the investment winners. Tables 5 and 6 depict the results of input feature selection. We analyze sensitivity by calculating the Error, Ratio, and Rank. The results of SA indicate that the Error (Ratio) of our input variables in discriminating between winners and losers surrounding the reorganization filing (Model 1) is 0.701 (21.832) for firm size, 0.560 (17.450) for leverage, 0.543 (16.915) for liquidity, 0.433 (13.490) for profitability, 0.490 (15.249) for historical stock returns, and 0.530 (16.492) for competition. The relative importance (i.e., Rank) of these six variables for our Model 1 is firm size, leverage, liquidity, competition, historical stock returns, and profitability in descending order. The eigenvalues gained from the PCA are all over 1, indicating that the six corresponding eigenvectors make an important contribution to the total dispersal. The GA further confirms the Table 5 Input feature selection for model 1 Firm size

Leverage

Liquidity

Profitability

Historical returns

Competition

2 0.560 17.450

3 0.543 16.915

6 0.433 13.490

5 0.490 15.249

4 0.530 16.492

Panel B: Principal components analysis Eigenv's 9.174 8.711 Inform'n 0.997 0.999

2.816 0.999

1.699 0.999

1.411 0.999

1.065 0.999

Panel C: Genetic algorithm Useful Yes Importance of Inputs 0.255

Yes 0.200

Yes 0.075

Yes 0.120

Yes 0.116

Panel A: Sensitivity analysis Rank 1 Error 0.701 Ratio 21.832

Yes 0.233

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763

Table 6 Input feature selection for model 2 Firm size

Leverage

Liquidity

Profitability

Historical returns

Competition

3 0.699 2.046

1 0.779 2.278

6 0.471 1.379

4 0.697 2.038

5 0.522 1.528

Panel B: Principal components analysis Eigenv's 6.130 5.836 Inform'n 0.997 0.998

2.605 0.999

1.883 0.999

1.268 0.999

0.927 0.999

Panel C: Genetic algorithm Useful Yes Importance of Inputs 0.090

Yes 0.658

Yes 0.045

Yes 0.066

Yes 0.034

Panel A: Sensitivity analysis Rank 2 Error 0.719 Ratio 2.104

Yes 0.107

usefulness of these six inputs. The results of SA, PCA, and GA suggest that all the six variables are rated as of high sensitivity and usefulness and should therefore be retained in subsequent analyses. As to the discrimination between winners and losers surrounding the filing resolution (Model 2), the results of the SA presented in Panel A of Table 6 reveal that the order of importance (i.e., order of descending Error) of each input variable is liquidity (0.779), firm size (0.719), leverage (0.699), historical stock returns (0.697), competition (0.522), and profitability (0.471). The eigenvalues are all over 1, indicating the six corresponding eigenvectors account for greater importance in the total dispersal. The GA further confirms that all inputs are useful for characterizing or accounting for the variation (spread) of each dimension. To sum up, no inputs are pruned as a result of these analyses — all six of the input variables remain in our Model 2. 3.4. Results of hybrid GA-BPN models Our output is shown not only in mean square error (MSE) and root mean square error (RMSE), but also in terms of Type I and Type II errors. Percentage accuracy alone is an inadequate measure of performance since it ignores the extent of mistakes. The results of our hybrid GA-BPN models are readily comprehensible in the form of Table 7. Table 7 Results of hybrid GA-BPN models Model 1

Model 2

Training

Testing

Training

Testing

Panel A: Hit rate Overall accuracy rate Hit rate for winners Hit rate for losers

85.00% 100% 78.57%

82.61% 94.74% 74.08%

84.78% 94.74% 77.78%

86.54% 90.00% 84.38%

Panel B: Error RMSE MSE Type I error Type II error Average error

0.416 0.208 0% 15.00% 15.00%

0.735 0.265 2.17% 15.21% 17.39%

0.377 0.159 2.17% 13.04% 15.22%

0.405 0.309 3.85% 9.62% 13.46%

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In this study, the 6-52-2 architecture for the Model 1 and the 6-50-2 architecture for Model 2 perform extremely well. Panel A in Table 7 shows the percentage of classification accuracy using the six-variable models based on the hybrid GA-BPN approach. The overall classification accuracies are 85.00% for Model 1 and 84.78% for Model 2. These results are significantly much higher than a proportionate two-group random classification of 54.88% and 50.62%, respectively. Further, classification accuracies are reported for each subset. The predictive performance of the two constructed models is evaluated using the untouched testing data (second period sets). This is due to the fact that superior training ability does not always guarantee the validity of the prediction accuracy. The next section of Panel A reveals the prediction accuracy for the testing sample. The prediction accuracies for Models 1 and 2 are 82.61% and 86.54%, respectively, significantly better than the proportionate chance predictions of 53.92% and 52.30%. The results suggest that the hybrid GA-BPNs' performance on the testing data provides a good indication of its ability to generalize and handle data it has not been trained on. Another approach in this endeavor for evaluating predictive performance is to investigate whether error measures between the actual testing data returns and their predicted values are small. The error measures of both models are reported in Table 7B. As indicated in this table, the training data lead to RMSE (MSE) values of 0.416 (0.208) for Model 1 and 0.377 (0.159) for Model 2. The rates of Type I error, Type II error, and average error are 0%, 15.00%, 15.00% and 2.17%, 15.04%, 15.22% for Models 1 and 2, respectively. The results of error measures for testing datasets are reported in the next section of Table 7B, and are generally similar to those reported for the training set. In sum, the results suggest that the models developed by hybrid GA-BPN produce a consistent estimate between the training set and testing set; that is, both Model 1 and Model 2 are consistent and stable. Another notable observation is that the results reveal that the hybrid GABPNs are superior in classifying winners. 4. Summary and conclusions Stock investment has become a means of individual finance. It is important for investors to estimate the stock price and either verify the trading chance or move against it accurately ahead of others in the Market. This paper presents the risky but significantly lucrative investment opportunities available in the stocks of financially troubled firms. More importantly, we demonstrate that it is possible to develop ex ante trading strategies and identify the characteristics of winners, and to predict between winners and losers to a high degree of accuracy. Distressed investors can, then, translate the often-confusing lexicon of the reorganization process into a profitable investment vehicle. Our study indicates that a respective 30.65% and 46.77% probability of being a winner generates one-month + 25.438% and + 27.956% cumulative abnormal returns around two major events, namely F0 and R0. Another observation is that the winners gain significantly during the two 191-day event periods, i.e. windows (F − 10, F + 180) and (R − 10, R + 180), while substantial reverse valuation effects are reported for losers. Furthermore, the returns between winners and losers differ in magnitude ranging from +5.065% to +88.777% and +2.651% to + 58.278%, respectively, over selected event windows (F − 10, F + 180) and (R − 10, R + 180) (Figs. 5 and 6). Another component of this study focuses explicitly on the classification and prediction of winners from distressed-stock investment using six variables available at the beginning of two major events, F0 and R0. We apply three input selection techniques relative to the rank of input importance, the SA, PCA, and GA, to hybrid GA-BPN models that can help us identify sensible and useful factors that play important roles as dependent variables. In addition, we employ a hybrid approach for

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Fig. 5. ARs from days F − 180 to F + 180 surrounding the filing.

discrimination that combines the population-based parallel search technique of GA and point-based gradient descent search of the BP algorithm. This procedure is used to select the test solution vector for the testing sample so that the overfitting in the training sample can be lowered. Our six-variable hybrid GA-BPN models perform quite well, correctly classifying 85.00% in Model 1 and correctly classifying 84.78% in Model 2. The prediction accuracies for the testing dataset are 82.61% and 86.54%, respectively, for Models 1 and 2. Our results may be particularly

Fig. 6. ARs from days R − 180 to R + 180 surrounding final resolution.

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