1 Bankruptcy Prediction, an Extension of the Campbell Model: Evidence From the United
States By: Ton Kremer1
University of Groningen Faculty of Economics and Business
MSc Finance Supervisor: P.P.M. Smid
Date: June 11, 2019
Abstract
This paper presents an answer to the question whether including the trading volume of the stock, in the bankruptcy prediction model as proposed by Campbell, Hilscher, and Szilagyi (2008), increases the fit of the model. The data used to determine the fit of the model is based on companies in the United States starting in 1990 up until and including 2018. In total, the population includes 121,623 observations, of which 308 are bankruptcies. The estimation sample includes 4,535 observations of which 64 are bankruptcies This paper presents evidence that trading volume, significant at the 1% significance level, improves the fit of the Campbell et al. (2008) model for predicting bankruptcies. Specifically, it improves the overall fit of the model by 1.17 percent point to 98.88%. Furthermore, the Pseudo R2 of the model including trading volume is 0.901 compared to 0.814 when not including trading volume.
JEL Classification: C53, G11, G33
Keywords: Forecasting and Prediction Methods, Investment Decisions, Bankruptcy Word count: 11,150
2 Introduction
The financial crisis of 2008 left a scar for investors, providers of debt and policymakers. The GDP in the United States took a hit of 2.08% in 20082. The damage caused to the economy was partially the result of firms going bankrupt. A lot of people lost their job, shareholders of these firms lost some, if not all, of their investments in the company, as mentioned by Wood (2011). Some people still experience the effect of the crisis to this day. Additionally, Altman (1984) argues that bankruptcy costs are not trivial and in some cases are as high as 20% of the firm value. If a bankruptcy would only harm the economy, it would be desirable to be able to prevent all bankruptcies. In contrast, Boratyńska and Grzegorzewska (2018), argue that a bankruptcy is good for the economy when bankruptcies eliminate individual unprofitable firms. On the other hand, bankruptcies are not good for the economy when it takes on a “knock-on effect” then it might seriously affect the economic equilibrium. In conclusion, it would be beneficial to have a model which predicts whether a company might go bankrupt or not, without any errors. However, due to the variety of causes, developing a model without errors is hardly possible. The best possible alternative is to give a probability of a firm going bankrupt. Being able to predict a bankruptcy would open the opportunity to act on such an event and hereby mitigate eventual damage. This research attempts to improve the predictive power of the Campbell et al. (2008) model by including the trading volume of the stock. Trading volume is expected to have predictive power because a perfectly rational, profit-maximizing, market participant, wants to sell shares which do not provide upside potential.
In the past, numerous bankruptcy prediction models have been developed; for example, by Altman (1968), Ohlson (1980), Campbell et al. (2008), and Cheng, Jones, and Moser (2018). These models have accounting statements as backbone and/or adjust the book values used in accounting to market data. Altman uses the discriminant analysis, whereas Campbell et al. (2008) and Ohlson (1980) use a logit model and Cheng et al. (2018) use a machine learning technique called the gradient boosting model.
When considering the ease of adjusting accounting statements and using several accounting tricks to delay investments, it might be tempting to argue that the models based on accounting statements contain a certain bias. The issue of adjusting accounting statements could be overcome by disconnecting accounting statements from the model and relying solely on market data. However, when only considering market data, there are only a few variables available and crucial accounting variables are omitted. Therefore, variables based on accounting statements must be included in the analysis. Nonetheless, market data is incorporated in the accounting statements via performance ratios.
3 Cheng et al. (2018) conducted an empirical research related to the approach of exclusively including market data in the model. Cheng at al. (2018) explain that the model keeps including new variables into the model, often more than 100 variables, and replaces the weak variables with new variables to increase the predictive power of the model. They conclude that insider trading behavior adds predictive power to the Campbell et al. (2008) model. However, insider trading is hard to measure directly because it is illegal. Furthermore, they also find that there is less insider trading activity six months prior to bankruptcy. Besides insiders, they have also added a variable of institutional ownership. By doing so they captured a large part of the investors, specifically those who are more likely to have more information about the company, due to excessive research or other sources of information. They conclude that institutional ownership also adds predictive power to the model proposed by Campbell et al. (2008). However, their model does not include the trading volume of the stock.
Unfortunately, not all accounting statements can be adjusted for market data, because financial statements are not published daily. A solution could be using quarterly reports, the so-called “10Q filings” as mentioned by Baldwin and Glenzen (1992). Even though quarterly reports are not audited, Baldwin and Glenzen (1992) state that these reports add predictive power because it contains more recent information in most cases compared to annual reports.
In this paper, the following research question is answered: does adding the trading volume of the stock to the Campbell et al. (2008) model improve the fit? A measure for the trading volume of the stock over the last quarter before bankruptcy is added to the model as proposed by Campbell et al. (2008). Specifically, a ratio which measures the previous quarterly trading volume divided by the quarterly average of the previous year. Whereas in previous research Cheng et al. (2018) measured insider trading and institutional ownership, this research uses the trading volume which is directly observable. The data used in the model is of United States exchange-listed firms from the period 1990 up until and including 2018. Furthermore, several control variables are added to the model to investigate whether there is a difference in the predictive power between different time periods, i.e. before the crisis of 2008 and after the crisis of 2008. Also, a lag of trading volume is added to the model to check for robustness of the effect.
4 This research finds evidence that trading volume improves the fit of the Campbell et al. (2008) model, compared to the model without trading volume. Specifically, in sample, firms that have a higher trading volume one quarter preceding a bankruptcy compared to the previous year quarterly average, are more likely to be predicted to go bankrupt compared to firms that do not go bankrupt. This result is robust when looking at two, three and four quarters ahead of the bankruptcy. This result is in line with Ramalingegowda (2014), Seyhun and Bradley (1997), Piotroski and Roulstone (2004), Zavgren, Dugan, and Reeve (1988), Yulung Ma (2001) and Frino, Jones and Wong (2007) who find that there is more trading volume preceding a bankruptcy. But it contrasts with Cheng et al. (2018), who claim that there is less trading activity preceding a bankruptcy. Furthermore, this research finds evidence that firms that are likely to go bankrupt have specific characteristics in common, for example the trading volume as mentioned above, as well as firms that do not go bankrupt.
Section two contains a review of the theoretical framework, followed by the empirical results of previous studies. The second section ends with formulating the hypotheses about the prediction of bankruptcy by incorporating the trading volume of the stock. The third section describes the research methodology. Section four gives an overview of the data. The fifth section presents the results of the study and explains the robustness of the results. This research will be concluded with the main results and a discussion of the limitations of the study.
2. Literature overview
The first part of this section contains theories that form the basis of the research, followed by a discussion of the different models that have been developed to predict bankruptcies. Thereafter, empirical results are discussed. Finally, this section will be concluded in formulating the hypothesis.
2.1. Theories to predict a bankruptcy
5 fail to provide better predictions than this model proposed more than 50 years ago. In addition, the model can also be used for private firms, since private firms do not have market data available. However, Altman, Iwanicz-Drozdowska, Liatinen, and Suvas (2017) find that occasionally some models do outperform the Altman Z-score. Nevertheless, Boda and Uradníček (2016) and Altman et al. (2017) find that the Altman Z-score is still applicable today. Furthermore, Altman (1983) argues that the Book Value of Equity must be replaced by the Market Value of the equity in the original model. Ohlson (1980) argues that there is a significant issue when using an MDA, namely the variance-covariance matrices of the predictors should be the same for the bankrupt firms and non-bankrupt firms in the analysis. In addition, it is also required that the predictors are normally distributed. Furthermore, Altman (1968) clusters the Z-scores in groups that infer at which level a company is likely to go bankrupt. The Z-score without the context; of the bankruptcy zone, grey zone, and survivor zone does not provide any information. In addition, Ohlsen (1980) argues that failed and non-failed firms must be matched on industry or other characteristics, such as size. He finds that there is a difference between firms when considering the industry. These industry characteristics tend to be arbitrary because the researcher can create his own characteristics. Furthermore, Jones (1987) argues that the MDA does not consider previous probabilities and assumes an equal probability of the group based on sample proportions. To avoid these two issues, Jones (1987) suggests using a logit or probit analysis.
Ohlson (1980) developed an alternative to the Altman Z-score, the Ohlson O-Score, which is based on a logit model. The Ohlson O-model is a 9-factor linear combination model, also based on accounting statements. The regressed variables are size, leverage, current assets, liquidity, capital structure, profitability, cash flow, income or loss, and net income. Ohlsen also addresses a disadvantage of his model, namely that it does not utilize any market transactions, and suggests that adding market data to the model would increase its predictive power. In addition, Jones (2017) also addresses the necessity to look beyond accounting statements. Nevertheless, Ohlson concludes that the model he proposed is better in predicting a bankruptcy than the Altman Z-score. In contrast to Ohlson, Campbell et al. (2008) argue that an upgrade to of the Altman Z-score is a better model compared to the Ohlson O-score.
6 Although they argue that the model can be used in forecasting a default it is not an improvement to already existing models. Campbell et al. (2008) and Jones (2017) did also include the Merton DD model in their analysis and conclude that it is not the best model in their analysis.
Campbell et al. (2008) improved the model proposed by Altman by adding market data to the model. Subsequently, They changed some of the Altman ratios to market-based ratios. In addition to the model as proposed by Altman (1968), they added market data to the model to increase its predictive power. Moreover, Pham Vo Ninh, Do Thanh and Vo Hong (2018) find financial ratios to be of significant importance when predicting bankruptcies in Vietnam.
Cheng et al. (2018) developed a new model to predict bankruptcies by adding the insider activity and institutional holdings to the model proposed by Campbell et al. (2008). They consider the model as proposed by Campbell et al. (2008), as the best-suited model. Their model is based on three stages. The first stage is to determine the “Campbell score”. The second stage considers trading behavior of insiders and institutions. In the last stage, one attempts to predict the bankruptcy, incorporating the first and second stage. Where Ohlsen (1980) suggested in 1980 to incorporate market data in the model, Cheng et al. (2018) added the trading volume of the stock, via an instrumental variable, to the model.
In conclusion, former researchers depended during most of their analysis on accounting statements provided by the firms. But as time passed, they started to focus more on data provided by the market in combination with data provided by the firms. Even though in recent years researchers have tried to use new or upgraded methods and data to improve the predictions concerning bankruptcies, they still use the accounting statements provided by the firms.
2.2. Empirical results of the trading volume of the stock in relation to bankruptcies
Where Ohlson (1980) suggested in 1980 to add market data to the model to predict bankruptcy, some studies have transformed accounting data into market adjusted data, such as Campbell et al. (2008) and Cheng et al. (2018). According to Ramalingegowda (2014), institutional investors are better informed compared to other investors and therefore sell more shares when they think a firm is likely to go bankrupt, specifically one quarter ahead of bankruptcy. This would indicate that trading volume could provide information about a future bankruptcy.
7 Ramalingegowda (2014), find that institutions sell more shares when they think a firm is likely to go bankrupt. This provides evidence that there is an increase in trading volume by some investors in the market. Furthermore, Frino et al. (2007) and Zavgren et al. (1988) find an overall increase in trading volume preceding a bankruptcy in Australia and the United States. According to Frino et al. (2007), this effect is caused by negative returns of firms that go bankrupt.
In other studies, Frino, Jones, Lepone, and Wong (2014), and Precourt and Oppenheimer (2015) find that there is no change in the trading volume directly preceding a bankruptcy. Frino et al. (2014) and Precourt and Oppenheimer (2015) find that there is a sell-off by institutional investors approximately one year preceding a bankruptcy. Unlike the research outcomes of Ramalingegowda (2014), Zavgren, Dugan, and Reeve (1988), Seyhun and Bradley (1997), Yulung Ma (2001) and Frino et al. (2007), who find an increase of trading volume directly preceding a bankruptcy.
In addition, Cheng et al. (2018) find less trading activity by insiders and institutional investors preceding a bankruptcy. They support their findings by the information institutions possess, and that institutional investors probably do not hold stocks of firms that go bankrupt. On the other hand, this kind of insider trading is illegal by United States law, and therefore the insiders should not trade.
Furthermore, Gebka, Korczak, Traczykowski, and Korczak (2017) find that portfolios mimicking the number of shares insiders hold in their own European company generate profits. Which is in line with the semi-efficient market hypothesis, that insiders have a competitive advantage according to Piotroski and Roulstone (2004). The insiders can trade on information prior to the aggregate market. Although, Gebka et al. (2017) do not provide a specific direction whether there is an increase or decrease in trading volume Ramalingegowda (2014), Zavgren et al. (1988), Seyhun and Bradley (1997), Yulung Ma (2001) and Frino et al. (2007) do observe a direction of this effect. In Addition, Clark and Weinstein (1983) address that the trading in stocks is usually prohibited a couple of days preceding a bankruptcy, this is because companies are sometimes mentioned in newspapers with the prediction that they might file for bankruptcy in a couple of days. Therefore, the days preceding a bankruptcy cannot be used in the proposed model within this research.
8 2.3. Hypothesis
The previous studies have predicted bankruptcies according to different models but did not incorporate the trading volume of the stock in the model. This research tests whether the trading volume of the stock increases the fit of the model proposed by Campbell et al (2008). The estimation period of the model focusses on firms that went bankrupt from 1991 until 2018 in the United States. Firstly, this research tests whether the trading volume of the stock is significantly related to a bankruptcy. Therefore, the following hypothesis is formulated:
H1 = The trading volume of a stock adds predictive power when predicting a bankruptcy.
Finally, via testing this hypothesis this research draws inference about whether to include trading volume in an estimation model when prediction a bankruptcy, or to leave it out of the model. This inference is tested via several robustness tests, which is explained in Section 5.2.
3. Methodology
The first part of this section contains the model as proposed by Campbell et al. (2008). The second and last part of this section contains a detailed description of the proposed model, which includes trading volume as used by Campbell et al. (2008).
3.1. The Campbell bankruptcy prediction model
To be able to measure the probability of future bankruptcies Campbell et al. (2008) use a logit model as suggested by Shumway (2001) and Chava and Jarrow (2004) to estimate the probabilities of next periods bankruptcy. They find that their model has the highest predictive power compared to the models as estimated by Shumway (2001) and Chava and Jarrow (2004). Furthermore, they transform accounting-based ratios using market data as suggested by Ohlsen (1980). Campbell et al. (2008) use the model in equation (1), where 𝛽𝑥𝑖 is estimated as expressed in equation (2). 𝑃𝑡−1(𝑌𝑖𝑡 = 1) = 1 1+exp (−𝛼− 𝛽𝑥𝑖,𝑡−1) (1) 𝛽𝑥𝑖,𝑡−1 = 𝛽1𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺𝑖,𝑡−1,𝑡−12+ 𝛽2𝑇𝐿𝑀𝑇𝐴𝑖,𝑡−1+ 𝛽3𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺𝑖,𝑡−1,𝑡−12+ 𝛽4𝑆𝐼𝐺𝑀𝐴𝑖,𝑡−1,𝑡−3+ 𝛽5𝑅𝑆𝐼𝑍𝐸𝑖,𝑡−1+ 𝛽6𝐶𝐴𝑆𝐻𝑀𝑇𝐴𝑖,𝑡−1+ 𝛽7𝑀𝐵𝑖,𝑡−1+ 𝛽8𝑃𝑅𝐼𝐶𝐸𝑖,𝑡−1+ 𝐶𝑂𝑁𝑆 + 𝜀𝑖𝑡 (2)
9 presented in equation (3) and (4) respectively. An overview of the definitions and the calculations of the variables is presented in Table F.1.
𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺𝑖,𝑡−1,𝑡−12= 1−∅3 1− ∅12(𝑁𝐼𝑀𝑇𝐴𝑡−1,𝑡−3 + ⋯ + ∅ 9𝑁𝐼𝑀𝑇𝐴 𝑡−10,𝑡−12) (3) 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺𝑖,𝑡−1,𝑡−12= 1−∅ 1− ∅12(𝐸𝑋𝑅𝐸𝑇𝑡−1 + ⋯ + ∅ 11𝐸𝑋𝑅𝐸𝑇 𝑡−12) (4) Where ∅ = 2−13.
10 market, hence have more growth opportunities, are expected to be riskier, and therefore more likely to go bankrupt. Moreover, this ratio could also be negative due to a negative book value of the equity, which is expected to indicate a higher probability of bankruptcy. Lastly, the log of one plus the price per share is measured as (𝑃𝑅𝐼𝐶𝐸𝑖,𝑡−1), which is also based on the price on the last day of the last quarterly available report. This contrasts with Campbell et al. (2008), who measure this as the log of the share price. This research is aimed to find a different way to measure the variable because this makes it easier to interpret the variable. This variable is included to capture the tendency for distressed firms to trade at low share prices as mentioned by Campbell et al. (2008). The log is taken to bring the variable to a more normal range. Firms that trade at low prices have experienced a huge sell off shares already, the market does not want to hold shares of the company and in turn, is expected to go bankrupt earlier. In case companies have not published the new quarterly report yet when bankruptcy happens in, for example, the first week of the next quarter, the 10Q report of the previous quarter is taken. Hence, the quarterly data used is not older than six months. 𝑆𝐼𝐺𝑀𝐴𝑖,𝑡−1,𝑡−3 = (252 ∗ 1 𝑁−1∑ 𝑟𝑖,𝑘 2 𝑘∈{𝑡−1,𝑡−2,𝑡−3} ) 1/2 (5)
Where N is the number of observations, k is the length of the lag, r is the return, multiplied by 252 for the number of trading days in a year. Finally, the square root is taken to obtain the standard deviation.
3.2. The Campbell model extended with the trading volume of the stock
To examine the effect of trading volume the model as proposed by Campbell et al. (2008) is extended. The variable added to the model is the trading volume of the stock, expressed as (TVOLi, t-1). The basic logit model does not change and remains the same as presented in equation
(1). The model is extended with the trading volume of the stock, see equation (6).
𝛽𝑥𝑖,𝑡−1 = 𝛽1𝑇𝑉𝑂𝐿𝑖,𝑡−1+ 𝛽2𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺𝑖,𝑡−1,𝑡−12+ 𝛽3𝑇𝐿𝑀𝑇𝐴𝑖,𝑡−1+
𝛽4𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺𝑖,𝑡−1,𝑡−12+ 𝛽5𝑆𝐼𝐺𝑀𝐴𝑖,𝑡−1,𝑡−3+ 𝛽6𝑅𝑆𝐼𝑍𝐸𝑖,𝑡−1+ 𝛽7𝐶𝐴𝑆𝐻𝑀𝑇𝐴𝑖,𝑡−1+ 𝛽8𝑀𝐵𝑖,𝑡−1+ 𝛽9𝑃𝑅𝐼𝐶𝐸𝑖,𝑡−1+ 𝐶𝑂𝑁𝑆 + 𝜀𝑖𝑡 (6) Trading volume is unlike Cheng et al. (2018) directly observed. Trading Volume (𝑇𝑉𝑂𝐿𝑖,𝑡−1) is measured by dividing the trading volume of the previous quarter by the average quarterly trading volume of the year before the previous quarter as shown in equation (7).
𝑇𝑉𝑂𝐿𝑖,𝑡−1 = ∑𝑡−3−1 𝛿𝑡
(∑−15𝑡−4𝛿𝑡) 1 4
(7)
11 of the company any longer, and therefore sell the shares. This results in a larger than average trading volume.
There might be a problem which reduces the reliability of the model, specifically because many observations could not be included while estimating the model due to missing data.
Besides that, the receiving operator curve (ROC) curve is estimated. The ROC curve, as explained by Woods and Bowyer (1997) estimates the best cut-off point based on sensitivity and specificity. Sensitivity is the number of correctly detected bankruptcies and specificity is the correct number of survivors detected by the model. A test with a perfect septation has a ROC curve which passes through the upper left corner. Zweig and Campbell (1993) explain that the closer the ROC curve to the upper left corner, the more accurate the test is. Subsequently, the model is extended with several lags on the trading volume of the stock to test which period of trading volume of the stock add the most value to the model. Also, the estimation period will be split in a period up until and including 2008 and 2009 up until and including 2018. In addition, the data will be trimmed, correcting for potential outliers, to check for robustness. Lastly, the sample will be censored for firms who do not hold any current assets, as will be explained in Section 5.2. To draw inference which model has a better fit, the classification tables will be compared. The model which has the best fit is the model with the highest number of correct classifications. The separate classifications will also be discussed.
4. Data description
The first part of this section contains a brief description of the population followed by a detailed description of the sample, starting with a definition of the bankruptcy variable and the data sources as well as an overview of the sample per year. The second and last part of this section contains a detailed discussion of the summary statistics, which contains the average, standard deviation, minimum, maximum, median, skewness, kurtosis and the number of observations per variable.
4.1. Description
12 during the dot com bubble. After the credit crisis of 2008, bankruptcies of exchange-traded firms continued to happen, indicating that some firms might still experience trouble from the crisis, even after the economy has recovered from most of the crisis. Furthermore, from COMPUSTAT the specific data about the companies was obtained. Whenever certain data was not available in COMPUSTAT, the data was obtained via Center for Research in Security Prices (CRSP) or Bloomberg.
Table I
Data Population: number firms and of (Non) Bankruptcies per year
This table contains an overview of the population and the firms included in the sample separated per year. In the first column, the year is specified, in the second column, the total number of firms in the year in the population is specified. In the third column, the non-bankrupt firms in the population are presented. In the fourth column, the number of bankrupt firms in the population are specified. The fifth column contains the total number of firms included in the estimation sample. The sixth column contains the firms that did not go bankrupt in the estimation sample. The last column contains the firms that went bankrupt in the estimation sample.
Population Estimation Sample
Year Total firms in population
Non-Bankruptcies
13 Certain companies did not provide quarterly reports at all or stopped providing them a couple of quarters ahead of the bankruptcy. Due to these missing values, these companies had to be eliminated from the sample, because they were no longer useable to estimate the model. Due to unavailability of data before 1998, all companies, the survivors and bankrupt firms, have been eliminated from the sample. If a company had other missing values for one of the explanatory variables, the entire company has been eliminated from the sample.
When considering 𝑅𝑆𝐼𝑍𝐸 90,446 observations are not taken into consideration in the analysis. 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺 leads to 45,697 missing values. 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺 results in 38,534 unavailable observations. 𝑇𝐿𝑀𝑇𝐴 consists of 91,565 unobtainable datapoints. 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 consists of 91.565 missing values. 𝑆𝐼𝐺𝑀𝐴 has 107,292 unavailable observations. 𝑃𝑅𝐼𝐶𝐸 consists of 45,790 unreported datapoints. 𝑀𝐵 consists of 91,544 missing values. Whereas 𝑇𝑉𝑂𝐿 contains 45,624 missing values. The number of bankrupt companies that were left, after correcting for missing values, is 64. Due to the missing data, in total 244 observations (bankruptcies) cannot be used in the estimation due to missing values. The firms that are included in the sample are all firms with observations between 1990 and 2018 on a quarterly basis. Hence, a firm with all data present in four quarters a year is included four times in that specific year. After the correction for missing value, 4,471 firms (zeros) were left on the estimation sample that did not go bankrupt, compared to 64 firms that did go bankrupt.
4.2. Summary Statistics
Table II summarizes the nine explanatory variables used to estimate the model. The top part of the table consists of the entire estimation sample, whereas the middle part consists of only bankrupt firms and the bottom part of the non-bankrupt firms. As can be observed in Table II, the total number of observations used to estimate the model deviate significantly between the bankrupt and non-bankrupt firms. When applicable the variables will be compared with the paper of Campbell et al. (2008).
16 Table II
Overview of the data estimation sample
The table stated below provides an overview of the estimation sample data. The first part contains data about the entire estimation sample, the second part contains data about the sample which only contains bankrupt firms and the last part contains data which only includes data about firms that did not go bankrupt. An explanation of the variables is given Section 3.2 and 3.3. The first column contains the name of the variable, the second column contains the number of observations. The third column contains the mean of the observations, including a † when the means differ at the 1% significance level. The fourth column contains the standard deviation of the observations. The fifth column contains the minimum value of the observations and the sixth column contains the maximum value of the observations. The seventh column contains the median of the observations. The eighth column contains the skewness of the observations, including a * when non-normally distributed. The last column contains the kurtosis of the observations. The last variable presented (𝐶𝑃𝑅𝐼𝐶𝐸) is the price as calculated according to Campbell et al. (2008).
Full Estimation Sample
N Mean Std.Dev min max Median skewness kurtosis
Bankrupt 4,535 .014† .118 0 1 0 8.239* 68.874 TVOL 4,535 .355† .51 .006 31.173 .323 49.993* 2951.703 NIMTAAVG 4,535 .021 .631 -1.584 42.386 .012 66.757* 4483.183 TLMTA 4,535 .661† .254 .043 2.596 .649 .361* 3.637 EXRETAVG 4,535 .001† .054 -.815 .632 0 .366* 40.179 SIGMA 4,535 .55† 12.613 .016 847.965 .247 66.895* 4494.357 RSIZE 4,535 -.1† .74 -4.846 1.572 -.026 -1.559* 8.753 CASHMTA 4,535 .197† .149 0 2.051 .177 1.491* 10.349 MB 4,535 .178 222.851 -12,900 3,399.45 2.364 -46.079* 2612.287 PRICE 4,535 1.635† .381 .001 3.676 1.684 -.815* 7.911 CPRICE 4,535 1.609† .456 -2.824 3.675 1.675 -2.436* 18.333 Bankrupt Sample
N Mean Std.Dev min max Median skewness kurtosis
17
Non-Bankrupt Sample
N Mean Std.Dev min max Median skewness kurtosis
Bankrupt 4,471 0 0 0 0 0 . . TVOL 4,471 .334 .089 .065 1.512 .323 4.808 47.477 NIMTAAVG 4,471 .023 .635 -1.584 42.386 .013 66.454 4,434.875 TLMTA 4,471 .658 .251 .043 2.051 .645 .262 2.873 EXRETAVG 4,471 .002 .054 -.815 .632 .001 .413 42.155 SIGMA 4,471 .332 .678 .016 28.969 .245 28.561 1,003.767 RSIZE 4,471 -.056 .639 -3.806 1.572 -.013 -.694 4.816 CASHMTA 4,471 .196 .148 0 2.051 .177 1.502 10.638 MB 4,471 .219 224.436 -12900 3399.45 2.397 -45.756 2575.663 PRICE 4,471 1.655 .343 .066 3.676 1.688 -.224 7.464 CPRICE 4,471 1.64 .364 -.783 3.675 1.679 -.658 8.797
* indicating a non-normal distribution
† indicating a difference in means at the 1% significance level
Furthermore, the data is also validated for correlation, as presented in Table A.1. Observing the table, it can conclude there is a no severe multicollinearity problem in the model. Decisively most explanatory variables differ significantly across the bankrupt and non-bankrupt firms. This would indicate that the estimated model has a good fit.
5. Results
This section discusses the results of the analysis. Starting in the first section with a discussion of the empirical results. Followed by several robustness tests in the second section. 5.1. Empirical Results
A linear probability model suffers in most cases from heteroskedasticity and/or the issue that the estimated probabilities exceed the zero and one bound. To overcome these problems robust standard errors are used, as well as a logit model. Firstly, the model is estimated, as presented in Table III. The first column presents the variables, whereas the second column presents the full model, and the third column presents the reduced model. As shown in Table III column two, 𝑇𝐿𝑀𝑇𝐴 is not significant at the 10% significance level, therefore the model is re-estimated without 𝑇𝐿𝑀𝑇𝐴 and presented in column three, see Table III. Hereafter, the log odds of the reduced model are converted into odds as presented in Table IV, column three. Furthermore, column one presents the variables, column two the reduced model with log odds, and the last column presents the average marginal effects.
19 Table III
Results estimated model
The table below contains the estimated model. The variables in the first column are explained in Section 3.2 and 3.3. In the second column, the full model is estimated via the logit model. The third column contains the reduced model. Both models have been corrected for heteroskedasticity using robust standard errors. 𝑇𝑉𝑂𝐿 measures the trading volume, 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺 is a measure for the profitability, 𝑇𝐿𝑀𝑇𝐴 is a measure for the amount of debt used by the firm, EXRETAVG is a measure for the excess return to the index, 𝑆𝐼𝐺𝑀𝐴 is a measure for volatility, 𝑅𝑆𝐼𝑍𝐸 is a measure for the size of the firm. 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 is a measure for liquidity, 𝑀𝐵 is the market to book ratio of the firm and 𝑃𝑅𝐼𝐶𝐸 is calculated as the log of one plus the price. The formulas behind the variables are presented in Table F.1.
(1) (2)
VARIABLES Model 1 Full model Model 2 Reduced model
TVOL 6.919*** 7.000*** (1.129) (1.085) NIMTAAVG -2.160** -2.226*** (0.878) (0.836) TLMTA -0.892 (1.894) EXRETAVG -4.589** -4.276** (2.168) (2.075) SIGMA 0.212** 0.206** (0.091) (0.089) RSIZE -2.474*** -2.379*** (0.455) (0.349) CASHMTA -5.446*** -5.555*** (1.887) (1.756) MB 0.001*** 0.002*** (0.000) (0.000) PRICE -2.127** -2.158*** (0.846) (0.799) Constant -7.084*** -7.582*** (1.559) (1.266) Observations 4,535 4,535 Pseudo R2 0.901 0.901
20 Table IV
Results estimated model
The table below contains the estimated model. The variables in the first column are explained in Section 3.2 and 3.3. In the second column, the model is estimated via the logit model. The third column contains the same model, but the log odds are converted into odds. In the last column, the odds are converted into the increase in probability to make them interpretable. Multiplying the presented value (3) by 100 provides the effect in percentage points. All models have been corrected for heteroskedasticity using robust standard errors. 𝑇𝑉𝑂𝐿 measures the trading volume, 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺 is a measure for the profitability, 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺 is a measure for the excess return to the index, 𝑆𝐼𝐺𝑀𝐴 is a measure for volatility, 𝑅𝑆𝐼𝑍𝐸 is a measure for the size of the firm. 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 is a measure for liquidity, 𝑀𝐵 is the market to book ratio of the firm and 𝑃𝑅𝐼𝐶𝐸 is calculated as the log of one plus the price. The formulas behind the variables are presented in Table F.1.
(1) (2) (3)
VARIABLES Model 1 Log Odds Model 1 Odds Model 1 Margins
TVOL 7.000*** 1,096.708*** 0.013*** (1.085) (1,189.983) (0.003) NIMTAAVG -2.226*** 0.108*** -0.004*** (0.836) (0.090) (0.001) EXRETAVG -4.276** 0.014** -0.008* (2.075) (0.029) (0.004) SIGMA 0.206** 1.229** 0.0004** (0.089) (0.110) (0.000) RSIZE -2.379*** 0.093*** -0.004*** (0.349) (0.032) (0.001) CASHMTA -5.555*** 0.004*** -0.010*** (1.756) (0.007) (0.003) MB 0.002*** 1.002*** 2.84e-06*** (0.000) (0.000) (0.000) PRICE -2.158*** 0.116*** -0.004*** (0.799) (0.092) (0.001) Constant -7.582*** 0.001*** (1.266) (0.001) Observations 4,535 4,535 4,535 Pseudo R2 0.901 0.901
Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
21 running the risk of being deemed to go bankrupt and making the proposed model more precise. Moreover, the model including trading volume has a 1.12% misspecification for specificity compared to 2.26% when not including trading volume. A 1.56% misspecification on sensitivity compared to 4.69% for the model not including trading volume. Furthermore, it has misspecification when predicting in sample survivors of 44.25% compared to 62.35% when not including trading volume. A 0.02% misspecification when prediction a bankruptcy compared to 0.07% when not including trading volume. Conclusively, adding trading volume to the model improved the goodness of fit of the model by 1.17 percent point from 97.71% to 98.88%. Including trading volume in the model resulted in a large improvement for predicting in sample whether a firm is a survivor or not (see Table V, positive predictive value). The high overall fit of the model is caused by variables which deviate significantly between the bankrupt firms and the survivors. For example, the TVOL for firms that go bankrupt is in most cases higher than firms that do not go bankrupt. Furthermore, the PRICE of a firm that does not go bankrupt is significantly higher than a firm that does go bankrupt. As expected, the firms that go bankrupt experience, mostly negative returns in comparison to the S&P 500 a quarter preceding a bankruptcy, whereas firms that do not go bankrupt experience mostly positive excess returns to the S&P 500.
Furthermore, in Figure I, the predicted versus the actual bankruptcies are plotted. This figure indicates that the model overclassifies the number of bankruptcies. The first bankrupt firm in the sample starts in 2000, whereas the first non-bankrupt firm starts in 2006, hence before 2006, no firm can be predicted to go bankrupt that did survive.
Table V Classification table
The table presented below contains the classification table of the logit model. The top part of the table contains the results of the estimated model. Whereas the middle part contains the incorrect predicted values. The bottom part contains the total fit of the model. The second column presents the results of the model including trading volume, the third column presents the results for the model as proposed by Campbell et al. (2008) with the data of this research. The last column presents the difference between the two models. Furthermore, the model as proposed by Campbell et al. (2008), does not include 𝑇𝐿𝑀𝑇𝐴, because as mentioned above, this variable is insignificant at the 10% significance level.
(1) Model with trading volume (2) Campbell et al. (2008) model (3) Difference Sensitivity 98.44% 95.31% 3.13% Specificity 98.88% 97.74% 1.14%
Positive predictive value 55.75% 37.65% 18.10%
Negative predictive value 99.98% 99.93% 0.05%
False + rate for true (Survivor) 1.12% 2.26% -1.14%
False - rate for true (Bankrupt) 1.56% 4.69% -3.13%
False + rate for classified + 44.25% 62.35% -18.10%
False - rate for classified - 0.02% 0.07% -0.05%
22 Figure I
Predicted versus Actual Failures
Figure I presents the predicted failures against the actual failures. From 2000 until 2018. As presented in Table I the bankrupt companies in sample start in 2000, and the non-bankrupt companies start in 2006, therefore the years before 2006, do not predict any firm to go bankrupt, as there is no data included in that part of the sample.
In addition, the receiver operating characteristic (ROC) curve, presented in Figure II, presents the in-sample AUC of 0.9993. This Figure Indicates that the model is excellent in distinguishing between true positive rates and false positive rates. The closer the AUC is to 1, the better the fit of the model. The AUC of 0.9993, indicates that the model is excellent.
0 2 4 6 8 10 12 14
23 Figure II Receiver Operating Characteristic Curve
The figure presented below contains the Receiver Operating Characteristic (ROC) Curve. The black line indicates a worthless model, whereas the grey line includes the model as proposed in this paper. This graph represents the in-sample AUC(Area Under the Curve). The ROC plots the sensitivity (true positive rate) against the 1-specificity (false positive rate). The AUC of the ROC is 0.9993.
5.2 Robustness
24 Furthermore, the second robustness test of the model tests the robustness by splitting the sample into two periods. The first period contains all data points before the crisis, hence before and including 2008. The second period contains all data points after 2008. The results of this robustness test are presented in Table C.1. Here the results present a slight difference compared to the full period, and between the two periods. Specifically, the coefficient for trading volume was approximately two units bigger before the crisis, compared to after the crisis. Furthermore, 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺 was not significant at the 10% significance level, before and after the crisis. In addition, 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺 was not significant at the 10% significance level before the crisis but significant at the 1% significance level after the crisis. The indicator for volatility 𝑆𝐼𝐺𝑀𝐴 was negative before the crisis of 2008, and significant at the 5% significance level, and is positive after the crisis of 2008 and during the entire period, at the 1% significance level. The indicator for size, 𝑅𝑆𝐼𝑍𝐸, is significant at the 1% significance level during both periods. Although, the indicator increased after the crisis. The indicator for liquidity 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 is significant at the 5% significance level before the crisis and at the 1% level after the crisis. Moreover, the indicator increased after the crisis. The indicator 𝑀𝐵 is not significant at the 10% significance level pre-crisis, but significant post-crisis at the 1% significance level. The indicator 𝑃𝑅𝐼𝐶𝐸 is not significant at the 10% significance level pre-crisis, but significant post-crisis at the 1% significance level. Subsequently, a quarter of the data has been used pre-crisis, whereas three-quarter of the data has been used in the post-crisis model. Also, 26 bankruptcies are used pre-crisis and 38 bankruptcies are used in the post-crisis model. Conclusively, the post-crisis model has a higher goodness of fit compared to the pre-crisis.
Besides that, a third robustness test has been conducted to assess the model when excluding outliers. As mentioned in Section 4.2., a lot of variables are driven by outliers and are non-normally distributed. The results of the model excluding outliers is presented in Table D.1. The variables corrected for outliers are the market to book ratio(𝑀𝐵), negative ratios have been eliminated and ratios in excess of seven have also been eliminated, which is in line with Campbell et al. (2008). Furthermore, 𝑇𝐿𝑀𝑇𝐴 is corrected for values above one, which are caused by lower market value than book value. Also, 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 is corrected for values above one, for the same reason as 𝑇𝐿𝑀𝑇𝐴. Lastly, 𝑆𝐼𝐺𝑀𝐴 has been corrected for outliers above 200% volatility, which is also in line with Campbell et al. (2008). The other variables did not contain extreme outliers which had to be removed. When considering the output of the logit model including the trimmed data, see Table D.1. second column, only 𝑇𝑉𝑂𝐿, and 𝑅𝑆𝐼𝑍𝐸 remain significant. The variables which have been adjusted are not significant at the 10% significance level. This indicates that the outliers which have been removed in this logit regression contain valuable information.
25 current assets, in total 538, have been eliminated from the sample to conduct this robustness test. This led to a reduction of bankrupt firms of one and a reduction of non-bankrupt firms of 537. The results for this analysis are presented in Table E.1. third column. The results remain robust, for 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺 and 𝑆𝐼𝐺𝑀𝐴 the significance level changes from the 5% level to the 1% level and for 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺 and 𝑃𝑅𝐼𝐶𝐸 the significance level changes from the 1% level to the 5% significance level. Furthermore, the coefficient for 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺 almost doubles in value to -8.870 and 𝑀𝐵 is reduced by 50% to 0.001. The other variables do not deviate much from the original model as presented in the second column of Table E.1. In addition, the Pseudo R squared increases from 0.901 to 0.902. Conclusively, the results remain robust when censoring for firms without current assets.
6. Conclusion
This paper contributes to the bankruptcy prediction literature in several ways. Firstly, it provides evidence that trading volume has predictive power when included in the model. Subsequently, it provides evidence that an increase in the trading volume relative to its previous year quarterly average increase the chance of bankruptcy, when estimating the model in the sample. This result indicates that there is more trading volume in stocks that are likely to go bankrupt compared to stocks of companies that do not go bankrupt. This effect is in line with the previous research of Ramalingegowda (2014), Zavgren et al. (1988), Seyhun and Bradley (1997), Piotroski and Roulstone (2004) and Frino et al. (2007), but in contrast with the results of Frino et al. (2014), and Precourt and Oppenheimer (2015), who find no abnormal trading behavior in the year preceding a bankruptcy. Furthermore, Cheng et al. (2018) find that there is less trading volume preceding a bankruptcy, which is in contrast with the results of this study.
In addition, this research provides evidence that in previous studies of Campbell (2008), Altman (1968) and Ohlson (1980), an important variable, namely trading volume, was omitted from the analysis. Whereas the Altman Z-score and Ohlson-O score are still used today, it is not expected that the model suggested in this research replaces these two already existing models. Because the variables used in this analysis are harder to obtain and calculate.
26 be that not all stocks are covered by analysts, but this must be researched further. Besides that, this research is focussed on generating a model with a better fit than the Campbell et al. (2008) model.
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30 Appendix A
Table A.1: Correlation table
This table presents below contains the correlation table of the explained and explanatory variables. For an exact definition of the variables, see Section 3.2 and 3.3, and Table F.1 for the calculations.
Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (1) Bankrupt 1.000 (2) TVOL 0.349* 1.000 (3) NIMTAAVG -0.023 -0.010 1.000 (4) TLMTA 0.086* 0.118* 0.008 1.000 (5) EXRETAVG -0.143* 0.012 0.013 -0.057* 1.000 (6) SIGMA 0.145* 0.003 -0.001 -0.015 -0.002 1.000 (7) RSIZE -0.494* -0.196* -0.035 -0.191* 0.081* -0.082* 1.000 (8) CASHMTA 0.053* -0.010 0.081* 0.157* -0.002 -0.008 -0.405* 1.000 (9) MB -0.002 0.001 -0.000 0.014 0.007 -0.000 0.006 0.010 1.000 (10) PRICE -0.436* -0.161* -0.037 -0.362* 0.091* -0.074* 0.631* -0.372* 0.006 1.000
31 Appendix B
Table B.1: Robustness analysis including lag of trading volume and original model
The table presented below contains the estimation of the different models. Where model 1 is the main model as presented and discussed in the main text. 𝑇𝑉𝑂𝐿 measures the trading volume, 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺 is a measure for the profitability, 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺 is a measure for the excess return to the index, 𝑆𝐼𝐺𝑀𝐴 is a measure for volatility, 𝑅𝑆𝐼𝑍𝐸 is a measure for the rise of the firm. 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 is a measure for liquidity, 𝑀𝐵 is the market to book ratio of the firm and 𝑃𝑅𝐼𝐶𝐸 is calculated as the log of one plus the price. The formulas behind the variables are presented in Table F.1. Model 2, 3 and 4 contain the lags of the trading volume, presented as 𝐿. 𝑇𝑉𝑂𝐿 for the first lag, 𝐿. 𝐿. 𝑇𝑉𝑂𝐿 for the second lag and 𝐿. 𝐿. 𝐿. 𝑇𝑉𝑂𝐿 for the third lag. Each of the models contains a lag of one quarter. The last column contains the original model as proposed by Campbell et al. (2008). All models have been corrected for heteroskedasticity using robust standard errors.
(1) (2) (3) (4) (5)
VARIABLES Model 1 Model 2 Model 3 Model 4 Model 5
TVOL 7.000*** (1.085) NIMTAAVG -2.226*** -1.590 -2.510** -3.662*** -2.502** (0.836) (1.169) (1.093) (1.192) (1.105) EXRETAVG -4.276** -5.844** -5.555*** -7.153*** -1.721 (2.075) (2.706) (2.058) (2.653) (1.607) SIGMA 0.206** 0.095 -0.003 0.234** 0.106* (0.089) (0.073) (0.002) (0.094) (0.058) RSIZE -2.379*** -2.817*** -2.322*** -1.827*** -1.927*** (0.349) (0.703) (0.349) (0.515) (0.347) CASHMTA -5.555*** -6.695** -5.201*** -3.483 -5.055*** (1.756) (2.608) (1.776) (2.507) (1.546) MB 0.002*** 0.001*** -0.000 -0.001** 0.001 (0.000) (0.000) (0.001) (0.000) (0.001) PRICE -2.158*** -1.136 -2.550** -4.994*** -2.976*** (0.799) (1.671) (1.243) (1.362) (0.882) TVOL.L 5.821*** (0.862) TVOL.L.L 7.240*** (1.169) TVOL.L.L.L 9.817*** (1.666) Constant -7.582*** -8.408*** -7.556*** -7.631*** -2.366* (1.266) (2.631) (1.312) (2.068) (1.231) Observations 4,535 4,534 4,532 4,531 4,535 Pseudo R2 0.901 0.908 0.908 0.930 0.814
32 Appendix C
Table C.1: Robustness analysis sample split
The table presented below contains the logit model up until and including 2008. This model has been corrected for heteroskedasticity, using robust standard errors. 𝑇𝑉𝑂𝐿 measures the trading volume, 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺 is a measure for the profitability, 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺 is a measure for the excess return to the index, 𝑆𝐼𝐺𝑀𝐴 is a measure for volatility, 𝑅𝑆𝐼𝑍𝐸 is a measure for the rise of the firm. 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 is a measure for liquidity, 𝑀𝐵 is the market to book ratio of the firm and 𝑃𝑅𝐼𝐶𝐸 is calculated as the log of one plus the price. The formulas behind the variables are presented in Table F.1.
(1) (2) (3)
VARIABLES Pre-Crisis Post-Crisis Complete Sample
TVOL 9.214*** 7.329*** 7.000*** (2.966) (2.219) (1.085) NIMTAAVG 0.059 -1.281 -2.226*** (0.063) (1.448) (0.836) EXRETAVG -1.650 -10.294*** -4.276** (6.162) (3.149) (2.075) SIGMA -1.605** 0.287*** 0.206** (0.672) (0.063) (0.089) RSIZE -4.118*** -3.088*** -2.379*** (1.126) (0.497) (0.349) CASHMTA -9.758** -7.632*** -5.555*** (4.707) (2.261) (1.756) MB 0.019 0.002*** 0.002*** (0.022) (0.001) (0.000) PRICE -2.006 -2.710** -2.158*** (1.766) (1.201) (0.799) Constant -9.292*** -7.908*** -7.582*** (3.233) (1.763) (1.266) Observations 1,205 3,330 4,535 Pseudo R2 0.915 0.931 0.901
33 Appendix D
Table D.1: Robustness analysis trimmed sample
The table presented below contains the logit model up until and including 2008. This model has been corrected for heteroskedasticity, using robust standard errors. 𝑇𝑉𝑂𝐿 measures the trading volume, 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺 is a measure for the profitability, 𝑇𝐿𝑀𝑇𝐴 is a measure for the amount of debt used by the firm, 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺is a measure for the excess return to the index, 𝑆𝐼𝐺𝑀𝐴 is a measure for volatility, 𝑅𝑆𝐼𝑍𝐸 is a measure for the rise of the firm. 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 is a measure for liquidity, 𝑀𝐵 is the market to book ratio of the firm and 𝑃𝑅𝐼𝐶𝐸 is calculated as the log of one plus the price. The formulas behind the variables are presented in Table F.1. Variables which have trim behind their name, have been trimmed as mentioned in Section 5.2.
(1) (2)
VARIABLES Trimmed Sample Full Sample
TVOL 11.596*** 6.919*** (3.040) (1.129) NIMTAAVG -1.618 -2.160** (2.041) (0.878) TLMTAtrim 5.446 (5.265) EXRETAVG -0.733 -4.589** (9.227) (2.168) SIGMAtrim -0.727 (2.230) RSIZE -3.114*** -2.474*** (0.906) (0.455) CASHMTAtrim -9.564 (9.965) MBtrim 0.072 (0.056) PRICE -4.334 -2.127** (3.069) (0.846) TLMTA -0.892 (1.894) SIGMA 0.212** (0.091) CASHMTA -5.446*** (1.887) MB 0.001*** (0.000) Constant -12.011* -7.084*** (6.238) (1.559) Observations 3,652 4,535 Pseudo R2 0.937 0.901
34 Appendix E
Table E.1: Robustness analysis censored sample
The table presented below contains the full logit model in the second column. The third column contains the logit model censored for films without current assets (CASHMTA > 0). Both models have been corrected for heteroskedasticity, using robust standard errors. 𝑇𝑉𝑂𝐿 measures the trading volume, 𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺 is a measure for the profitability, 𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺 is a measure for the excess return to the index, 𝑆𝐼𝐺𝑀𝐴 is a measure for volatility, 𝑅𝑆𝐼𝑍𝐸 is a measure for the rise of the firm. 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 is a measure for liquidity, 𝑀𝐵 is the market to book ratio of the firm and 𝑃𝑅𝐼𝐶𝐸 is calculated as the log of one plus the price. The formulas behind the variables are presented in Table F.1.
(1) (2)
VARIABLES Full Model Firms with CASHMTA > 0
TVOL 7.000*** 7.655*** (1.085) (1.308) NIMTAAVG -2.226*** -1.992** (0.836) (0.919) EXRETAVG -4.276** -8.870*** (2.075) (2.912) SIGMA 0.206** 0.251*** (0.089) (0.084) RSIZE -2.379*** -2.230*** (0.349) (0.370) CASHMTA -5.555*** -5.930*** (1.756) (2.026) MB 0.002*** 0.001*** (0.000) (0.000) PRICE -2.158*** -2.086** (0.799) (0.831) Constant -7.582*** -7.706*** (1.266) (1.555) Observations 4,535 3,997 Pseudo R2 0.901 0.902
35 Appendix F
Table F.1: Variables
All variables mentioned in the table below are constructed using the COMPUSTAT database. Whenever the variables were not available in the COMPUSTAT database, CRSP was used as an alternative to retrieve the correct data.
Variable Name Description Formula
𝑇𝑉𝑂𝐿𝑖,𝑡−1
𝛿
The trading volume of one quarter before the bankruptcy was obtained by adding the monthly trading volume (𝛿) together. This was divided by the quarterly average (1
4) of the sum of the monthly trading volume (𝛿) one year before the specific quarter. Where 𝛿 measures the trading volume in million. The Compustat security monthly database was used with code CSHTRM. Hereafter the months in each quarter are summed to obtain the quarterly trading volume, which is plugged into the formula as stated above.
∑−1𝑡−3𝛿𝑡 (∑−15𝑡−4𝛿𝑡)14
𝑁𝐼𝑀𝑇𝐴𝐴𝑉𝐺𝑖,𝑡−1,𝑡−12
𝑁𝐼𝑀𝑇𝐴
∅
Measures the sum of the net income four quarters before the bankruptcy of each quarter and multiplies this with ∅ to the power three for -two quarters, six for -three quarters and nine for -four quarters. Thereafter this is multiplied by one minus ∅ to the power three divided by one - ∅ to the power 12.
Where 𝑁𝐼𝑀𝑇𝐴 is measured as the net income of the quarter divided by the market value of the total assets in the quarter. For Net Income the Compustat quarterly database code NIQ was used. For the Market Value Total Assets, the following Compustat code was used [ATQ+CSHOQ+(ATQ-LTQ)]
Where ∅ acts as a vector to reduce the weight by half each quarter 1 − ∅3 1 − ∅12(𝑁𝐼𝑀𝑇𝐴𝑡−1,𝑡−3 + ⋯ + ∅9𝑁𝐼𝑀𝑇𝐴𝑡−10,𝑡−12) 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 2−13
The total liabilities one quarter ahead of the
36 𝑇𝐿𝑀𝑇𝐴𝑖,𝑡−1
assets at the same moment. For Total Liabilities the Compustat code LTQ was used. For the Market Value Total Assets, the following Compustat code was used [ATQ+CSHOQ+(ATQ-LTQ)]
𝑇𝑜𝑡𝑎𝑙 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑒𝑠 𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠
𝐸𝑋𝑅𝐸𝑇𝐴𝑉𝐺𝑖,𝑡−1,𝑡−12
𝐸𝑋𝑅𝐸𝑇
The excess return to the index is measured as the sum of the monthly excess return multiplied by ∅ to the power one for the second month back, two for the third month back, until the twelfth month back, but not for the first month back. Hereafter this is multiplied by one minus ∅ and divided by one minus ∅ to the power twelfth accordingly.
Where 𝐸𝑋𝑅𝐸𝑇 is measured as the excess return to the S&P 500. The returns are obtained by dividing the price by the price of t-1. For this the Compustat code PRCCD was used. To calculate the index returns the Compustat code PRCCM was used.
1 − ∅ 1 − ∅12(𝐸𝑋𝑅𝐸𝑇𝑡−1 + ⋯ + ∅11𝐸𝑋𝑅𝐸𝑇 𝑡−12) 𝑅𝑖− 𝑅𝑠&𝑝500 𝑆𝐼𝐺𝑀𝐴𝑖,𝑡−1,𝑡−3
The volatility is measured as the sum of the squared daily returns one quarter before the bankruptcy. This is in turn multiplied by one divided by N minus one and multiplied by 252, to generate the annual variance. To arrive at the volatility the square root of the annual variance is taken.
Where N is the number of observations, r measures the returns and k is the length of the lag. The returns are obtained by dividing the price by the price of t-1. For this the Compustat code PRCCD was used.
(252 ∗ 1 𝑁 − 1 ∑ 𝑟𝑖,𝑘 2 𝑘∈{𝑡−1,𝑡−2,𝑡−3} ) 1/2 𝑅𝑆𝐼𝑍𝐸𝑖,𝑡−1
The 𝑅𝑆𝐼𝑍𝐸 is measured as the market value of the firm equity divided by the total market value of the S&P 500 one quarter before the bankruptcy. For the market value of the equity the Compustat code CSHOQ was used. To obtain the Total S&P500 Market Value the CRSP Total Market Value code was used.
37 𝐶𝐴𝑆𝐻𝑀𝑇𝐴𝑖,𝑡−1
The liquidity measured as 𝐶𝐴𝑆𝐻𝑀𝑇𝐴 is calculated by dividing the current assets as reported one quarter before the bankruptcy by the market value of the total assets one quarter before the bankruptcy. For Current Assets the Compustat code ACTQ was used. For the Market Value Total Assets, the following Compustat code was used [ATQ+CSHOQ+(ATQ-LTQ)]
( 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑠𝑠𝑒𝑡𝑠
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠)
𝑀𝐵𝑖,𝑡−1
The market to book value is measured by dividing the market value one quarter before the bankruptcy by the book value of the firm one quarter before the
bankruptcy. For the market value of the equity the Compustat code CSHOQ was used. For the book value of the equity the Compustat code (ATQ - LTQ)
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝐸𝑞𝑢𝑖𝑡𝑦 𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝐸𝑞𝑢𝑖𝑡𝑦
𝑃𝑅𝐼𝐶𝐸𝑖,𝑡−1
The price is measured by taking the log of one plus the price at the end of the quarter before the bankruptcy. For price the quarterly Compustat database was used with code PRCCQ.
log (1 + 𝑆ℎ𝑎𝑟𝑒 𝑃𝑟𝑖𝑐𝑒)
