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Available online at www.sciencedirect.com Journal of Financial Markets 16 (2013) 33–60 Investing in Chapter 11 stocks: Trading, value, and performance $ Yuanzhi Li a,1 , Zhaodong (Ken) Zhong b,n a Department of Finance, Fox Business School, Temple University, Philadelphia, PA 19122, United States b Department of Finance, Rutgers Business School, Rutgers University, Piscataway, NJ 08854, United States Received 1 March 2012; received in revised form 10 September 2012; accepted 29 September 2012 Available online 31 October 2012 Abstract We address questions about Chapter 11 stocks regarding their trading environment, fundamental value, and performance. First, there exists active trading for Chapter 11 stocks throughout the bankruptcy process. Second, equity value after filing is positively related to asset value, asset volatility, risk-free rate, and expected duration and is negatively related to liabilities. Furthermore, the return correlation between bankrupt stocks and their matching samples exhibits non-linearity similar to out-of-money call options. Third, investing in Chapter 11 stocks incurs large losses. Consistent with heterogeneous beliefs and limits to arbitrage, stocks with higher levels of information uncertainty and more binding short-sale constraints experience more negative returns. & 2012 Elsevier B.V. All rights reserved. JEL classification: G33; G12; G14 Keywords: Chapter 11; Option theory; Heterogeneous beliefs; Limits to arbitrage www.elsevier.com/locate/finmar 1386-4181/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.finmar.2012.09.006 $ We want to thank Edward Altman for providing the bankruptcy resolution data and Carl Giangrasso from Pink OTC Markets Inc. for providing the pricing data of delisted stocks. We also want to thank Edward Altman, Nicholas Barberis, Hank Bessembinder, Kose John, Ronald Masulis, Stewart Mayhew, Robert Mooradian, Stephen Treanor, Robert Whitelaw, Hong Yan, David Yermack, conference participants at the 2009 European Finance Association annual meeting, and the seminar participants at Temple University for their helpful comments. This research is supported in part by the David Whitcomb Center for Research in Financial Services from the Rutgers Business School of Rutgers University. Special thanks go to an anonymous referee and Tarun Chordia (the Editor) for their valuable suggestions that significantly improved the quality of our paper. n Corresponding author. Tel.: þ1 848 445 5109. E-mail addresses: [email protected] (Y. Li), [email protected] (Z. Zhong). 1 Tel.: þ1 215 204 8108.

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Page 1: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Available online at www.sciencedirect.com

Journal of Financial Markets 16 (2013) 33–60

1386-4181/$ -

http://dx.doi

$We wan

Pink OTC M

Nicholas Ba

Stephen Trea

Finance Ass

comments. T

from the Ru

Chordia (thenCorrespo

E-mail ad1Tel.: þ1 2

www.elsevier.com/locate/finmar

Investing in Chapter 11 stocks: Trading,value, and performance$

Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n

aDepartment of Finance, Fox Business School, Temple University, Philadelphia, PA 19122, United StatesbDepartment of Finance, Rutgers Business School, Rutgers University, Piscataway, NJ 08854, United States

Received 1 March 2012; received in revised form 10 September 2012; accepted 29 September 2012

Available online 31 October 2012

Abstract

We address questions about Chapter 11 stocks regarding their trading environment, fundamental

value, and performance. First, there exists active trading for Chapter 11 stocks throughout the

bankruptcy process. Second, equity value after filing is positively related to asset value, asset

volatility, risk-free rate, and expected duration and is negatively related to liabilities. Furthermore,

the return correlation between bankrupt stocks and their matching samples exhibits non-linearity

similar to out-of-money call options. Third, investing in Chapter 11 stocks incurs large losses.

Consistent with heterogeneous beliefs and limits to arbitrage, stocks with higher levels of information

uncertainty and more binding short-sale constraints experience more negative returns.

& 2012 Elsevier B.V. All rights reserved.

JEL classification: G33; G12; G14

Keywords: Chapter 11; Option theory; Heterogeneous beliefs; Limits to arbitrage

see front matter & 2012 Elsevier B.V. All rights reserved.

.org/10.1016/j.finmar.2012.09.006

t to thank Edward Altman for providing the bankruptcy resolution data and Carl Giangrasso from

arkets Inc. for providing the pricing data of delisted stocks. We also want to thank Edward Altman,

rberis, Hank Bessembinder, Kose John, Ronald Masulis, Stewart Mayhew, Robert Mooradian,

nor, Robert Whitelaw, Hong Yan, David Yermack, conference participants at the 2009 European

ociation annual meeting, and the seminar participants at Temple University for their helpful

his research is supported in part by the David Whitcomb Center for Research in Financial Services

tgers Business School of Rutgers University. Special thanks go to an anonymous referee and Tarun

Editor) for their valuable suggestions that significantly improved the quality of our paper.

nding author. Tel.: þ1 848 445 5109.

dresses: [email protected] (Y. Li), [email protected] (Z. Zhong).

15 204 8108.

Page 2: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6034

1. Introduction

During the recent financial crisis, many firms fell into distress and filed for bankruptcy. Thenumber of total bankruptcy filings surged 32% in 2008 compared to 2007.2 Meanwhile, therehas been increasing coverage in the major media about investing in bankrupt equity afterChapter 11 filing.3 However, this is an area that academic research has largely overlooked.Many important questions involving the trading environment, fundamental value, andperformance of these stocks remain unanswered. Presumably, the lack of research is due to thelack of data since most bankrupt stocks are delisted from major exchanges before or aroundbankruptcy filings, rendering subsequent market data unavailable in traditional databases suchas CRSP. Using a unique dataset from Pink OTC Markets Inc., this paper sheds light onthese topics.In our sample of 602 Chapter 11 filings from 1998 to early 2006, most stocks are delisted

from major exchanges and resume trading on Pink Sheets, an electronic quotation systemoperated by Pink OTC Markets Inc. In contrast to the traditional view that trading is scarceexcept for initial short-covering by previous short-sellers, we find that active trading activityexists throughout the Chapter 11 process. Despite the initial decline in prices and wideningof bid–ask spreads, more than 50% of these stocks are traded on any given day, even for thefirms that have been in Chapter 11 for as long as three years. There is also a significantdecrease in the institutional ownership for these stocks accompanying the bankruptcy filings.After the filing, more than 90% of the investors are individual investors.Although in most cases shareholders eventually receive nothing in the final reorganiza-

tion or liquidation plans, our sample indicates that these stocks trade well above zeroimmediately after Chapter 11 filings. The majority of previous studies (e.g., Franks andTorous, 1989; Weiss, 1990, Eberhart, Moore, and Roenfeldt, 1990, Franks and Torous,1994; Betker, 1995a) about bankrupt equity valuation focus on the violation of theabsolute priority rule (APR). APR violation occurs when creditors are not fully satisfiedbefore shareholders get any payments. In particular, Eberhart, Moore, and Roenfeldt(1990) show that equity valuation right after filing reflects the market expectation of APRviolation. In contrast, we resort to the hypothesis that bankrupt equity is, although out-of-money, a call option on firm assets. Chapter 11 allows the firm to continue its ongoingbusiness operation. It is possible that business might improve and the equity might beevaluated in-the-money again.4 Applying the option theory enables us to expand the scopeof bankrupt equity valuation to include factors that have not been examined in the priorliterature, such as asset volatility, risk-free rate, and expected duration.

2A more detailed description about the number of bankruptcy filings over time can be found at: http://www.

creditslips.org/creditslips/2009/01/bankruptcy-filings-rise-32-in-2008.html.3See ‘‘Betting on the Equity in Bankrupt Companies’’ by Aaron Pressman on June 11, 2009, in Business Week;

‘‘Zombie Stocks: Speculators Gamble on Firms Whose Shares May Be Worthless’’ by Ken Bensinger on

September 24, 2009, in Los Angeles Times; and ‘‘Bankrupt Firms: Who is Buying?’’ by Eugene Fama and Kenneth

French on February 23, 2010, at the online Fama/French Forum.4For example, ‘‘In the energy sector, some companies filed for bankruptcy after getting squeezed between the

credit crunch and plummeting oil prices. But oil prices have rebounded, increasing cash flow as well as the value of

potential drilling sitesy The shares have been trading for less than 25 cents since the filing; the analyst thinks they

could be worth $1.50 to $5y,’’ quoted from ‘‘Betting on the Equity in Bankrupt Companies’’ by Aaron Pressman

on June 11, 2009, in Business Week.

Page 3: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 35

Using the Black-Scholes model to calculate the option values of bankrupt stocks, we areable to explain about 25–35% of the cross-sectional variation of the observed marketvalues of these stocks. More specifically, we find that the bankrupt equity value right afterfiling is positively related to asset value, asset volatility, risk-free rate, and expectedduration, and is negatively related to liabilities. This finding is robust even after controllingfor the expectation of APR violations.5 Turning to the payoff structure of investing inthese stocks, we show that buy-and-hold returns of bankrupt stocks from bankruptcy filingto resolution are heavily right-skewed and resemble the payoff structures of out-of-moneycall options: most of them die out without any payoff, while a few pay off tremendously.To further investigate whether these payoffs are related to the underlying businessfundamentals in the way predicted by option theory, we construct a proxy for each firm’sbusiness performance using an industry-and-size matching sample over the Chapter 11duration. We find that the return correlation between bankrupt stocks and their matchingsamples exhibits strong non-linearity: it is significantly positive when the matching sampleperforms well and is zero otherwise. This finding suggests that the payoff structure ofbankrupt stocks indeed has the same ‘‘hockey stick’’ shape as call options.

Examining the distribution of the buy-and-hold returns of Chapter 11 stocks, we findthat betting on these stocks on average generates large losses, both before and after riskadjustments.6 Our sample’s median matching-sample-adjusted monthly return is �15%,and market-adjusted monthly return is �14%. The negative abnormal returns do notcluster in a particular year but persist over time. In addition, this finding is not attributableto the negative delisting returns documented in the prior literature since more than half ofour sample firms are delisted two days before their bankruptcy filings. Therefore, ourfinding of negative returns of Chapter 11 stocks from the first trading day after bankruptcyfiling to the final resolution is an indication of the poor performance during the Chapter 11process, which can last from a few months to a few years.

It is surprising that investors lose so much money investing in Chapter 11 stocks, even giventhe fact that shareholders are residual claim holders in bankruptcy. Thus, the finding thatChapter 11 stocks underperform indicates the existence of market frictions. Our explanationfor the negative returns is motivated by the Miller (1977) theory, which argues that, wheninvestors have heterogeneous beliefs about the value of a risky asset in a market with restrictedshort-selling, prices will reflect the more optimistic valuation.7 After Chapter 11 filings, thesestocks are mostly traded on Pink Sheets, which does not require information disclosure toinvestors. Meanwhile, as the stock ownership data shows, institutional investors dramaticallyreduce their stock holdings around bankruptcy filings, and more than 90% of the shareholderspost-filing are individual investors. Many analysts stop covering these stocks due to the lackof interest from institutional investors. Individual investors are presumably less efficient in

5It is worth mentioning that the option theory is not mutually exclusive with the APR literature. As

documented in prior studies, shareholders can engage in the bargaining process with creditors in the bankruptcy

court to lower the amount of debt paid back to creditors, which essentially lowers the strike price of the call option

and causes the option to be in-the-money.6Our finding of Chapter 11 stocks being out-of-money call options on firm assets is not inconsistent with the

negative returns. While the cross-sectional variation in the value of these stocks indicates they are call options on

firm assets, it does not rule out the possibility that they can be systematically mispriced, thus leading to negative

returns.7Another potential explanation is the behavioral model as in Barberis and Huang (2008), which we defer to

future research.

Page 4: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6036

gathering information and interpreting the available information (Barber and Odean, 2000).Therefore, the information uncertainty and the divergence of opinion regarding the true valueof these stocks increase dramatically after filing. In addition, low institutional ownershipproduces binding short-sale constraints for these stocks.8 As a result, the high informationuncertainty and binding short sale constraints cause bankrupt stocks to be overvalued.9

Finally, a unique feature of Chapter 11 stocks is that, on the final resolution date, thereorganization/liquidation plan states explicitly the true value of the stock.10 In other words, itprovides a condition for the stock prices to return to their fundamental values eventually.Thus, the buy-and-hold return from filing to resolution becomes negative.Many studies (e.g., Chen, Hong, and Stein, 2002, among others) develop price-optimism

models following the approach of Miller (1977). Two important implications of thesemodels are as follows: (1) the larger the disagreement about a stock’s value, the lower itsexpected return; and (2) the more binding the short-sale constraint, the lower the expectedreturn. Using the bid–ask spread, intraday volatility, and turnover as proxies forinformation uncertainty, and the percentage of institutional ownership and number ofinstitutional investors as proxies for short-sale constraints, we show that stocks with higherlevels of information uncertainty and more binding short-sale constraints experience morenegative returns during the Chapter 11 process.The remainder of the paper is organized as follows: Section 2 provides a brief literature

review related to our paper. Section 3 describes the data used in this study. Section 4investigates the trading environment and ownership of bankrupt stocks. Section 5 tests thehypothesis that Chapter 11 stocks have fundamental values based on the call options onfirm assets. Section 6 tests the hypothesis that negative returns of Chapter 11 stocks are dueto the initial overvaluation by optimistic investors at filing in the context of heterogeneousbeliefs with short-sale constraints. We conclude in Section 7.

2. Related literature

The value of bankrupt equity has been scrutinized primarily under the framework ofviolations of the absolute priority rule. Franks and Torous (1989) analyze a sample ofbankruptcies from 1970 through 1984 and find that 21 of 27 sample cases exhibit APRviolation. Weiss (1990) reports that priority of claims is violated in 27 cases in a sample of

8D’Avolio (2002) shows that the main suppliers of stock loans are institutional investors, and Nagel (2005) finds

that stock loan supply tends to be sparse and short selling more expensive when institutional ownership is low.9Short-sellers may face various arbitrageur risks, even if they manage to borrow in the first place. Due to the

extreme lack of information about these stocks, rumors about bankrupt companies often lead to rapid increases in

the stock price without any justifiable reason, and the arbitrageurs will face high short-squeeze risk. The high

collateral requirement of short-selling relative to the low price level of these stocks imposes another type of

arbitrageur risk for bankrupt stocks. ‘‘The problem here is that an arbitrageur can tie up a lot of capital shorting

in-bankruptcy securities... if the stock price is $0.10 and the arbitrageur shorts 1 million shares, he receives only

$100 thousand from the sale but he must post collateral worth perhaps $1.2 million,’’ as quoted from ‘‘Bankrupt

Firms: Who is Buying?’’ by Eugene Fama and Kenneth French on February 23, 2010, at the Fama/French

Forum. Therefore, the difficulty to borrow Chapter 11 stocks and high arbitrageur risks explain why it is hard for

arbitrageurs to profit from the negative abnormal returns.10More precisely, this is true only when the equity is worthless, which accounts for most of sample cases. In

other cases, the value of old equity is specified as a conversion ratio to new stocks or warrants. Although the exact

value of new stocks and warrants is not known at the resolution time, it provides significantly more guidance to

value the old equity, compared to before the confirmation of a reorganization or liquidation plan.

Page 5: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 37

37 bankruptcy filings between 1979 and 1986. Eberhart, Moore, and Roenfeldt (1990)examine the amount paid to shareholders in excess of the amount they would have receivedunder the APR, and find that it represents an average of 7.6% of the total amount awardedto all claimants from a sample of 30 filings from 1979 to 1986. They further show thatcommon share values reflect the value received in violation of APR, suggesting thatdeviations from the rule are expected by the equity market. Betker (1995a) examines thecross-sectional determinants of APR violations in 75 Chapter 11 bankruptcies during1982–1990, and finds evidence that APR violations are larger when the firm is closer tosolvency, banks hold fewer claims, the CEO holds more shares, CEO pay and shareholderwealth are positively related, and the firm retains the exclusive right to propose abankruptcy plan. Bharath, Werner, and Panchapegesan (2010) find that the APRviolations have become less common in recent periods, and they attribute it to thedevelopment of debtor-in-possession (DIP) financing and key employee retention plans.

Several papers on bankruptcy also evaluate claims on bankrupt firms in an optionframework. Bebchuk (1988, 2000) proposes a new method of dividing the reorganizationpie among claim-holders in the Chapter 11 reorganization process by issuing tradableoptions, replacing the current bargaining process. Bebchuk argues that when the truefirm value is unknown, bargaining is inefficient. However, the value of all claims on thebankrupt firm can be synthesized using options with different strike prices, regardlessof the true value of the firm. Bebchuk and Chang (1992) develop a sequential bargainingmodel of the negotiations between shareholders and creditors within Chapter 11.Shareholders have incentives to delay the reorganization process to prolong the optionmaturity they have on firm assets, while delayed reorganization can hurt overall firm valuedue to additional financial distress costs. In the equilibrium, creditors are willing tosacrifice some of their claims for shareholders to achieve faster reorganization resolution.The argument is empirically supported by Franks and Torous (1994), who find thatChapter 11 reorganizations have lower equity deviations from absolute priority and lowercreditor recovery rates, compared to out-of-court exchange offers. Building on the priorliterature, our paper conducts a comprehensive analysis with the newly available in-bankruptcy data in the option framework.

There are a few papers studying stock performance before bankruptcy filing. Forexample, Clark and Weinstein (1983) examine filing cases before the 1978 BankruptcyReform Act and find evidence of large equity losses over long periods of time prior tofiling. Aharony, Jones, and Swary (1980) compare risk and return characteristics ofbankrupt stocks with matched non-bankrupt firms using pre-filing capital market data.They find that the bankrupt sample displays significant negative cumulative returnsstarting from four years before filing. Several studies have focused on the performance ofbankrupt firms and their securities after the bankruptcy resolutions. Hotchkiss (1995)studies the accounting performance of bankrupt firms after they emerge from Chapter 11and shows that more than 40% of them continue to experience operating losses in thethree years following emergence. Eberhart, Altman, and Aggarwal (1999) evaluate post-bankruptcy performance of ‘‘orphan stocks’’—new issuance of equity for firms emergingfrom bankruptcy. They report evidence of large positive excess returns in the 200 daysfollowing emergence. Very few papers have examined the stock performance during theChapter 11 process. A few exceptions are Dawkins, Bhattacharya, and Bamber (2007),who study the price patterns in the short period (one to two weeks) after Chapter 11 filingsand find a return reversal from the negative filing price reaction during bull markets, and

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Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6038

Morse and Shaw (1988), who examine a sample of 56 stocks traded after filing in the 1978–1982 period and find no abnormal returns within three years. Our finding of substantialnegative returns for a large cross-section of firms during the Chapter 11 process contrastssharply with the findings in the prior literature.Our paper is also related to the literature on heterogeneous beliefs and limits to

arbitrage. There have been both theoretical and empirical developments following theseminal paper by Miller (1977). See, for example, Chen, Hong, and Stein (2002), Duffie,Garleanu, and Pedersen (2002), and Hong, Scheinkman, and Xiong (2006), among others,for new theoretical models, and see Figlewski (1981), Figlewski and Webb (1993), Diether,Malloy, and Scherbina (2002), and Boehme, Danielsen, and Sorescu (2006), among others,for empirical studies. Most previous empirical studies focus on one of the following twoconditions: the degree of disagreement and the short-sale constraints. Theoretically, theovervaluation can last forever if the bubble persists over time. By studying the performanceof bankrupt stocks from the bankruptcy filing date to the final resolution date (when thebubble ‘‘bursts’’), our paper provides a test that meets three conditions: the existence ofdisagreement, short-sale constraints, and the eventual return of prices to their fundamentalvalues.

3. Data description

We first compile a sample of Chapter 11 filings between 1998 and early 2006 from anonline data vendor, http://www.bankruptcydata.com. The sample starts from 1998 since itis when the daily trading information became available from Pink Sheets. On any givenday before or after Chapter 11 filings, if the stock is already delisted from major exchanges,we collect the trading data from Pink Sheets, which provides the daily highest, lowest, andclosing prices, as well as bid–ask quotes and trading volume. If the stock is not delisted, wecollect the same data from CRSP. The final bankruptcy resolution dates and outcomesare mainly provided by Edward Altman. We supplement the missing values withBankruptcydata.com and Lynn Lopucki’s Bankruptcy Research Database. If the firm issuccessfully reorganized, the resolution date is the confirmation date of the reorganizationplan. If the firm is liquidated or converted to Chapter 7, the resolution date is theconfirmation date of the liquidation plan or the conversion date. In addition, whether afirm negotiates its reorganization plan with creditors before filing (a ‘‘prepackaged’’ filing),whether it receives additional financing after filing (DIP financing), and whether an equitycommittee is formed are the important aspects of Chapter 11 filings as documented in thebankruptcy literature (e.g., Betker, 1995b; Tashjian, Lease, and McConnell, 1996; Dahiya,John, Puri, and Ramirez, 2003; Bharath, Werner, and Panchapegesan, 2010; amongothers). Thus, we collect this information for all cases from three sources: http://www.bankruptcydata.comLynn Lopucki’s Bankruptcy Research Database, and through newssearch.11 We also gather the accounting information of these firms from the last quarterlyfilings with the SEC before Chapter 11 filings. To guarantee that the accountinginformation accurately describes sample firms’ conditions at the time of Chapter 11 filings,we require all quarterly filings to be within 12 months of bankruptcy filing. Around 90% ofthe sample firms have the last quarterly filing within six months before Chapter 11 filing.

11In our sample, about 22% of cases are prepackaged filings, 41% of cases have DIP financing, and 27% of

cases have equity committees.

Page 7: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Table 1

Outcome and duration of chapter 11 filings.

Distribution of final outcomes and durations of Chapter 11 filings. The sample consists of 602 cases between

1998 and 2006. There are five categories of outcome: (1) Emerged or Reorganized; (2) Liquidated or Converted to

Chapter 7; (3) Acquired, Merged, or Sold; (4) Case Dismissed by the Court; and (5) Unknown. Duration is the

length of time from the Chapter 11 filing date to the final resolution date (reorganization confirmation date,

liquidation date, or the date of conversion to Chapter 7), which is measured in calendar days.

Outcome Number of Cases Percent Duration

Min Median Max Mean Std. Dev.

Emerged or Reorganized 260 43.2 29 266 1584 355 285

Liquidated or Converted to Ch7 227 37.7 13 401 1955 510 381

Acquired, Merged, or Sold 64 10.6 47 392 1495 457 286

Case Dismissed 33 5.5 11 490 2126 555 506

Unknown 18 3.0 43 299 1093 343 248

Total 602 100.0 11 350 2126 435 346

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 39

We also exclude cases from our study that do not have the same economic meaning as astandard Chapter 11 filing, and the ones that are insignificant in terms of size. Specifically,we drop firms in any of the following cases: (1) firms filing for Chapter 11 for non-distressreasons such as litigations;12 (2) firms filing for Chapter 11 for the second time; (3) firmswith a pre-filing asset size of less than $1 million; and (4) firms with the first post-filingtrading price of less than $0.01. Our final sample consists of 602 Chapter 11 filing cases.

Table 1 shows the distribution of final resolution outcomes of Chapter 11 filings andtheir durations. We classify the final outcomes into five categories: (1) Emerged orReorganized; (2) Liquidated or Converted to Chapter 7; (3) Acquired, Merged, or Sold; (4)Case Dismissed by the court; and (5) Unknown. Note that even for the ‘‘Unknown’’ cases,there is a confirmation date available in the data; only the outcome cannot be determined.So these cases are by no means abandoned by the court or claim-holders. Among the 584firms with known outcomes, successful reorganization cases account for slightly less thanhalf of the sample, while liquidation and acquisition cases account for the other half. Wealso calculate the length of time (in terms of calendar days) from the bankruptcy filingdate to the final resolution date (reorganization confirmation date, liquidation date, or thedate of conversion to Chapter 7). The median duration of all bankruptcies is 350 days.Interestingly, we find that firms that are reorganized successfully spend less time inbankruptcy than the ones that are liquidated, with median durations of 266 days and 401days, respectively. One reason is that the reorganized group includes more prepackagedfilings, which spend less time in bankruptcy. Our sample distribution of the resolutionoutcome and duration is comparable to Bharath, Werner, and Panchapegesan (2010).Their sample of Chapter 11 filings from 1979 to 2005 contains 626 filing cases, around 60%of which are successfully reorganized, and the median duration is 14 months. The fact thattheir sample firms are more likely to be reorganized successfully and tend to stay inChapter 11 longer is due to the larger asset size of their firms. The majority of their sample

12There have been some Chapter 11 filings due to asbestos-related litigation. For example, ‘‘W. R. Grace & Co.

(NYSE: GRA) announced that the Company has voluntarily filed for reorganization under Chapter 11 of the

United States Bankruptcy Code in response to a sharply increasing number of asbestos claims on April 2, 2001,’’

as quoted from the official website of W. R. Grace & Co., http://www.grace.com.

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Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6040

firms are collected from Lynn Lopucki’s Bankruptcy Research Database, which onlycovers filings by firms with asset size above $100 million.Table 2 gives the descriptive statistics of variables reported or constructed with

information in the last quarterly filings with the SEC before Chapter 11 filings. We are ableto find or compute total assets, book equity, and leverage ratio for all sample firms. Only asmall number of firms have missing data for net income, tangible ratio, or return on assets(ROA). Panel A provides the distribution summary statistics of these variables. Since werequire our sample firms to have a pre-filing asset size of more than $1 million, theminimum total asset value is $1 million. The mean asset value of the sample is $857 millionwith a standard deviation of $3,209 million, which means that the sample is notconcentrated on small or large firms. The averages of net income, book equity, and ROAare negative. However, not all firms have negative net income, book equity, or ROA beforebankruptcy filings. The maximum net income is $48.21 million, the maximum book equityis $6,584 million, and the maximum ROA is 10%. We hand-checked firms with positive netincome, book equity, or ROA to make sure that these firms indeed file for Chapter 11 due

Table 2

Firm characteristics.

Characteristics of firms that filed for Chapter 11 between 1998 and 2006. Panel A reports the summary

statistics. Panel B reports the correlation matrix (Pearson below the diagonal and Spearman above the diagonal).

Accounting information is from the last quarterly filing before Chapter 11 filings. Leverage is the ratio of total

liabilities over total assets; Tangible Ratio is the ratio of tangible assets over total assets; ROA is the ratio of

EBITDA (earnings before interest, taxes, depreciation, and amortization) over total assets.

Panel A: Summary statistics

N Min Q1 Median Q3 Max Mean Std. Dev.

Total Assets (MM$) 602 1.00 37.73 150.69 535.75 52285.60 856.63 3209.24

Net Income (MM$) 596 �3197.00 �38.77 �9.25 �2.67 48.21 �61.88 226.19

Book Equity (MM$) 602 �7316.70 �37.60 0.11 27.46 6584.07 �32.54 625.28

Leverage 602 0.06 0.76 0.96 1.25 12.53 1.16 0.98

Tangible Ratio 592 0.00 0.12 0.28 0.50 0.94 0.33 0.24

ROA 596 �4.06 �0.08 �0.02 0.01 0.10 �0.08 0.26

Panel B: Correlation matrix

Total Assets Net Income Book Equity Leverage Tangible Ratio ROA

Total Assets 1 �0.60 0.06 �0.01 0.26 0.50

(0.00) (0.12) (0.78) (0.00) (0.00)

Net Income �0.56 1 0.19 �0.19 �0.25 0.10

(0.00) (0.00) (0.00) (0.00) (0.02)

Book Equity 0.02 0.21 1 �0.78 �0.15 0.05

(0.65) (0.00) (0.00) (0.00) (0.26)

Leverage �0.04 �0.01 �0.15 1 0.11 0.00

(0.27) (0.76) (0.00) (0.01) (0.91)

Tangible Ratio 0.16 �0.13 �0.11 �0.07 1 0.19

(0.00) (0.00) (0.01) (0.07) (0.00)

ROA 0.07 0.02 �0.01 �0.02 0.10 1

(0.07) (0.66) (0.77) (0.68) (0.02)

p-Values in parentheses.

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Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 41

to distress.13 Leverage is calculated as the ratio of total liabilities to total assets, with amedian value of 0.96.14 The tangible ratio ranges from 0% to 94%. The financial variablesindicate that sample firms are, on average, in bad operating condition and highly leveragedat the time of their Chapter 11 filings. Panel B is the correlation matrix of firmcharacteristics. It suggests that in our sample, there is no significant correlation betweensize and leverage ratio. Larger firms tend to be more profitable and have higher tangibleasset ratios.

4. Trading of Chapter 11 stocks

In the bankruptcy literature, trading of distressed stocks after Chapter 11 filings is notwell studied. The common perception is that equity is wiped out upon Chapter 11 filings,and thus trading must be scarce. The fact that traditional databases, such as CRSP, do notcover delisted stocks also creates the problem of data availability. Using the daily tradingdata provided by Pink OTC Markets Inc., our intent is to shed some light on this topic.For each sample firm, we also collect the institutional ownership data before and afterthe Chapter 11 filing from the Thomson-Reuters Institutional Holdings Database. Thisdataset is based on Form 13F filed quarterly with the SEC by institutional managers with$100 million or more in assets under management. With the available data, we mainlyinvestigate the following questions: (1) On any given day after filing until the finalbankruptcy resolution date, what is the percentage of Chapter 11 stocks that are traded?(2) Who trades Chapter 11 stocks: institutional investors or individual investors?

To investigate the percentage of stocks traded in Chapter 11 on each trading day afterfiling, we first calculate the total number of firms remaining in the Chapter 11 process afterfiling. After 252 trading days (one calendar year), approximately 300 firms (around half ofthe sample) have exited Chapter 11. This result is consistent with the overall durationdistribution in Table 1, which shows that the sample median duration is around 350calendar days. We then use the number of firms remaining in the Chapter 11 process as thedenominator and the number of firms with available daily closing prices and tradingvolume as the numerator to calculate the percentage of firms traded on each trading day.Fig. 1 shows the percentage of traded Chapter 11 stocks on each trading day through thethree years following the Chapter 11 filing. Panel A suggests that, after a brief reduction oftrading in the few days immediately following Chapter 11 filing, trading picks up steadily

13For example, the firm with the highest net income of $48.21 million is Waxman USA Inc., which filed for

Chapter 11 on October 2, 2000. Checking all 10-Q filings of the company before its Chapter 11 filing, we

discovered that the reported net incomes were negative except the last pre-Chapter 11 10-Q on September 30,

2000, which was because of the sale of a subsidiary. ‘‘The company completed the sale of all of the remaining

common stock of Barnett Inc. owned by Waxman USA Inc., a wholly owned subsidiary of the Company, and

applied the proceeds to repay Waxman USA’s 11 1/8% Senior Notes due 2001, reduce working capital

borrowings from Congress and to pay taxes and other expenses associated with the transaction,’’ as quoted from

its last 10-Q report. The firm with the highest ROA of 10% is Metrocall Inc., which filed for Chapter 11 on June 3,

2002. This is because we compute ROA using EBITDA, which is before depreciation. The company has a large

amount of depreciation of $18 million, which accounts for 10% of total assets. Thus, its net income is �$29

million.14Marchfirst Inc. has the minimum leverage ratio of 6%. It filed for Chapter 11 on April 12, 2001. It is a short-

lived international systems integrator and Internet consulting company at the tail end of the dot-com boom. It was

a NASDAQ-traded public company whose peak stock price reached $52. By the time the company filed for

bankruptcy, it traded for pennies ($0.16 on March 28, 2001).

Page 10: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

100%

90%

80%

70%

60%Perc

enta

ge o

f Fi

rms

Trad

ed

50%0 10 20 30 40 50

Event Date after Chapter 11 Filing

90%

100%

70%

80%

60%

40%

50%

20%

30%

Perc

rent

age

of F

irms

Trad

ed

0%

10%

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750

Event Date after Chapter 11 Filing

Fig. 1. Percentage of Chapter 11 stocks traded after bankruptcy filing. Panel A: Up to 50 trading days after filing.

Panel B: Up to 750 trading days after filing.

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6042

within a month. Overall, as shown in Panel B, trading of Chapter 11 stocks happens farmore than what is generally perceived: the percentage is well above 50% on most tradingdays, even after three years post-filing.Given the frequent trading of Chapter 11 stocks, we turn to the question of who is

trading these stocks: Are they institutional investors or individual investors? We collect theinstitutional ownership data in each quarter around the Chapter 11 filing time from theThomson-Reuters Institutional Holdings Database. Out of 602 sample firms, we are ableto find 592 firms covered at some point by this database. One relevant caveat of thedatabase is that it is only mandatory to report positions in exchange-traded securities.15

Thus, a firm can be missing from the dataset in any quarter for either of the two followingreasons: (1) the stock is exchange-traded, but the total institutional holding for the stock iszero; or (2) the stock is delisted, thus institutional investors are not required by the SEC to

15According to the SEC, ‘‘Section 13(f) securities generally include equity securities that trade on an exchange

or are quoted on the NASDAQ National Markety.’’ Official lists of Section 13(f) securities each quarter can be

found at: http://www.sec.gov/divisions/investment/13flists.htm.

Page 11: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 43

report their holdings of the stock, which can be zero or positive. Since many of the samplefirms are delisted at some point around Chapter 11 filing, not all firms are covered in everyevent quarter. To resolve this issue, we analyze the data in two ways.

As the first step of the analysis, we look at the number of firms found in the databaseand the percentage of institutional ownership in each quarter around their Chapter 11filings (see Panel A of Fig. 2). The x-axis is the event quarter relative to the Chapter 11filing date, the left y-axis is the number of sample firms reported in Form 13F filings, andthe right y-axis is the percentage of institutional ownership. The number of sample firmsheld and reported by institutional investors decreases sharply from well above 500 toaround 200 through one year before to one year after filing. Without making anyassumptions about the actual holdings for firms not found by the Form 13F Database, wecompute the sample median of percentage institutional ownership across reported firmsin each event quarter. Chapter 11 filings apparently have a significant negative effecton institutional ownership. There is a persistent trend that institutional investors are unloadingthe stocks as a firm approaches Chapter 11 filing. The median percentage decreases fromaround 20% one year before filing to below 5% at the time of filing, and close to 1% one yearafter filing.

0.10

0.15

0.20

200

300

400

500

600

0.00

0.05

0

100 Perc

enta

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titut

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hip

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of F

irm

s with

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itutio

nal

Ow

ners

hip

Dat

a

Event Quarter Relative to Chapter 11 Filing

No. of Firms

Median of Reported Firms

0.20

0.30

0.40

20

30

40

50

0.00

0.10

0

10No.

of

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s with

Inst

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nal

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ners

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a

Event Quarter Relative to Chapter 11 Filing

No. of Firms

Median of Reported Firms Perc

enta

ge o

f Ins

titut

iona

l Ow

ners

hip

-4 -3 -2 -1 0 1 2 3 4

-4 -3 -2 -1 0 1

Fig. 2. Institutional ownership of Chapter 11 stocks in event quarters. Panel A: Full sample. Panel B: Subsample

delisted one-quarter after Chapter 11 filing or never delisted.

Page 12: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6044

In the second step, as shown in Panel B of Fig. 2, we conduct a more robust analysis bystudying only the subsample of 48 firms that remain exchange traded until the secondquarter after their Chapter 11 filings. Since it is mandatory to report positions in thesestocks on Form 13F through the period of quarter (�4, 1) around filing time, theinstitutional ownership data are robust in regards to the above-mentioned no-coverageissue due to delisting. The median institutional ownership for these firms also decreasesmonotonically from around 30% one year before filing to below 10% one-quarter afterfiling. Considering that when institutional investors choose to hold Chapter 11 stocks, theyshould prefer exchange-traded ones due to better liquidity, a conservative upper-bound foraverage institutional ownership after Chapter 11 filing is 10%. Both panels in Fig. 2 thussuggest that institutional investors start to unload bankrupt stocks before and aroundChapter 11 filings. This finding contrasts sharply with our earlier results on active tradingof Chapter 11 stocks, as shown in Fig. 1. Combining these results, we conclude that mostactive trading of Chapter 11 stocks is by individual investors. It is worth mentioning thatour result is not inconsistent with the notion that institutional investors often engage in‘‘vulture investing’’ by taking control of distressed firms. The latter is mostly done bybuying distressed debt rather than distressed equity (Gilson, 1990; Jiang, Li, and Wang,2012).We summarize our main findings on the trading of Chapter 11 stocks as follows:

(1) Active trading exists for Chapter 11 stocks on Pink Sheets. The percentage of stockstraded is above 50%, even after the firms stay in Chapter 11 for three years. (2)Institutional investors sell stocks upon the Chapter 11 filing news. Institutional ownershipof Chapter 11 stocks post-filing is less than 10%, suggesting that the active trading ofbankrupt stocks is mainly generated by individual investors.

5. The valuation of Chapter 11 stocks

As shown in the previous section, Chapter 11 filings have a significant negative effect onstock prices. However, stock prices do not drop to zero after filing. Rather, they are mostlytraded well above zero, and trading remains active long after the filings. So what is thefundamental value of these stocks? We argue that the value of Chapter 11 stocks comesfrom the call option value on firm assets. Shareholders could end up getting no payoff inthe final reorganization plans or liquidation plans, but ex ante the option value shouldbe positive unless the chance of getting anything is zero. Chapter 11 allows the firm tocontinue its business operations. It is possible that business might improve by the time thefirm is evaluated to determine payoffs to claim-holders. Meanwhile, as documented in theAPR violation literature, shareholders can negotiate with creditors in the bankruptcy courtto lower the amount of debt paid back, which essentially lowers the strike price of the calloption and causes the option to be in-the-money.In the following sections, we use two different but related methods to test our option

pricing explanation of the valuation of Chapter 11 stocks. First, we use the Black-Scholespricing model to explain the initial value of Chapter 11 stock at the time of filing. Second,we examine whether the payoff structure of buying the Chapter 11 stocks is related to thefirm’s fundamental value as predicted by the option theory. To obtain a useful sample forthe analysis in this section, we restrict the stocks to satisfy the following conditions: (1) thefirst trading day after Chapter 11 filing is within 30 days after the filing date; (2) there istrading on the bankruptcy resolution date, or within 30 days after the resolution date; and

Page 13: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 45

(3) the time between the first trading day after Chapter 11 filing to the first trading day onor after the bankruptcy resolution date is no less than 30 days.

5.1. The Black-Scholes call option value and market value of Chapter 11 stocks

Merton (1974) shows that when a firm’s debt is a zero-coupon bond, the equity value asa contingent claim on firm value, V, can be solved using the Black-Scholes option formula,where the underlying value process is the firm value process and the strike price is the facevalue of the debt. When a firm needs to make interest payments before the debt maturitydate, or not all of its debts mature on the same date, this method is not very accurate.However, there are no interest payments during the Chapter 11 process, and all debts needto be paid off at the same time on the Chapter 11 resolution date. Thus, it is reasonable touse the Black-Scholes formula to calculate the equity value after Chapter 11 filing asfollows:

CðV ,X ,r,T ,s2Þ ¼VNðd1Þ�Xe�rT Nðd2Þ,

d1 ¼lnðV=X Þ þ ðrþ s2=2ÞT

sffiffiffiffi

Tp ,

d2 ¼ d1�sffiffiffiffi

Tp

, ð1Þ

where V is the current firm value, X is the strike price of the call option, s is the underlyingasset volatility, r is the risk-free rate, and T is the maturity of the option, i.e., the length oftime that the firm expects to stay in Chapter 11.

Measuring V, X, and r is relatively straightforward. Both V and X can be found in thelast pre-bankruptcy quarterly filing. We use total assets as firm value V.16 X is measured bythe face value of the sum of short-term debt and long-term debt. Risk-free rate r is theannualized one-month T-bill rate in the month of Chapter 11 filing.17

The asset volatility s needs to capture the underlying business risk of the firm. Wecompute it using a ‘‘matching firms’’ approach. We do not use any volatility measure ofthe bankrupt firms themselves since the volatility of these firms can capture more ofthe ‘‘filing uncertainty’’ rather than the underlying business risk. Thus, we use the averageasset volatility of matching firms for each bankrupt firm. The matching firms areconstructed by industry and size: for each bankrupt firm, at the time of Chapter 11 filing,we select all the firms that are in the same Fama-French 48-industry group and in the samedecile sorted by book asset value. We calculate an annualized asset volatility for each firmin the matching group of each bankrupt firm at the time of its Chapter 11 filing. The assetvolatility is constructed using the KMV-Merton model as in Bharath and Shumway(2008).18 Then, the average of all matching firms’ asset volatilities is used as the proxy forthe bankrupt firm’s asset volatility s.

16We also use an alternative measure defined as Firm Value¼EVþShort Term Debtþ0.5nLong Term Debt,

where EV is the market value of equity one day after the Chapter 11 filing date. The results remain similar.17We get similar results using longer term Treasury rates.18Using daily data from the past one year, an initial annualized asset volatility is estimated as a standard

deviation of daily percentage change of firm asset value, which is assumed to be equal to daily equity market value

plus the book value of debt. Then the Black-Scholes formula is used to calculate the model implied daily firm asset

value given that the equity market value, which is the call option value, is observed each day. After that, a second

asset volatility is calculated with the model-implied daily firm asset value. The iteration continues until the two

asset volatility numbers converge (i.e., difference is smaller than 0.001).

Page 14: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6046

The maturity of the call option T should be the expected Chapter 11 duration at the timeof the filing. Although we do observe realized durations of sample firms, they are not thesame as expected durations. Therefore, we approximate investors’ expectation with asimple linear regression model to get the conditional mean. Denis and Rodgers (2007) findthat Chapter 11 duration is related to firm size, leverage, profitability, and industry. Weregress realized durations on these variables and use the fitted value as the expected durations.The regression equation is: Duration¼ aþ b1 � Total Assetsþ b2�Leverage Ratioþ b3� ROAþ

b4 � Tangible Ratioþ G�Fama French Ten Industry Dummy Variablesþ E. The accountingvariables are measured in the last quarterly filing before bankruptcy.As a first-step analysis, we plot the observed market value of equity one day after

Chapter 11 filing against the Black-Scholes option value, as shown in Fig. 3. Toaccommodate the heterogeneity of size among sample firms, we take the logarithm of thevariables. The scatter plot shows a significant relation between the observed market valueof Chapter 11 stocks and the theoretical Black-Scholes option value.To further test the hypothesis that the market value of Chapter 11 stocks depends on the

intrinsic option value, we run a regression analyzing the relation of the two:

EV ¼ aþ b1C þ e, ð2Þ

where EV is the logarithm of the market value of Chapter 11 stocks on the first trading dayafter bankruptcy filing, and C is the logarithm of the Black-Scholes option value. In addition,

22

18

20

16

12

14

10

88

10 12 14 16 18 20 22

Mar

ket E

quity

Val

ue

Black-Scholes Option Value

Fig. 3. Log market equity value against log Black-Scholes option value. The market equity value is observed one

day after Chapter 11 filings. The Black-Scholes option value is calculated using the call option formula:

CðV ,X ,r,T ,s2Þ ¼VNðd1Þ�Xe�rT Nðd2Þ,

d1 ¼lnðV=X Þ þ ðrþ s2=2ÞT

sffiffiffiffi

Tp ,

d2 ¼ d1�sffiffiffiffi

Tp

,

where V is the value of total assets in the last pre-bankruptcy quarterly filing, X is the sum of short-term debt and

long-term debt in the last pre-bankruptcy quarterly filing, r is the risk-free rate at filing, s is the underlying asset

volatility constructed as the average of matching firms’ asset volatilities, and T is the predicted duration of the

Chapter 11 process.

Page 15: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 47

we also expand the explanatory variables to the inputs of the Black-Scholes formula:

EV ¼ aþ b1Assetsþ b2Volatilityþ b3Short-Term Debtþ b4Long-Term Debt

þb5Risk-Freeþ b6Durationþ Control Variablesþ e, ð3Þ

where EV is the logarithm of the market value of Chapter 11 stocks on the first trading dayafter bankruptcy filing, Assets is the logarithm of total assets, Volatility is the average annualasset volatility of matching firms, Short-Term Debt is the logarithm of short-term debt, Long-

Term Debt is the logarithm of long-term debt, Risk-Free is the risk-free rate, and Duration isthe predicted duration. The Black-Scholes formula predicts that b140, b240, b3o0, b4o0,b540, and b640.

It is worth noting that Franks and Torous (1994) consider the ‘‘option-to-delay,’’ which is aform of threatening to enter Chapter 11 or once in Chapter 11, delaying the firm’s emergencefrom reorganization. The main variable of interest in Franks and Torous is the ratio of debt tovalue: options that are closer to being at-the-money, according to Franks and Torous,increases shareholder bargaining power and causes more APR violations. In contrast, ourpredictions of the option theory rely on the idea that the stock value upon filing also consistsof an embedded call option on firm assets. In other words, our predictions are based on acollection of variables including total assets, debts, volatility, risk-free rate, and duration.Therefore, the main difference distinguishing the option valuation we discuss here and theAPR violations related to option-to-delay discussed by Franks and Torous lies in thepredictions regarding the coefficients of volatility, risk-free rate, and duration.

To further control for the effect of APR violations on equity value, we use three dummyvariables: Prepack¼1 if the filing is pre-negotiated with creditors and 0 otherwise; DIP¼1 ifthe firm receives DIP financing during bankruptcy and 0 otherwise; and Equity Committee¼1if an equity committee is formed and 0 otherwise. Tashjian, Lease, and McConnell (1996)document that the frequency of APR violations is higher for secured creditors in prepackagedfilings than in traditional Chapter 11 filings. Bharath, Werner, and Panchapegesan (2010) findthat the likelihood of an APR violation increases in prepackaged filings. They also suggestthat DIP financing could act as an effective deterrent to APR violations through stringentrestrictions for financing, and that the existence of an equity committee increases the probabilityof an APR violation. If the expectation of an APR violation is a significant determinant ofstock value after bankruptcy filing, we expect the coefficient of Prepack to be positive, thecoefficient of DIP to be negative, and the coefficient of Equity Committee to be positive.

The estimation results are shown in Table 3. In model 1, the call option value C issignificantly related to the equity value EV and can explain 27.5% of the cross-sectionalvariation of the latter. In model 2, all inputs in the Black-Scholes formula show the expectedsigns as predicted by the option theory, and all of them are statistically significant except forShort-Term Debt.19 The adjusted R-square further increases to 36.8%. It is worth noting that,in any option pricing model, one of the most important determinants of option price isvolatility. Therefore, the success of our option-based explanation hinges on the coefficient forVolatility, which turns out to be positive and significant in all specifications.20 Moreover, thecoefficients of Risk-Free and Duration also support the hypothesis that Chapter 11 stocks have

19One possible explanation is that we use the last quarterly financial statement before the bankruptcy filing to

measure the liabilities at filing. Thus, long-term debt is a more reliable measure than short-term debt.20The fact that we have to use the volatility measure of matching firms as a proxy suggests that the results

should be even stronger if the asset volatility of the Chapter 11 firm is available.

Page 16: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Table 3

Explaining market value of Chapter 11 stocks with the Black-Scholes option value.

Coefficients and t-statistics (in parentheses) of the following regression equations:

EV ¼ aþ b1C þ e,

where EV is the logarithm of the market value of Chapter 11 stocks on the first trading day after Chapter 11 filing,

and C is the logarithm of the Black-Scholes option value. The construction of C is described in Section 5.1.

EV ¼ aþ b1Assetsþ b2Volatilityþ b3Short-Term Debtþ b4Long-Term Debtþ b5Risk-Freeþ b6Duration

þControl Variablesþ e,

where Assets is the logarithm of total assets; Volatility is the average annual asset volatility of matching firms;

Short-Term Debt is the logarithm of short-term debt; Long-Term Debt is the logarithm of long-term debt; Risk-

Free is the risk-free rate; Duration (in calendar days) is the predicted duration with explanatory variables of total

assets, leverage ratio, ROA, tangible ratio, and the Fama-French 10 industry dummy variables; Prepack is a

dummy variable of whether the filing is pre-negotiated; DIP is a dummy variable of whether the firm receives

debtor-in-possession financing; and Equity Committee is a dummy variable of whether an equity committee is

formed.

Model 1 Model 2 Model 3 Model 4 Model 5

Intercept 7.075nnn 1.839n 2.039nn 2.677nnn 2.898nnn

(13.50) (1.83) (1.99) (2.86) (3.04)

C 0.411nnn

(14.03)

Assets 0.616nnn 0.600nnn 0.615nnn 0.599nnn

(13.87) (12.74) (13.79) (12.68)

Volatility 0.670nn 0.656nn 0.573nn 0.566nn

(2.50) (2.43) (2.16) (2.11)

Short-Term Debt �0.009 �0.009 �0.009 �0.009

(�0.78) (�0.80) (�0.80) (�0.79)

Long-Term Debt �0.028nnn �0.028nnn �0.027nnn �0.027nnn

(�3.48) (�3.42) (�3.36) (�3.31)

Risk-Free Rate 7.880nn 8.414nn 8.071nn 8.442nn

(2.30) (2.44) (2.35) (2.44)

Duration 0.002nn 0.002nn

(2.20) (2.25)

Prepack 0.040 �0.024

(0.28) (�0.17)

DIP �0.050 �0.028

(�0.38) (�0.21)

Equity Committee 0.265 0.262

(1.95)n (1.92)n

Adj-R2 27.5% 36.8% 36.9% 36.3% 36.4%

F-Value 196.93 51.14 34.59 59.95 37.98

N 518 518 518 518 518

npo0:10, nn po0:05, nnn po0:01.

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6048

intrinsic option value. In model 3, we add the variables for APR violations to the regressionmodel. The coefficients of Prepack and DIP have the signs predicted by the APR literature,but they are not significant. The coefficient of Equity Committee is positive and significant,suggesting that APR violation expectations explain part of the equity value. Moreimportantly, after controlling for APR violation, the inputs of the option model remain

Page 17: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 49

significant, suggesting that the option theory explains the valuation of bankrupt equity beyondthe expected APR violation.21

To address the concern that predicted duration as an explanatory variable could becorrelated with the other variables (debt and asset), we run robustness checks excluding thepredicted duration variable from the explanatory variables. The results, as shown in models 4and 5 of Table 3, remain similar to those in models 2 and 3. The indicator of the success of theoption theory: the coefficient on the asset volatility variable is still significantly positive. Thecoefficients of all other option variables also have the same signs as predicted.

5.2. The payoff structure of Chapter 11 stocks

If Chapter 11 stocks are indeed out-of-money call options on firm assets, the holding periodreturn of these stocks should depend on the underlying firm performance in a non-linear way:the correlation of the two should be high when firm performance is high and zero otherwise.Since the underlying firm performance is not directly observable, we construct a proxy for itusing the performance of an equal-weighted portfolio of industry- and size-matching firmsover the Chapter 11 duration of the bankrupt firm. The matching firms are constructed thesame way as in the asset volatility calculation described in Section 5.1. Since all matching firmsare in the same decile, the equal-weighted and value-weighted results are similar. Furthermore,we calculate the buy-and-hold return of each matching firm before we take the average toavoid rebalancing bias. When calculating the buy-and-hold return for each matching firm, wetake into account the delisting return following the method used in the prior literature.22

The holding period return of Chapter 11 stocks is defined as the return from the firsttrading day after Chapter 11 filing to the bankruptcy resolution date. If there is no tradingon the bankruptcy resolution date, we use the price on the first trading day after theresolution date. We consider this period to be the holding period. Denote holding periodreturns (HPR) by23

HPR¼ ðPlast�PfirstÞ=Pfirst, ð4Þ

where Plast is the price on the last trading day of the holding period, and Pfirst is the priceon the first trading day of the holding period.

Fig. 4 shows the scatter plot of the HPR of Chapter 11 stocks against the buy-and-holdreturn of an equal-weighted portfolio of matching firms over the same period.24 There arequite a few stocks with very large positive HPR on the right-hand side of the graph (where theperformance of matching firms is relatively good), while most stocks have returns close to�100% on the left-hand side. To systematically test the relation between the performance ofChapter 11 stocks and the matching firms, we estimate a piecewise linear regression:

HPRi ¼ ð1�yiÞnðglow þ blownHPRmatch,iÞ þ yinðghigh þ bhighnHPRmatch,iÞ, ð5Þ

21Our results remain the same if we use moneyness (the ratio of debt over total assets) to replace the level of

debts in the analysis.22When a stock is delisted, we include its delisting return in CRSP if it is available. If the delisting return is

missing in CRSP and the delisting code is either 500 or falls between 505 and 588, we assume the stock is delisted

for negative reasons. For these stocks, we replace the missing delisting return with �30% for NYSE/AMEX

stocks and �55% for NASDAQ stocks.23Since there is no dividend for Chapter 11 stocks, the only gain/loss is the price appreciation or depreciation.24Due to scale limitation, a few extreme values, such as [1.01, 141], are not shown in the graph.

Page 18: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

131415

101112

6789

11

345

Hol

ding

Per

iod

Ret

urn

012

-1-1 -0.5 0 0.5 1 1.5

Matching Sample Return

Fig. 4. Holding period return of Chapter 11 stocks against matching sample returns. The holding period return of

Chapter 11 stocks is defined as: HPR¼ ðPlast�PfirstÞ=Pfirst, where Plast is the price on the last trading day of the

holding period, and Pfirst is the price on the first trading day of the holding period. The holding period is from the

first trading day after filing to the resolution date, or the first trading day after the resolution date if there is no

trading on the resolution date. The matching sample return is the buy-and-hold return of an equal-weighted

portfolio matched by industry and size over the same holding period.

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6050

where HPRi is the holding period return for the bankrupt stock i; HPRmatch,i is the buy-and-hold return of an equal-weighted portfolio of matching firms for bankrupt stock i over thesame holding period; and yi is a dummy variable (1 if HPRmatch,i is above a certain threshold,and 0 otherwise).To ensure continuity, we impose the following restriction on glow, blow, ghigh and bhigh:

glow þ blownThreshold ¼ ghigh þ bhighnThreshold: ð6Þ

We set Threshold¼0 exogenously to estimate the parameters. The regression results showthat blow ¼ 0:10 with t-statistic¼0.36, and bhigh ¼ 2:40 with t-statistic¼2.46. Panel A ofFig. 5 plots the fitted lines of the piece-wise regression for the entire sample. The returncorrelation between a bankrupt stock and its matching firms exhibits strong non-linearity:the correlation is significantly positive when the return of matching firms is positive and iszero otherwise. This finding suggests that the returns to Chapter 11 stocks are similar tothose obtained from buying out-of-money call options on equal-weighted portfolios ofmatching firms.We further conjecture that the option payoff structure could be more pronounced for

some Chapter 11 stocks than others, depending on whether a firm is expected to bereorganized. The option value should only be viable if the firm is expected to continue itsbusiness, and there is a time value regarding its future business success. If a firm is expectedto be liquidated, then there is hardly any option value embedded in equity. In this case, thereturn correlation of the stock and matching firms should be close to zero regardless of theperformance of the latter. Panels B and C in Fig. 5 show the fitted lines of piece-wiseregressions for two subsamples: the ones successfully reorganized and the ones liquidatedor converted to Chapter 7. For the subsample that is reorganized, the resemblance tooption payoffs is more dramatic: blow ¼ 0:34 with t-statistic¼0.99, and bhigh ¼ 2:23 witht-statistic¼3.22. For the subsample that is eventually liquidated or converted to Chapter 7,it is almost one flat line: blow ¼�0:11 with t-statistic¼�0.18, and bhigh ¼�0:04 witht-statistic¼�0.26.

Page 19: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

5

4

3

1

2

0

Hol

ding

Per

iod

Ret

urn

Matching Sample Return

1

2

3

4

5

0Hol

ing

Per

iod

Ret

urn

Matching Sample Return

0

0.2

Hol

ding

Per

iod

Ret

urn

Matching Sample Return

d

Fig. 5. Piecewise linear regression of Chapter 11 stocks’ holding period returns on matching sample returns. The

regression equation is as follows:

HPRi ¼ ð1�yiÞnðglow þ blownHPRmatch,iÞ þ yinðghigh þ bhighnHPRmatch,iÞ,

with the restriction of glow þ blownThreshold ¼ ghigh þ bhighnThreshold, where HPRi is the holding period return for

the bankrupt stock i; HPRmatch,i is the buy-and-hold return of an equal-weighted portfolio of matching firms for

bankrupt stock i over the same holding period; and yi is a dummy variable (1 if HPRmatch,i is above a threshold,

and 0 otherwise). We set Threshold¼0. Panel A: Full sample. Panel B: Emerged or reorganized. Panel C:

Liquidated or converted to Chapter 7.

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 51

In summary, the analysis on the value of Chapter 11 stocks and their return correlationwith underlying firm performance supports the hypothesis that Chapter 11 stocks aretraded well above zero because they have a fundamental option value on firm assets.

6. The performance of Chapter 11 stocks

We investigate the performance of Chapter 11 stocks in the holding period as defined inSection 5.2. Since some Chapter 11 cases get resolved earlier than others, HPR of differentstocks represents performances over different time horizons. Thus, we calculate a standardized

Page 20: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Table 4

Performance of Chapter 11 stocks.

Return distributions of Chapter 11 stocks. The holding period is defined as the number of days from the first

trading day after filing to the resolution date, or the first trading day after the resolution date if there is no trading

on the resolution date. The holding period return (HPR) is defined as: HPR¼ ðPlast�PfirstÞ=Pfirst, where Plast is the

price on the last trading day of the holding period, and Pfirst is the price on the first trading day of the holding

period. The average monthly return (MHPR) is defined as: MHPR¼ ð1þHPRÞ21=t, where t is the number of

trading days during the holding period. The market-adjusted average monthly return (MHPRMarketAdj) is defined

as: MHPRMarketAdj ¼ ð1þHPRÞ21=t�ð1þHPRMarketÞ

21=t, where HPRMarket is the buy-and-hold return of the

value-weighted NYSE/AMEX/NASDAQ market index over the holding period. The industry- and size-adjusted

average monthly return (MHPRMatchAdj) is defined as: MHPRMatchAdj ¼ ð1þHPRÞ21=t�ð1þHPRMatchÞ

21=t, where

HPRMatch is the buy-and-hold return of an equal-weighted portfolio matched by industry and size over the

holding period.

HPR MHPR MHPRMarketAdj MHPRMatchAdj

Min �1.00 �0.96 �0.98 �1.10

Median �0.88 �0.15 �0.14 �0.15

Max 141.00 0.45 0.43 0.51

Mean �0.06 �0.16 �0.16 �0.16

Std. Dev. 6.45 0.19 0.19 0.19

Skewness 20.08 �0.37 �0.45 �0.53

Kurtosis 435.16 1.83 1.86 2.43

t-Value �0.22 �19.48 �19.52 �19.88

p-Value of student’s t 0.83 0.00 0.00 0.00

p-Value of sign 0.00 0.00 0.00 0.00

p-Value of signed rank 0.00 0.00 0.00 0.00

N 531 531 531 531

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6052

monthly holding period return, MHPR¼ ð1þHPRÞ21=t, where t is the number of tradingdays in the holding period. We then calculate the risk-adjusted returns in two ways: using thebuy-and-hold return of the value-weighted NYSE/AMEX/NASDAQmarket index, and usingthe buy-and-hold return of an equal-weighted portfolio matched by industry and size over theholding period as described in the previous section.25 They are defined as follows:

MHPRMarketAdj ¼ ð1þHPRÞ21=t�ð1þHPRMarketÞ

21=t, ð7Þ

MHPRMatchAdj ¼ ð1þHPRÞ21=t�ð1þHPRMatchÞ

21=t: ð8Þ

Table 4 gives distribution statistics of HPR, MHPR, MHPRMarketAdj, and MHPRMatchAdj forsample stocks. The mean and median for all return measures are negative. Specifically, themedian market-adjusted monthly return is �14% and the industry- and size-adjusted monthlyreturn is �15%. Because HPR is heavily left-skewed, we conduct the Wilcoxon rank tests forall return measures to examine whether they are different from zero. The p-values are all closeto zero, suggesting that the performance of Chapter 11 stocks is significantly negative bothbefore and after the risk adjustment.Table 5 describes the distribution statistics of HPR and MHPRMatchAdj sorted by the initial

price level, final outcome, and delisting time. The initial price level is a proxy for firm size. Thefinal outcome is relevant because successfully reorganized firms are supposedly the ones with

25Using equal-weighted market index return or value-weighted matching portfolio return does not change the

results.

Page 21: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Table 5

Distribution statistics of HPR and MHPRMatchAdj sorted by price, outcome, and delisting time.

Distribution statistics of HPR and MHPRMatchAdj sorted by the initial price level right before filing, resolution

outcome, and delisting time. The holding period return is defined as: HPR¼ ðPlast�PfirstÞ=Pfirst, where Plast is the

price on the last trading day of the holding period, and Pfirst is the price on the first trading day of the holding

period. The industry- and size-adjusted average monthly return is defined as: MHPRMatchAdj ¼ ð1þHPRÞ21=t�

ð1þHPRMatchÞ21=t, where HPRMatch is the buy-and-hold return of an equal-weighted portfolio matched by

industry and size. There are three sub-groups by the initial price level: (0, $0.1), ($0.1, $0.5), and ($0.5, $10).

Resolution outcomes are classified as either (1) Successfully Reorganized or (2) Others. Delisting time is classified

as either (1) Delisted within the holding period or (2) Others.

Panel A: Distribution statistics of HPR sorted by price, outcome, and delisting time

N Mean Std. Dev. Min Median Max

(0, 0.1) 170 �0.28 2.31 �1.00 �0.71 27.47

Initial Price ($1) (0.1, 0.5) 237 0.25 9.40 �1.00 �0.90 141.00

(0.5, 10) 124 �0.36 1.40 �1.00 �0.92 9.96

Resolution Outcome Successfully Reorganized 237 �0.06 2.12 �1.00 �0.63 21.31

Others 294 �0.06 8.46 �1.00 �0.95 141.00

Delisting Time Delisted within Holding Period 163 �0.43 1.29 �1.00 �0.91 9.96

Others 368 0.10 7.69 �1.00 �0.83 141.00

Panel B: Distribution statistics of MHPRMatchAdj sorted by price, outcome, and delisting time

N Mean Std. Dev. Min Median Max

(0, 0.1) 170 �0.16 0.21 �1.10 �0.13 0.38

Initial Price ($1) (0.1, 0.5) 237 �0.17 0.18 �0.75 �0.16 0.51

(0.5, 10) 124 �0.15 0.17 �0.82 �0.15 0.33

Resolution Outcome Successfully Reorganized 237 �0.12 0.17 �0.66 �0.12 0.51

Others 294 �0.20 0.19 �1.10 �0.18 0.30

Delisting Time Delisted within Holding Period 163 �0.16 0.17 �0.82 �0.16 0.33

Others 368 �0.16 0.19 �1.10 �0.15 0.51

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 53

better operating performance during Chapter 11. We expect these stocks to exhibit betterreturns, as long as the resolution outcome is not 100% predictable at the time of filing.Delisting is generally a result of bad performance, and in return it also affects stock pricesadversely, as shown in Harris, Panchapagesan, and Werner (2008). Results shown in Table 5confirm that firms eventually reorganized experience less negative returns, while firms delistedwithin Chapter 11 have more negative returns. However, returns do not seem to depend on theinitial price level of the stocks. In addition, untabulated results indicate that the negativereturns are persistent over time and do not cluster in a particular year.

Given the observation of large negative abnormal returns of Chapter 11 stocks in thesample, we investigate two related questions. First, why do the negative abnormal returnsexist in the first place? Second, given the existence of the negative abnormal returns, whydo not arbitrageurs short the stocks and correct the prices? Our answers to these questionsare motivated by the information uncertainty surrounding the Chapter 11 stocks atbankruptcy filings and the difficulty of short-selling these stocks. Miller (1977) argues thatthe very uncertain nature of financial markets implies heterogeneous evaluations of thesame financial asset. Therefore, in a market with restricted short selling and when investorshave heterogeneous beliefs about the value of a risky asset, prices will reflect a more

Page 22: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6054

optimistic valuation. In the next section, we show that this is exactly the case for thevaluation of stocks after Chapter 11 filings. Furthermore, we address a unique feature ofChapter 11 stocks: at the final bankruptcy resolution date, the reorganization/liquidationplan states explicitly the true value of the stock. At this point, fundamental value isrevealed, and prices are corrected to reflect the true fundamental value. As a result, thebuy-and-hold return from filing to resolution becomes negative.

6.1. Information uncertainty, short-sale constraints, and arbitrageur risk of Chapter 11 stocks

When a firm files for Chapter 11, it significantly increases the information uncertainty of itsstock. There are several reasons for this effect. First, most stocks are delisted before or aroundChapter 11 filings. They can resume trading on Pink Sheets, where listing rules are far lessstrict than in the major exchanges. SEC filings and disclosures are not mandatory for thesestocks. Second, most institutional investors, such as mutual funds and pension funds, cannothold bankrupt stocks, as stipulated in their investment mandates. Thus, sell-side analysts lackthe incentive to research and publish on these stocks.26 Therefore, the problem of scarceinformation available for Chapter 11 stocks is further exacerbated. Third, as the stockownership data shows, more than 90% of the investors are individual investors post-filing.Presumably, individual investors are less efficient in gathering information and less adept atcorrectly interpreting the available information (Barber and Odean, 2000). The increasedinformation uncertainty can clearly be seen in the data of average quote spread and intradayvolatility around the filing date. Fig. 6 plots the time series of quoted spreads and intradayvolatilities from one month (21 trading days) before to one month after the filing date. Thelarge spike for both series centering around the Chapter 11 filing date shows dramaticallyincreased information uncertainty of stocks due to filings.Short-selling is generally very difficult for Chapter 11 stocks traded on Pink Sheets, and

short-sellers face high arbitrageur risks even if they manage to short these stocks in the firstplace. First, most institutional investors do not hold these stocks. As shown in D’Avolio(2002), the main suppliers of stock loans are institutional investors. In addition, Nagel (2005)finds that stock loan supply tends to be sparse and short-selling more expensive wheninstitutional ownership is low. Therefore, the substantially increased search and borrowingcosts make bankrupt stocks much less attractive to arbitrageurs. Second, Pink Sheets is not asliquid as major exchanges, especially for bankrupt stocks. Quoted spreads for some can beas high as 30%, as shown in Fig. 6. Therefore, the recalling risk from share lenders issubstantially higher for these stocks: If the borrowed shares are called, it may be difficult forthe arbitrageur to find a new lender, and it will be expensive to buy the shares in the market.27

6.2. The cross-section of Chapter 11 stock returns

If the negative abnormal returns of Chapter 11 stocks are indeed caused by the initialovervaluation by optimistic investors at the time of filing, cross-sectionally stocks with higher

26As pointed out by Harris, Panchapagesan, and Werner (2008), there is limited analyst coverage on stocks

trading on Pink Sheets.27Short-sellers of Chapter 11 stocks are vulnerable to a short squeeze because rumors about bankrupt

companies often lead to a rapid increase in the stock price without any justifiable reason. In addition, the high

collateral requirement of short-selling relative to the low price level of these stocks imposes another type of

arbitrageur risk for bankrupt stocks.

Page 23: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

0.25

0.3

0.35

0.15

0.2Ave

rage

Quo

ted

Spre

ad

Trading Days around Chapter 11 Filing

0.4

0.6

0.8

1

0

0.2

Ave

rage

Intr

aday

Vol

atili

ty

Trading Days around Chapter 11 Filing

Fig. 6. Average quoted spread and intraday volatility around Chapter 11 filing. Average Quoted Spread is the

cross-sectional average of quoted spread (bid–ask spread divided by the bid–ask midpoint); and Average Intraday

Volatility is the cross-sectional average of intraday volatility (difference between the daily highest price and lowest

price divided by the closing price). Panel A: Quoted spread. Panel B: Intraday volatility.

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 55

information uncertainty and more severe short-sale constraints should experience morenegative returns after filing. Glosten and Milgrom (1985) show that dealer bid–ask spreads arerelated to heterogeneous information among traders. Volatility is used as a standard measureof information uncertainty in the literature (see Zhang, 2006, among others). Scheinkman andXiong (2004) provide a detailed survey of literature analyzing how heterogeneous beliefsamong investors generate speculation and trading volume. Following the previous literature,we measure the level of information uncertainty with the following variables: the average dailybid–ask spread, the average intraday volatility, and the average trading turnover over theChapter 11 duration. To measure the short sale constraint, we use the proportion of sharesheld by institutional investors. Following Chen, Hong, and Stein (2002), we also use thebreadth of institutional ownership as another measure of short sale constraint, which is thenumber of institutional investors holding the stocks. We estimate the following regression:

MHPRMatchAdj ¼ aþ b1Quoted Spread þ b2Intraday Volatilityþ b3Turnover

þb4Institutional Ownershipþ Control Variablesþ e, ð9Þ

Page 24: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6056

where MHPRMatchAdj is the industry- and size-adjusted monthly return; Quoted Spread is theaverage daily quoted spread (bid–ask spread divided by the bid–ask midpoint) over theholding period for each firm; Intraday Volatility is the average intraday volatility (differencebetween the daily highest price and lowest price divided by the closing price) over the holdingperiod for each firm; Turnover is the average trading volume over shares outstanding over theholding period; and Institutional Ownership is measured by either the proportion of shares heldby institutional investors at the end of the quarter when the firm files for Chapter 11, or thelogarithm of one plus the number of institutional investors.The results, shown in Table 6, confirm our hypothesis that stocks with higher quoted

spreads, higher intraday volatilities, and higher turnover have significantly lower returns,and that stocks with lower institutional ownership (more severe short-sale constraints)have lower subsequent returns in Chapter 11.28 Our proxies for information uncertaintyand short-sale constraints alone can explain a substantial amount of the cross-sectionalvariation in stock returns, with adjusted R-squared equal to about 17%. Moreover, all ofour proxies for information uncertainty and the percentage of institutional ownershipremain highly significant after controlling for firm characteristics and industry-year fixedeffects. Examining the effects of control variables on post-filing performance, we find thatfiling cases that are prepackaged have better returns during Chapter 11. While such afinding is consistent with the APR literature prediction, it also may be that these firmshave less information uncertainty, and so the optimistic bias of investors is less severe.Consistent with the APR literature prediction, the existence of an equity committee ispositively related to return. Finally, other pre-filing firm characteristics, such as size,leverage, and profitability, have little explanatory power after considering the informationvariables and short-sale constraint proxies. Overall, our findings indicate that the negativereturns of Chapter 11 stocks are mainly caused by initial overvaluation by optimisticinvestors in the context of heterogeneous beliefs with short-sale constraints.Since average daily bid–ask spreads and average turnover are also liquidity measures,

Table 6 can be interpreted as controlling for the liquidity condition of the stock,information uncertainty proxied by the average intraday volatility is negatively related toreturns in Chapter 11. Additionally, as a robustness check, we run the same regression asin Table 6 excluding these two variables, and use the average intraday volatility as the solemeasure for information uncertainty. The results essentially remain the same, as shown inTable 7. The magnitude and statistical significance of the coefficient on Intraday Volatility

are both larger as compared to in Table 6, suggesting the other two measures also correlatewith the level of information uncertainty.Our findings that institutional investors are dropping Chapter 11 stocks imply that the

individual investors may have beliefs that are different from institutional investorsregarding the value of these stocks. There are many well-documented behavioral biasesrelated to individual investors (see a survey by Barberis and Thaler, 2003). In particular,Barberis and Huang (2008) rely on an idea in the field of psychology that the brain weightsprobabilities in a nonlinear way. They show that, in a financial market, such psychologybias will cause some investors to overvalue risky assets with lottery-like payoffs. Given ourfindings that Chapter 11 stocks resemble out-of-money call options, these stocks providelottery-like payoffs to investors. Therefore, our results are consistent with the idea thatindividual investors are more likely than institutional investors to suffer from the probability

28Results using market-adjusted monthly returns are similar and available upon request.

Page 25: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Table 6

Explaining the performance of Chapter 11 stocks.

Coefficients and t-statistics (in parentheses) of the following regression equation:

MHPRMatchAdj ¼ aþ b1Quoted Spread þ b2Intraday Volatilityþ b3Turnoverþ b4Institutional Ownership

þControl Variablesþ e,

where MHPRMatchAdj is the industry- and size-adjusted monthly return; Quoted Spread is the average daily quoted

spread (bid–ask spread divided by the bid–ask midpoint) over the holding period for each firm; Intraday Volatility

is the average intraday volatility (difference between the daily highest price and lowest price divided by the closing

price) over the holding period; Turnover is the average trading volume over shares outstanding over the holding

period; Institutional Ownership is measured by either the proportion of shares held by institutional investors at the

end of the quarter when the firm files for Chapter 11, or the logarithm of one plus the number of institutional

investors; Delisted is a dummy variable of the delisting time (1 if the stock is delisted within the Chapter 11

process, and 0 otherwise); Prepack is a dummy variable of whether the filing is pre-negotiated; DIP is a dummy

variable of whether the firm receives debtor-in-possession financing; and Equity Committee is a dummy variable of

whether an equity committee is formed. Other control variables are defined as in Table 2.

Model 1 Model 2 Model 3 Model 4

Intercept �0.090nnn �0.107nnn �0.132 �0.096

(�6.18) (�4.55) (�1.26) (�0.91)

Quoted Spread �0.125nnn �0.114nnn �0.090nnn �0.088nnn

(�5.19) (�4.50) (�3.24) (�3.13)

Intraday Volatility �0.057nnn �0.062nnn �0.067nnn �0.070nnn

(�4.00) (�4.30) (�4.60) (�4.74)

Turnover �1.691nnn �1.730nnn �1.594nnn �1.669nnn

(�4.45) (�4.48) (�3.80) (�3.93)

Percentage of Institutional Ownership 0.252nnn 0.282nnn

(2.70) (2.82)

Breadth of Institutional Ownership 0.017n 0.011

(1.75) (0.89)

Log(Total Assets) �0.002 �0.003

(�0.31) (�0.36)

Leverage 0.005 0.002

(0.43) (0.16)

Tangible Ratio 0.049 0.049

(1.30) (1.30)

ROA �0.018 �0.014

(�0.61) (�0.48)

Delisted �0.002 0.002

(�0.10) (0.09)

Prepack 0.056nnn 0.052nn

(2.78) (2.58)

DIP �0.006 �0.006

(�0.30) (�0.30)

Equity Committee 0.034n 0.032n

(1.83) (1.72)

Industry and Year Dummies Included Included

Adj-R2 17.0% 16.2% 21.0% 19.6%

F-Value 23.23 21.96 4.88 4.55

N 436 436 424 424

npo0:10, nn po0:05, nnn po0:01.

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 57

weighting bias, thus causing the heterogeneous beliefs regarding Chapter 11 stocks. A detailedanalysis of the behavioral biases related to individual investors is outside the scope of ourpaper, and we will leave it for future research.

Page 26: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Table 7

Explaining the performance of Chapter 11 stocks—robustness checks.

Coefficients and t-statistics (in parentheses) of the following regression equation:

MHPRMatchAdj ¼ aþ b1Intraday Volatilityþ b2Institutional Ownershipþ Control Variablesþ e,

where MHPRMatchAdj is the industry- and size-adjusted monthly return; Intraday Volatility is the average intraday

volatility (difference between the daily highest price and lowest price divided by the closing price) over the holding

period; Institutional Ownership is measured by either the proportion of shares held by institutional investors at the

end of the quarter when the firm files for Chapter 11, or the logarithm of one plus the number of institutional

investors; Delisted is a dummy variable of the delisting time (1 if the stock is delisted within the Chapter 11

process, and 0 otherwise); Prepack is a dummy variable of whether the filing is pre-negotiated; DIP is a dummy

variable of whether the firm receives debtor-in-possession financing; and Equity Committee is a dummy variable of

whether an equity committee is formed. Other control variables are defined as in Table 2.

Model 1 Model 2 Model 3 Model 4

Intercept �0.146nnn �0.172nnn �0.233nn �0.201n

(�12.55) (�8.78) (�2.18) (�1.88)

Intraday Volatility �0.091nnn �0.094nnn �0.090nnn �0.092nnn

(�6.89) (�7.03) (�6.65) (�6.76)

Percentage of Institutional Ownership 0.279nnn 0.282nnn

(3.07) (2.86)

Breadth of Institutional Ownership 0.025nnn 0.008

(2.73) (0.61)

Log(Total Assets) 0.006 0.007

(0.98) (0.91)

Leverage 0.010 0.008

(0.92) (0.70)

Tangible Ratio 0.046 0.045

(1.19) (1.17)

ROA �0.022 �0.021

(�0.75) (�0.67)

Delisted �0.017 �0.010

(�0.93) (�0.54)

Prepack 0.051nn 0.049nn

(2.54) (2.40)

DIP �0.004 �0.006

(�0.22) (�0.31)

Equity Committee 0.035n 0.034n

(1.86) (1.79)

Industry and Year Dummies Included Included

Adj-R2 11.7% 11.4% 18.0% 16.4%

F-Value 31.06 29.96 4.56 4.19

N 453 453 441 441

npo0:10, nn po0:05, nnn po0:01.

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–6058

7. Conclusions

Our paper provides a thorough understanding regarding the trading, value, and performanceof the stocks in Chapter 11 using a unique dataset from Pink OTCMarkets Inc. First, we showthat there is far more active trading of these stocks through the Chapter 11 process than isgenerally perceived. Institutional investors unload the stocks when firms approach bankruptcyfilings, and around 90% of the investors are individual investors post-filing. Second, we show

Page 27: Investing in Chapter 11 stocks Trading, value, and performance · Investing in Chapter 11 stocks: Trading, value, and performance$ Yuanzhi Lia,1, Zhaodong (Ken) Zhongb,n aDepartment

Y. Li, Z. Zhong / Journal of Financial Markets 16 (2013) 33–60 59

that Chapter 11 stocks have positive fundamental values because they are call options on firmassets. The option value calculated using the Black-Scholes model can explain a substantialportion of the cross-sectional variation in the observed market equity values right after filing.Even after controlling for the expectation of APR violations, the equity value after filing ispositively related to asset value, asset volatility, risk-free rate, and expected duration, and it isnegatively related to liabilities. Moreover, the return correlation between Chapter 11 stocks andan industry- and size-matching sample exhibits strong non-linearity as predicted by the optiontheory. Third, we document large negative returns of Chapter 11 stocks, both before and afterrisk adjustments. Recognizing the increased information uncertainty and tightened short-saleconstraints accompanying the bankruptcy filing, as well as the unique feature of Chapter 11stocks that the true value is revealed upon bankruptcy resolution, we provide an explanation forthe negative abnormal returns in the context of heterogeneous beliefs with short-sale constraints.Consistent with our hypothesis, we show that stocks with more information uncertainty andlower institutional ownership, and thus more binding short-sale constraints, tend to have morenegative returns over the duration of the Chapter 11 process.

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