UFDC Home  Search all Groups  UF Institutional Repository  UF Institutional Repository  UF Theses & Dissertations  Vendor Digitized Files   Help 
Material Information
Subjects
Notes
Record Information

Full Text 
BANKRUPTCY STUDIES: EMPIRICAL WORKS ON PREDICTION AND FINANCIAL MARKETS By KEQIAN BI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1989 ACKNOWLEDGEMENTS I am greatly indebted to the members of my dissertation supervisory committee: Dr. Roy L. Crum and Dr. Haim Levy, committee cochairmen, and Dr. David Denslow. Their support, advice, and guidance have made this dissertation a reality and have greatly enhanced my academic experience at the University of Florida. I would also like to thank my family for their unwavering support, without which this dissertation would have been impossible. Even as I write now, I think of my kind, loving parents, Professors Zhongjie Bi and Shaoxiang Huang, who, though half a world away, have wished so much for my success in this Ph.D. program. I want to share it today with many people, but with them most of all. Finally, I want to dedicate my dissertation to a new future for my homeland, China. The lessons and memories of May and June 1989 will be remembered forever. TABLE OF CONTENTS ACKNOWLEDGEMENTS . . ABSTRACTS. ..... . . CHAPTERS 1 OVERVIEW AND OUTLINE. ... . 1 Topic Overview. . . 1 Dissertation Outline. .. . .. 5 Note. . . 7 2 LITERATURE REVIEW ... . .. 8 Summary of Current Literature . 8 Significance of this Dissertation .. 14 3 METHODOLOGY TO STUDY FINANCIAL MARKETS AND BANKRUPTCY . .. 17 Note . . 22 4 RESULTS ON FINANCIAL MARKETS AND BANKRUPTCY 27 Notes . . .. 35 5 EMPIRICAL MODEL OF BANKRUPTCY .. 48 Variable Definitions. . ... 51 Hypotheses. ..... . .. 57 6 METHODOLOGY TO TEST EMPIRICAL MODEL .. 62 The Logist Analysis Methodology .. 62 Logist versus Discriminant Analysis .. .64 Sample Design . .. .. 67 7 RESULTS OF EMPIRICAL MODELS OF BANKRUPTCY 8 SUMMARY AND CONCLUSIONS .. Research Summary. . . Future Research . . APPENDIX . .. .. REFERENCES .. . . BIOGRAPHICAL SKETCH. . . . 74 . 99 . 99 . 102 . 104 . 154 . 157 iii o o Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy BANKRUPTCY STUDIES: EMPIRICAL WORKS ON PREDICTION AND FINANCIAL MARKETS By Keqian Bi August 1989 Chairman: Roy L. Crum Cochairman: Haim Levy Major Department: Finance, Insurance, and Real Estate This dissertation studied two areas not covered by current bankruptcy research. First, the question whether financial markets could assess bankruptcy risk beforehand was addressed. Second, the problems of longterm bankruptcy prediction models were discussed, and a new model with reasonably accurate long as well as shortterm predictive powers was developed. On the subject of financial markets, this dissertation looked at whether the market could assess bankruptcy risk ahead of time. The risk premia of corporate bonds of bankrupt companies were used to investigate whether there was any rise in risk premia as companies approached bankruptcy. Then, an event study was done to determine whether bond downgrades affected the performance of a laterbankrupt company's stock's daily rates of return. It was found that risk premia did increase as companies approached bankruptcy, and that the risk premia of companies which were later liquidated rose more than the risk premia of companies which later reorganized. The eventstudy showed that the daily rates of returns of stocks of companies which later went bankrupt did fall significantly during the first downgrade, unlike those of companies which did not. On the subject of bankruptcy prediction, this dissertation looked at whether an accurate, longterm bankruptcy model could be developed using variables which assess a company's fundamental characteristics as well as its current financial position. A model based on the following eight variables was developed: return on assets, fixed charge coverage, balance ratio, markettobook ratio, relatedness ratio, net rate of management stock acquisitions, relative sales growth, and capital intensity. It had achieved high classification success and predictive accuracy, and, unlike those of past models, its predictive powers did not decrease over time. Finally, work was done on the use of logist analysis in bankruptcy predictions. It was shown that any nonrandom, statebased sample selection technique would distort the probabilities generated by logist models. A formula was derived to remedy this problem by providing an adjustment scheme whereby the resulting probabilities could be made to work for a general population. CHAPTER 1 OVERVIEW AND OUTLINE Topic Overview Bankruptcy is one of the most important topics in modern finance. It plays a strong, visible role in all dimensions of financial economics, such as the efficient market theory, portfolio theory, capital asset pricing theory, option pricing theory, and agency theory. Thus, understanding bankruptcy is important to financial research in both theory and practice. In theory, if we thoroughly understood the dynamics and causes of bankruptcy, we should be able to make the risk of bankruptcy a parameter in market valuations of debt and equity. Assuming that investors are naturally risk averse, such formulas can determine how the probability of bankruptcy affects the average investor's utility. In practice, researchers have tried to develop predictive models of bankruptcy that can alert interested parties to the impending dangers of bankruptcy before it is too late to take corrective actions. Because practically any group involved with a company would be interested in the risk of bankruptcy it 2 faces, potentially widespread demand for such a model has inspired much research in this area. To date, several approaches have been taken to develop predictive models; they are discussed in the Literature Review section. While substantial work has been done on various aspects of bankruptcy, including empirical forecasting and prediction, we believe that past works have left a few areas unexplored. First, many successful predictive models of bankruptcy have been developed, but most of these models base their assessment of a company's bankruptcy risk primarily on its current financial position. They rely heavily on such accounting data as retained earnings and capitalization ratios. Some of these predictive models have grown quite complex. Because they use mostly current financial data, however, their predictive power is limited to a relatively short period before bankruptcy, usually one year. When they are used to predict bankruptcy further into the future than one year, their accuracy falls significantly. Second, no one, to date, has studied whether the market can somehow predict bankruptcy. Modern finance considers financial markets to be efficient, but no research has yet been done on whether this efficiency extends to the evaluation of companies' bankruptcy risk. After all, if the market were truly efficient, then it should include the risk of bankruptcy as one of the determinants of the value of a company's securities. Hence, the market's assessment of a company's 3 securities' risk should include as a component the company's chances of bankruptcy. In this dissertation, we address both of these areas that present bankruptcy research has largely overlooked. First, we explore the market's ability to "sense" coming bankruptcy by looking at the risk premia of corporate bonds. We first examine whether such risk premia rise as the event of bankruptcy approaches. Then, we investigate what role the bond rating agencies, Standard & Poor's and Moody's, play in the market assessment of a company's overall risk in general and bankruptcy risk in particular. In other words, if the market actually does include bankruptcy risk in its overall assessment of a company's risk, then how do S&P's and Moody's ratings affect this market assessment? Do they provide new information to the market and, therefore, serve as a crucial link in the process, or does the market itself already reflect all of the information these rating agencies provide? To answer this question we have to study two problems. First, assuming that the first consistent downgrade of a corporate bond provides the most relevant information, we determine whether S&P's and Moody's downgrades precede or follow increases in the bond's risk premium.1 Second, with the same assumption, we explore what impact, if any, the first bond downgrade has on the performance of the company's stock. Arguably, if nothing happens to the stock's return or the bond risk premium after a bond downgrade, then we can infer that 4 the market has already absorbed all the information S&P's and Moody's provide in the rating change. In that case, we can say that S&P's and Moody's provided no new information in the market's assessment of a company's bankruptcy risk. If, however, the market reacts strongly after a bond downgrade and the bond's risk premium rises or the stock return changes significantly with the downgrade, then we can say that S&P's and Moody's do provide new information to the market in its assessment of bankruptcy risk. In that case, we can further conclude that bond downgrades are good indicators of increased bankruptcy risk and correspondingly higher risk premia. To study bond risk premia and bankruptcy, we first compile the yieldtomaturity of bonds of companies that went bankrupt and subtract from them the yield to maturity of government bonds. Then, to assess the impact of bond rating downgrades, we use the methodology known as "event study," which is described in greater detail later in Chapter 3. The second area that has largely been overlooked in bankruptcy research is the "nearsightedness" problem of current predictive models of bankruptcy. We attempt to overcome this shortcoming by building an empirical model that includes new sets of variables with a longterm orientation. We believe that as one tries to predict bankruptcy farther ahead in time, a company's current financial position becomes less significant, while other, currently unexplored factors play increasingly larger roles. For example, a company's 5 current return on assets (ROA) may be critical to whether it is solvent or bankrupt within the next few years, but its longterm financial health would probably depend less on current profit levels than on the fundamental characteristics of the company that predetermine future ROA. Hence, to make accurate longterm bankruptcy forecasts, we must examine not only a company's current financial position, but also its more fundamental operating characteristics, such as its lines of business, degree of diversification, management efficiency, and growth. We adopt this approach to develop an empirical model of bankruptcy that can forecast the extent of bankruptcy risk. In addition to a group of four variables designed to assess a company's current financial position, we adopt variables that describe a company's management ownership position, its degree of diversification, the lines of business in which it operates and their relationship, and its growth relative to the rest of the industry. We expect that a model based on this broader specification of variables will have high long term as well as shortterm predictive powers. Dissertation Outline In the following chapters, we present the research design and findings of our dissertation. Chapter 2 examines current literature on both bankruptcy prediction and the effects of bond rating changes, which, as stated earlier, are used to 6 study financial markets' signals about bankruptcy. Chapter 3 discusses the techniques and methodologies we employ to study the financial market's ability to sense impending bankruptcy. Then Chapter 4 identifies the data sources for our work on financial markets and bankruptcy and presents the results we obtained in the marketoriented part of the dissertation. Chapter 5 discusses in depth the rationale for and the variables used in our empirical model of bankruptcy. Attention is focused on why each variable was chosen, what values each variable should have, and what we expect our model to tell us about the role each of our variables should play in assessing bankruptcy risk. In Chapter 6 the methodology we used to build our empirical model is described. This is logist analysis, and we will discuss the advantages it has over the more traditional discriminant analysis. Chapter 7 gives the results we obtained from tests of our empirical model. Finally, Chapter 8 summarizes our research, presents the conclusions we reach, and points out possibilities for future research. Note 1. "Consistent" means a bond downgrade after which there were no upgrades until the company filed for Chapter 11. In other words, this downgrade is the first of a series of downgrades which eventually lead to bankruptcy, uninterrupted by any upgrades of the same bond. CHAPTER 2 LITERATURE REVIEW Summary of Current Literature Market Efficiency Studies of Bond Rating Changes Katz (1974), in one of the earliest works on bond rating changes, developed an eventoriented methodology for testing the efficiency of the bond market. He looked for "unusual behavior" in a bond's yield to maturity twelve months prior to and five months after a rating change. His data consisted of electric utilities bonds from 1966 to 1972. Katz derived a quadratic regression equation of yield to maturity at any given time, t, based on maturity, total float, and coupon rate. Then, he compared his expected yields with the actual yields and the changes in the actual yields with premium differentials of two rating classes. He concluded that no anticipation exists prior to a public announcement of a rating change. After the rating change, there was a lag of six to ten weeks before yieldtomaturity fully adjusted to the new rating class. 9 Weinstein (1977) tried to determine if bond rating changes contained new information by studying the bonds' prices during the time period surrounding rating change announcements. His sample consisted of utilities and industrial bonds from July 1962 to July 1974. Weinstein started with portfolios which, for every month, contained all bonds with a given rating. He then constructed a series of riskadjusted returns for each bond by subtracting the return on the appropriate rating class portfolio from the return on the given bond. He selected the bonds that had a rating change and looked at if those bonds had abnormal returns during periods of rating changes. Weinstein concluded that bond rating changes caused no significant price change during or after the announcement, and that adjustments in the market were made 18 to six months before the event. Hence, his study suggested that rating changes provided no new information. Pinches and Singleton (1978) studied the effects of bond rating changes on the market returns of stocks during the period from January 1950 to September 1972. For each stock, they derived a market return based on its beta and measured the actual return against the expected return for a period of thirty months before to twelve months after a rating change. Their study calculated disturbance terms (residuals) of stock returns during the period. Pinches and Singleton concluded that all changes attributable to companies' financial situations were fully anticipated 15 to 18 months ahead of 10 time, while all changes attributable to companyspecific events were anticipated six months ahead of time. Thus, although there were abnormally high and low returns corresponding to upgrades and downgrades, respectively, before a rating change, there were normal returns after the rating change. Again, a study concluded that bond rating downgrades provided no new information to the market. Finally, Griffin and Sanvincente (1982) used three different methodologies to study the effects of rating changes on common stock prices. Their study contained 180 rating changes from 1960 to 1975. First, they used a portfolio method similar to that of Weinstein (1977). Then they employed a onefactor and a twofactor model, basing their expected stock prices on betas, as had Pinches and Singleton (1978). They found that although rating upgrades had no effect on stock prices, downgrades did have significant effects. Because of the inconclusive nature of their results, further research in this area was necessary. The methodology employed in this dissertation differs from previous works in several important ways. First, previous authors used yieldtomaturity, an absolute value, as their indicator of return. It is our position that absolute yieldtomaturity, in this application, is not an accurate measure of return. Instead, we suggest using a relative value, the risk premium, which is defined as the difference between a bond's yieldtomaturity and the yield 11 tomaturity of a riskfree security. Second, we construct our samples not by industry but by the nature of the event. In other words, we defined the event as the filing of Chapter 11 under the Federal Bankruptcy Act. As far as we know, this is the first study of bond rating changes to be based on data of companies from all industries. Theoretical Models of Bankruptcy Wilcox (1971) is one of the earliest and most primitive theoretical models of bankruptcy. It assumes that a company starts with a positive amount of capital, K, which changes randomly over time. Positive changes in K indicate positive cash flow and increases in the company's assets, while negative changes in K indicate financial losses which require the company to liquidate assets. When a company's K is sufficiently negative, it becomes bankrupt. Expressions for the expected probability of bankruptcy, as well as time to bankruptcy, are mathematically derived, just as they would be for the gamblers' game. Scott (1976) and (1977) attempted to improve on this simple model. Scott's early models assumed that a company has a potentially infinite life and can meet losses by selling debt or equity in an efficient market without incurring flotation costs. They further assumed that the secondary market for real assets is imperfect and that a firm begins 12 with an optimal level of assets. Therefore, it would much rather sell securities and debt than liquidate assets to cover its losses. Scott then showed that a company would remain solvent as long as stockholder wealth, measured by market value, remained positive. Scott (1981) developed a revised version of the earlier model. In this newer model, Scott assumed that a company may have imperfect access to external capital, so it might incur flotation costs when it sells securities, or there may be a tax system which favors internallyfinanced corporate investments. Further, systematic imperfections in the market valuation of securities can hinder corporate access to external capital. This model, however, also assumed that the company has no debt and can issue only equity. Thus, according to this model, a company will go bankrupt when the market value of its securities is less than the amount of investment needed at times of negative income. Therefore, bankruptcy is not the result of a conflict of the benefits and costs of debt, but rather the product of investment managers' mistakes. Empirical Works on Bankruptcy Beaver's 1966 paper was the first empirical work that tried to build a predictive model of bankruptcy. He looked at 30 accounting ratios which could be used to predict 13 bankruptcy, and for each ratio he derived a cutoff point for bankruptcy. He concluded that three ratios were the best predictors of financial failure: Cash Flow/Total Assets, Net Income/Total Debt, and Cash Flow/Total Debt. Altman, Haldeman, and Narayanan (1977), a followup of Altman (1969), used the more complex multivariate discriminant analysis approach to build a predictive model. Their work included all industrial failures from 1969 to 1975 with at least $20 million in assets, which made a sample of 53 bankrupt firms, and Altman et al. found a matching sample of 58 nonbankrupt firms. The samples were matched by industry, year of bankruptcy, and size of assets. Their model included seven variables: return on assets (ROA), stability of earnings, debt service (timesinterestearned or TIE), cumulative profitability, current assets/liabilities ratio, capitalization, and size. After using various statistical techniques, Altman et al. derived a value ZETA as the cutoff for bankruptcy. This model, commonly known as the ZETA model, is highly accurate, especially when bankruptcies are near. Today, it is the leading model for predicting bankruptcy, and because many financial institutions use it, it has become an industry standard. Ohlson (1980) took another approach to bankruptcy prediction by using logist analysis to build his model. His sample included 105 failed firms, but he did not find a matching sample by asset size. Hence, among his nine 14 variables, size became the most significant one. Since his model had error rates of 17.4% for nonbankrupt (type I error) and 12.4% for bankrupt firms (type II error) even just one year before bankruptcy, it has remained moreorless an academic curiosity and has not attained the same widespread use as Altman's ZETA model. Zavgren (1985) extended Ohlson's work by including more variables and extending the length of the study. Her work looked for the important factors in the short and longterm predictions of bankruptcy. Zavgren found that profitability was not significant in either the short or longrun. Rather, her study showed that the ability to meet obligations is significant in the shortrun, while efficiency ratios and liquidity are important in the longrun. Zavgren's study, then, reduces a company's bankruptcy risk to two issues, that of shortterm endurance (as measured by the ability to meet obligations) and fundamental characteristics (as measured by the efficiency ratio and basic liquidity.) Significance of this Dissertation While the existing literature is already quite advanced, we believe a few areas have been left unexamined. First, while work has been done on bond rating changes, there has been no research that tries to link bankruptcy with financial market reactions. No one to date has looked at the trend that 15 bond risk premia take as a company approaches bankruptcy, even though bankruptcy risk, in theory, should be a primary risk included in risk premia. Further, while researchers have studied bond rating changes' effects on both the stock and bond markets to see if such rating changes contained new information, no study has linked the information these downgrades provide with a company's risk of filing for Chapter 11 and thus declaring bankruptcy. Since bond downgrades are meant to warn investors of possible default and bankruptcy, whether such downgrades have any impact on financial markets should be directly linked to the market's assessment of a company's bankruptcy risk. So far, however, research has left this area untouched. Second, as we stated in the previous Chapter, current bankruptcy prediction models have looked mostly at current financial data. Only Zavgren (1985) has tried to examine certain fundamental characteristics, and her study shows that such information does indeed have a role in empirical studies of bankruptcy, especially when we are dealing with longterm bankruptcy prediction. Hence, we assert that fundamental characteristics have largely been overlooked by present bankruptcy research, and our dissertation will address this area more systematically than Zavgren did. Our research contributes to the financial research of bankruptcy and market efficiency in several ways. By studying the bond market and bankruptcy, we attempt to determine 16 whether the financial market can adequately assess bankruptcy risk on its own and whether bond ratings play a part in this assessment of risk. We then look at ways to augment or reinforce market signals via prediction models with significant early warning capabilities. In this regard, our study covers a period longer than those of its predecessors. Further, we introduce variables that assess the fundamental characteristics of a company to forecast longterm bankruptcy. On the theoretical side, this research can lead to establishing a relationship between certain fundamental characteristics of a company and its financial position a few years into the future. In the area of market efficiency, we attempt to assess whether the markets are truly efficient in anticipating one specific type of riskbankruptcy risk. Further, in our event study, we study whether the bond rating downgrades actually do provide new information to the market. We do not, however, do this by merely looking at whether the downgrade trailed or led a rise in the risk premium, because we believe such indications are in themselves not significant. After all, a downgrade that trails a rise in risk premium might be regarded as the leading downgrade to a subsequent rise in the risk premium. Hence, we will instead concentrate on whether downgrades make a significant impact on the market. CHAPTER 3 METHODOLOGY TO STUDY FINANCIAL MARKETS AND BANKRUPTCY Our research on financial markets and bankruptcy encompasses two topics. First, we look at the trend of the risk premia of corporate bonds of companies that later went bankrupt. This trend tells us if the markets can correctly assess increasing chances of bankruptcy and default as bankruptcy nears. Then we examine the impact of bond downgrades on the returns of a company's stock. We determine if ratings play a significant role in providing the market with new information. To study whether bond risk premia increase as a company approaches bankruptcy, we selected a sample of bonds based on two criteria. First, they had to be publicly traded bonds listed in the Standard & Poor's Bond Guide with a bond rating from either S&P's or Moody's. The second criterion was that the companies which issued the bonds later filed for Chapter 11 between September 1977 and October 1988. Only 50 corporate bonds had bond ratings and other available data from S&P's or Moody's adequate for our purposes. These 50 bonds, listed in Table 1, are used to study risk premia and bankruptcy. Then, 18 from the Analytical Record of Bond Yields and Yield Spreads, published by the Salomon Brothers, we obtained the monthly yieldtomaturities for US government securities. The risk premium for each of our companies is the excess of the yield tomaturity of its bond over the yieldtomaturity of an US government bond with the same maturity. We then studied the risk premia of our 50 companies as they moved towards bankruptcy. We separated the companies into two groupsthose companies which later reorganized and those that were later liquidated.1 Next, we compared the risk premia of bonds in those two groups as the companies approached bankruptcy to see if the market's assessment of risk went so far as to differentiate companies which could later reorganize from those that could not. To study the impact of bond downgrades, we use the event study methodology. An event study compares the impact of an event on security holders with the predictions made by a model that approximates what would have happened if the event had not taken place. In effect, we try to compare what happened with what a model tells us should have happened. Our event is the first consistent downgrade rating change, and the size of the impact is measured by the disturbance of the stock's daily rates of return. The number of months between the first downgrade bond rating change and the month of filing Chapter 11 for our sample is given in Table 2. In our work, the Mean Adjusted Returns Model, as 19 discussed in Fama (1976) and Masulis (1980) is used as the basis for the statistical studies. This model uses the mean returns on an individual stock over a representative period of time before the event period to estimate a stock's expected mean return. This "comparison period" is then compared with the daily rates of return over the period of rating change. Because our research focuses on financial distress and bankruptcy, both of which are longterm processes, we selected a twoyear time period before the event as the "comparison period." Since there are a different number of business days in any given year, we simplified things by defining 510 business days as "two years." Thus, our comparison period is 510 days to 11 days before the rating change. The actual event, the bond rating change, is taken as the 21day period beginning ten days before and ending ten days after the downgrade announcement. For this study, we construct a sample of companies that were listed on the New York or American Stock Exchanges, that had bond downgrades, and that later filed for bankruptcy. We then found a matching sample of companies that satisfied the first two criteria but did not later file for bankruptcy. Once we have used our comparison period to determine a stock j's mean daily return, Aj, the event period disturbance term Et, which measures the impact caused by the bond rating change, is given by: Ejt = Rjt ~j, 20 with t being the date in the comparison period, t = 10..10, where Rj is the realized daily return of the stock j at time t, which was read from the CRSP Daily Return Tape. The average disturbance term for N events (firms) is: avg E, = 1/N (E Eit) with j = 1..N. The null hypothesis, avg Et equals zero, means that a downward bond rating change has no effect on shareholders' daily returns. Since we believe that the first downgrade of a bond gives the earliest signal and, hence, the most information to stockholders about the risks of financial distress, we expect the null hypothesis to be rejected for our Chapter 11 sample. Conversely, we expect not to be able to reject the above null hypothesis for our matching sample of firms that did not file for Chapter 11. The variance of avg E. is: Var (E) = (1/499) E (avg Et X(E)) where X(E) = (1/500) Z (avg Et) When t=0, we would be testing for the disturbance on event date. The tstatistic used to determine whether avg E0 differs significantly from zero with 499 degree of freedom is: t = avg E0 / J (Var (E)) The cumulative error over a particular event time interval is: CE(a,b) = Z (avg Et) where 10 5 a < b < +10 21 We hypothesize that the cumulative errors in the bankrupt and matching groups are statistically different, implying different effects of bond rating changes on stock rates of return. Finally, we separate the Chapter 11 group into two sub groups: one subgroup of companies that filed for Chapter 11 and later reorganized and another of companies that filed but were later liquidated. We compute an average Et for bond downgrades of companies in the two subgroups. Then, we employ the ttest and Ftest to analyze the differences for statistical significance between the two subgroups. The null hypothesis is that the means for the two subgroups of companies should become statistically equivalent. By reasoning explained previously, we expect that the null hypothesis will be rejected. Thus, we expect the means for the two subgroups of companies to become statistically significantly different as we approach the filing of Chapter 11. 22 Note 1. A company, by our definition, is "liquidated" if it satisfies one or more of these conditions: 1. acquired by another company or liquidated 2. listed on COMPUSTAT as "bankrupt" 3. no longer on the Wall Street Journal Index 4. no longer on the Predicasts F&S Index of Corporate Change 5. no longer on Qfile 6. no longer on the Directory of Corporate Affiliations 7. no longer listed on the CD System 8. no longer described in the Chapter 11 Report ) id a 4 tiBi ( . .0 Q d(ISo U 4)U 0) ?30 A 4l4 m4 4 to vH m oiWw 0%0m0oo if o fn oo0fo 0rf 00 D0H000H0OHD000OO00C Ol00 COD000000OD0 0 ('V 0 o0 o I 0 ( HMH 0 0 U) .Q M QF)Q Cc Q) VI[11 o 0 N  0 0 *O OOLA cc cN mcO in o( co O 0o N o o ro d O0r c HH %D c O  I \OCN I ON *0 ri P HoPOO dC O 14 a CA 'c *P \ r4 N m Un r ODOD 0 d\ CD O% oiPOP ODCO mv CODM Hi'r, Hl 0> \ r N 0n s CO'ON 00 cp 0 \ I H W r\ C nL d m O *NC 'o O in o r0Co 't I dpa O oC I 4 M I mdP O U i I N H I0 (A 4) wt 0 Ns O ) Od sk v r l a) de 0 1 N NIm% I q O I  I 0 i ar L H c inLO cccHmEDODLO HHLOMinopLL\H I H A CM I \* I \\H I I ainn o 0  n nl Hr I N H H ( I I ) l ) aQ r ) 0 H m 4QQcc Q Qo QQ~0) Q0A40 QA I .Q Q QA M 4i cPcWc) 5c 0 #)00 4 Wc c r4 0) IQ o ) 4) wc IQ0 aM 0 1 <)I p 4 a w 0 EaQ : (U)Q l Qw m copa s r5 s s s ^ as s a s s s s A U *4 0 p HQ) HM .) HH H .) , .0 4 0 G 3 HH MH 0 0 rH 0 P H ca HU O 4 OHOO :3 rq Ea 0 (o ca 0 * C *P *. OW *Hc 0 Q 0 0d 04 04 0C OH M CO  H44 1 P r HH 4 d 4M 10 0 4(0 4 4 1H (04)V 0 U 4.) W 4 0 t4V (4 O 0 mi 0 0 34 34 0 14 E H 0 90 M M U U U U Pq 4 4H r U C a U] C4 H * UC0 4 0 *C HOHUI HO C) m <)> C 14 Sr* Q u I r 0 0 u O C0 c) 0n u0OgCO H 0 H O O 4) 0 0 H E0 ooaHH3F3lI4s (0 QM OCO Nu SHo H*O tp 0 (U *r *> 4434 4 44 0 490' rT00 0 C0 CO 000r co r. % a w wcoco~ 0000 co co Cco co Nei Nq Im149 0 ri0 0 00 co0CO C coco 0 0 0 C c 0 e Scoo o  cMu co *e de I 000VO N CODONsON\m * ioco i'o O C vI C'j 0,0 %, d ri .* G 0 \d( rl Ieq r('NH 40v oP 1  co I I (ANI 0 1 d dp * Ir oA q 0 M d 4r o0 v'Wr4 de O N *) de rr de N l rmirHHr4 VO HE I PN1 ,i ,0 .I 0I d Q0 I 0 4 O 1 0* L o4 N ZSQ r ,Q , SE4 cm ,Q In m a a 040 04 Q 0 0 QQow k& 4XA M( AP w t W :3 :1Pl) X 0) ED U k N P\hP4 N U WM~mmm mQXumNWWQ 4 o H > 0u 0 0 O 0 C 00a 0440JU O .I UQ I 04. 0 U S0 0 V E. ,U , 40 H4 4 0 0 4004 ODN t J)3 EZ13 9mmmmp 00 *4 n14 A a a *H A r Uim 00 EHC E4 0U E2 O OM oU Um E # #0) 0 o0 o a ^urii U) )0 ) 50 EwofS SS 0) 0 *p r4 14 ..4 O" I u40 qM 0 P4 *a ta ,0 O0  0 too 4.M ,p 0 H m Sr4 r4 .aV srF r r N coo (n M i 0Doo NW Hn H Q 0 p NyHNHMHHNNCAMqNHOMOHIHO 0 N coV4 HN0 CCO< col co co 00C CO co On N OOO 000 Scn co OC100 HIOO C(n co CD 00 00 IAO4Il. 000 n o ri co o co V)Or cOOcO 00CD% 0000 00 0 0 COCN  CCOD OOH C 00 O ,coco coco tr M 00H CDOCO I NOcO* H10 0i o cococo COOOo o0 r oi ,.000 co co OOO c O Ci co HOO r co co HOO I O 0 r 1 o 0 0\4o tbtb# + I U UI U I I U U+ U U QU OI IQI I U+ UU UQUamuOQQQ Ua4DU r, CV r 00 0 co cCD 000 oo co NCN O COOCO H 0 0 coo00o r. , M 000 D H r coD c0 U + + + U m QQOQ(QQMQUU(Q + U O I 4+ I1 U O co 0 (A NI 0 f OO CO (O C. OP>0  00 I d O 0 NCV \I dp I co i r 0Q r 4 3 n 1 SCO0 CO m m+ m U I I U + U Q40 C I U CQ 0 0)p *h  OOf00 00 M Co No M% ON N\  r * C> co H fD c I A dp*o HO 0 co C co'4o\ O p LtoN co co oko C)r oa0iM c o ONi Cor MCOM H1 C(A . ri N ON W 1 ( o ON. o N. I N OD I p M n cl c I coo N0H 4  Qco Hn ONH HrH.EOcOtn H IW Ln d0'%% H r 3 'p IHI H iu n \dp 0 (dlo AAmme oa o loi NQ E0 I N dp ar ade 4) ( 1 13 A 0) A I H M B %D 1 ) OH M 4MQQ MO 0aW r Q ON Q N A IA U Q0 QA 4 A MO A 4 04 N1 N A A 44343 4 MA 43 N4 A Q 0 Er4 0 0 x n Z U2 i a t k AA 4a34 A 443 434o 0) 0n 3 h 3 N ( k p k P 03 0 N 0 N w 0 U rH 0 3 ) )  0 .4 O l O H OH a U H 4J 0U01 m M U *4 *r4 H(. 0 r ~r uO~m r uoa o> CH c0 H n H*O > 0 O H ) 0 4) 0 4( ) rI 4 SHU40 0 0 4 i (0 0 r4q 3 $4$4 H > CO 'Hr aC > CH r 4 )4d4I 004 U o 0 ) o *0 H C HIOO I OC 1 OH r(Dl04 Z MId UH04H C QU 0U CUH<44 M r4 HH m m0 M UOXOE 0 C 4: I H 04 4i M 4 u 0 ( O o Ur O aO U O I ro CIH ~O ?1U0 0 >X .Md0J OO P MU ) Uil <00U0 '14 MH (D 0) HM 0 X54 a)4 ) >.O M 0 4J Q OU .O (d m ) CO>H ~ U rHlr4E C B403 k04r r 0 k 0 O MId rH d 9CV40 0HE4 U O4 4 e < ccD~ou u ~ &&< u rHi3>isa s N% 00 00CO rn O COIH + co +m smM In 0O4 0 N 0 0 CV 00 0 0) 4 t H mc Q) Q l PP 023 Pt Ca 4u)o 26 4J4 0 $43 o oooooooooo oooo Sa+ 3 . 000000p000000H0000 +mC 1r ro mMNw n i t I u a T 0 1+ I H1 oa 000 4 N V Sa C0 CCNC CD tv S o o at co m 0 * I H N O c4m do do ) H CNNo' de( oO O(* I r M 4. 0 o I 0I \ 4  Q I NAn U M WpHU MS 4 *Q raHe .QmO I AA0 Q AA l I i.  )Oo(S MCh Q 0LO P , Z Z t M % A o 0)0 a I0 o o o .4 0 U ME4a 0 0 m Ca QQ o.4 0 V I Q W iC Q I AU CQ A g C V a (P 0 0 04 M 4 P ) . P rl 010 *0 4 0 0 HM 9H M rr C) .H 4 *4 U U.i l 4 4 u 0  H A4 V+ 4 $4 14 C a)4 U>M 0Q) 4U 4kH ( *M4 4 0 d O 4 O W 0)0 U40V>000 k 0 00 V X: 0) 0 M 0 P4J VE4U 0Cp 9 aUV VOO C0o 0 U 0CWm H0UOR H 00 .0 r O 0 0 AC U W B (0 U 0M0 0 0 0 4 0 *3 tC 0 +VH H k V N(UA0 ( 4V4VPV4J+ W 44VJ 9 k 00 BH0 # O X X XX 0UO r Ur4 0 0 3 0 0 ( MA04 VJ W ) W0 (D )AiH CA 0 !0 0 ZZ04.E4E zr+ U)W CHAPTER 4 RESULTS ON FINANCIAL MARKETS AND BANKRUPTCY For our research on risk premia and bankruptcy, we computed and drew risk premium curves for each of our 50 companies' bonds. (These curves are presented in the Appendix.) A solid line indicates a bond rating change by S&P, a dotted line one by Moody's. The arrows on the graphs indicate a bond upgrade. In 80% of our sample, or 40 of the risk premium curves, there is a definite upward trend: risk premia rise steadily as the company approaches bankruptcy. Nine (18%) have ambiguous, fluctuating trends, and only one, or 2% of our sample, shows a downward trend where the risk premium on its bond actually fell as it moved towards bankruptcy. Hence, our data suggest that the market generally incorporates the likelihood of bankruptcy adequately in its overall assessment of risk and includes this particular risk in the valuation of securities. When we compare the relationship between bond rating changes and risk premia curves, we find that for most cases where there was an obviously increasing risk premium, the 28 rating downgrade came after the risk premium had begun to increase. Hence, in the shortterm, a lag of one to seven months does exist. This conclusion confirms that of Weinstein (1977), who found that markets had anticipated bond rating changes 18 to six months before the change. It, however, conflicts with Katz (1974), who concluded that yieldto maturity adjusted to the rating change sixtoten weeks after it happened. We believe the reason for this discrepancy is that for measuring marketassessed risk, our risk premium, a relative value, is better than the yieldtomaturity, an absolute value, used by Katz. This is because while factors such as added risk and inflation would eat away the nominal returns of yieldtomaturity and bias the results of any study based on it, risk premium would account for such factors and hence provide an accurate indication of the returns on the bond. Our data, then, seem to suggest that bond ratings, though popular since the early 1900's, cannot predict risk premium changes or any upcoming default. We believe, however, that the lag phenomenon is not particularly meaningful. For example, a bond downgrade that trails an increase in the risk premium may lead a later increase. Since bond rating changes should warn investors of coming bankruptcy and default, what really matters in the longrun is whether a bond rating provides new information to the market on companies that later went bankrupt. That can be determined only by seeing if bond 29 rating changes have any impact on the market. Assuming that the first bond downgrade provides the market with the greatest amount of new information about changes in risk, we must further study the impact of the first bond downgrade on the market. Our data can be used to compare the two rating agencies, S&P and Moody's, to see which warns investors earlier. Table 3 gives the relevant information. On average, S&P gave the first bond downgrade 24.54 months before a company filed for Chapter 11, while Moody's gave the first consistent bond downgrade 21.58 months, or 2.96 months after S&P, before a company filed for Chapter 11. Out of a sample of 50 companies, there were five bonds that received no downgrades whatsoever from S&P's and six that received no downgrades whatsoever from Moody's before the companies which issued them filed for Chapter 11 bankruptcy. Although there was no rating change, the markets did foresee the coming bankruptcy, and the risk premia on these bonds began increasing an average of three to five months before Chapter 11. Finally, six companies which S&P's rated were not rated at all by Moody's. Hence, it would seem that in this specific instance S&P provided more timely and more complete bond ratings and changes than Moody's in the sample and for the period we studied. We emphasize that this is a onesided test only, and that it by no means can be thought of as a definitive conclusion. 30 As described earlier in Chapter 3, we divided the sample of companies which filed Chapter 11 into those that later re organized and those that were liquidated. Nine out of the 50 companies in our sample were "liquidated," while the other 41 reorganized. The average risk premium curves for these two groups are shown in Figure 1. From this graph, we can roughly conclude some interesting patterns. Long before Chapter 11, the companies that would eventually be liquidated had lower risk premia than those which would later reorganize. The two groups had about the same risk premia 41 to 27 months before Chapter 11. Then, as the companies approached bankruptcy, risk premia of companies which were later liquidated rose steadily above those of later reorganized companies. After performing ttests with Montgomery's formula for the three periods (65to42 months before bankruptcy, 41to 27 months before bankruptcy, and 26toi months before bankruptcy), however, we found that this was not so. We had tested for the null hypothesis that the means between the two groups during each month were equal. During the first period of 65to42 months before bankruptcy, 20 out of 24 (83%) t tests were significant, and all t values were negative. By our definition for t, this means that the mean values of risk premia for the later liquidated firms are lower than those for later reorganized firms. During the second period, however, 12 out of 15 (80%) ttests were significant, and 12 of those 15 ttests were positive. This means, contrary to what might 31 be discerned from the graph, that the mean values of risk premia for later liquidated and later reorganized firms were different and that the mean risk premia of the later liquidated firms were higher. Hence, although from just looking at a graph we had thought that the differences, which were clearly visible, would not be statistically significant, the ttests show that this is not so. Finally, during the third period, 19 out of 26 (73%) ttests are significant, and only one of the 26 was negative. All other ttests during this final period were positive. This means that during the final period, the mean risk premia of later liquidated firms were also significantly greater than those of the later reorganized firms, as we had expected from looking at the graph. Table 4 gives the means and the ttests. This means that the market can sense the coming of liquidation and therefore place an added risk premium to such risk much earlier than the 27 months we had earlier expected. For our event study of the effects of the bond downgrade on the daily rates of return, we first had to find the exact press release dates of the bond rating changes. We selected only those companies that were listed on the New York or the American Stock Exchanges.1 Because we could not find relevant data for two continuous years from the COMPUSTAT Daily Return tape for all our companies, some of the observations in our sample had to be dropped. This left us a samples of 22 pair of bankrupt and matching companies. The matching samples have 32 equivalent downgrades during the same time period, but did not later file Chapter 11. The companies in the two samples are listed in Tables 5 and 6. Tables 7 through 10 give the statistical results of our event study. In Table 7, the tstatistic for testing the null hypothesis that the average disturbances at event day, E,(0), equals zero for the Chapter 11 group is 21.81, with 499 degree of freedom. This tstatistic is significant at the 0.5% level. Thus, as expected in the Research Design and Methodology section, the null hypothesis that the average disturbance at the event day for the Chapter 11 group is zero can be strongly rejected. For the matching sample, however, the tstatistic for testing E2(0) equals zero is 1.45, which is significant only at a marginal level. The negative signs on both the tstatistics mean that bond downgrades negatively affect shareholder wealth. To see if the means in the Chapter 11 and matching samples are equal, we employ a special ttest (see Montgomery(1984)), which is suitable for cases when we cannot assume equal variances and when the number of observations is less than 30. The tstatistic for testing the equality of two means is 15.545, with 42 degree of freedom. It is significant at the 0.5% level, so the null hypothesis that the two means are equal is rejected. This means that the daily rates of return of companies in the Chapter 11 sample suffered more with bond downgrades than those in the matching sample. 33 The variances of the two groups, as given by the Ftest, were not significantly different.2 Table 8 shows the statistical analysis of the two sub groups in the Chapter 11 sample, the companies which re organized and those that were liquidated. The tstatistics are 4.98 for companies which later reorganized and 26.94 for companies which did not. Since both are significant, the null hypotheses are rejected. Using Montgomery's formula, we find that the ttest is 0.32 with 9 degree of freedom, which is not significant. Hence, the two means are not statistically significantly different. Finally, the variance of the reorganized companies is lower than that of the companies which were later liquidated.3 Tables 9 and 10 give the daily prediction error and cumulative daily prediction errors in the 21 days surrounding the downgrade announcement. Figure 2 shows the cumulative error curves for both the Chapter 11 and the matching samples. These curves show that the rating downgrades had a definite negative impact on the daily rates of return. Most importantly, the relationship between these two curves tells us that the impact of the first bond downgrade is much more severe on companies which would later file for Chapter 11 than those that would not. Hence, we may conclude that the market does react to downward rating changes and that the rating agencies therefore do provide significant new information to the market with rating changes. These results conflict with 34 those of previous works mentioned in Chapter 2. We believe, however, that the issue is still very much unresolved, as can be seen by the seemingly contradictory results of Griffin and Sanvincente (1982). Therefore, our work should contribute to the ongoing debate. Notes 1. Our two criteria for selecting companies into the Chapter 11 and matching samples for event study were: 1. The companies had to be listed either on the New York or the American Stock Exchanges. 2. There must be two years of continuous data available for the companies. 2. The Ftest value is 1.13, with degree of freedom (21, 20). This Fvalue is not significant, so the variances of the two groups are not significantly different. 3. The Ftest value is 8.13 with a positive sign, and it is significant at the 1% level. * In H N %u 0Q in I OIN N(M NN H N 0 O N r N  MIN MNHIVl NN .oCoCrN CO0O' cO(0N.4'.4~NNN Io N PI 0HII0 0 C HO 00 OMMo0o o 0 0i o  O Co C OCOr rl 4o 0oo00 4 0 rN w D\ io 0 cwcocoZcwwcow co cn 1 M NrH#N()HM4 H NN 0 O C4 CO OD CD cWc(X '0 0 94 V r4' CO 0000 00 0 OOHO N SOOO N 0 0 0 r1 0cOc' IA 0lcr.4UNN N c o0 NNNIA \ O O IA N '.0 Cowowzzzwoz!r%rlcwwO 0o0 0oZco OeN co IA.i 0%%DO I In .NNOm0HmOlNHOINai HOOHOOO NN 00r0004w CO COV?0C On C~eO ~0FCOCfC[ OHO C. 0o0, Co,. 000 o0 O N CD00 00 OLANV cCOCOQ N% H M O 00000 in %O0 Hi r o00 00 c 00 co 0 0 ON CIO 0 N N CO N 0 0 0 do 0 o d0 o 00 o co 4 o N coN 04Mo aNO n M (A M N \, eo.  0 * Nr oo co D iI 0 c IdONI e 004 COdP O mCO w' dP 4 dp V r4 NNI Coco o dp Co' 0 ON 00 cn o oo\ o r* H n \\C (M o% \0a .o o \mcnol N r. dp pdp nr \d. n do C4 n 0 or'~0 * I A oQ o IJ OD o I omde 1d I (I r 0 0 CO 00o \01 O ,'N 04)dd oe I \dPCO N OdP N 0 Hl dp ri C rH tI in 0 CoD n 0 HH tU 0 0 uODo M rl %r Ln 'd,OrV ,HN HA m In I \d N.\NII HI Ain ln M d o  (D 0 Hl On Q r <r t I Mdp in <4) CA I )IM 0 4) \0 4l Q 44 A0NCND) A oH()O oc N44 AI 4 O A4 0 (i)IQ 0)NA(P )44 A Q 0 0 EQU 0 0 WZ CW m 4M EQ w a np E U om oIn& lc M En to V) ril ')m aU)> c~acc~ccucuQW UociiccucCCQ 2aoc camQC 2 0 4. o0 S 0 H H 00 0H 0 4 . l 4J r.U CH 0 10 tm C H ( 0 4 0 0 . OU ) U0 aQCr U H 44 H. I N M w 14I 4M M r#i*i e e CHi( iHi<<; M * C* *0 0 O~0 lH S H40 S H 4 r 10 04 OHOO P M 1 S rLH 1 k *U *V. r a 0 00 *HC2 'CO Ht* C D * U0 A *rM 4 o 4 T 0 C o0 o V'4 VIAU HC * 3 4HW 0 lOH .4 H 4orI Q5 HHrC0 04 UIOds p) 0 H C M ,>, ou o a= o # 30u 0OH $3or( Z (0 UO04H C m4 r4 H 9 0 HU 000 X H 4 C4 0 O n noOO( C O C (D OO H O k Hmmo mi5O4 04 0.0 > g 00 )4 .40 0 4 r 0 l H rl 0 9 4 0 0 4 E 0 0 H l4 UUUw44h u ZHH h 0 zSzzz O 0 CI 10 N0 C HIo 0 r HCoH I I Nr 1 o 0 NN m in OHNOW r HNHVmcOHW~Hl (mN 00 COCO co OI CO 000 N t 0 C0 CO CO 0 r.I 0( 0 H0 0 CO 00 CO NM Oc in in N co co00O N c NM 1 LO in M N ON linON(NMH rNI 00 coc 000 NNCO O 000 000 C0 O 0 0 0 oN < 0C %0 do CN 0 oo co  N %O o d o1 o N  q NN 0 No OmdH 0i rH c'. LA H N m) c 0 *pP n I o \c0 I I d Nde N d0 ) 0l H d N I N H, 0 o1 ~ed I0 H \NaacmcHHto u *EaHi *u) im Uoo2 I ##QQcninin.i\ Q Qc I 0 n *4 3 4 o H I N CfEl CQ  ki C'u) ( )O 0 r44)rPk X 0) : V) X .IoM to twNOm w NHWWWE MQWW 54 0 U $4 >1 cd Z U 0 c OH r C a u M C 0O H a S4H U 0 .C 4. 4+ r4 4 P 4) &4 MC000 4 P A 0 H 0 0 0) C 0 439 4 0Pa4 mA im U) 0 ,4 t H ,4 SCd I U (0 9 4 SH r 0d00 wOO 3 0) Q) (1 tI > .4 0 v o Mo O M M cv trN C O S00l ~~ 0,140ON.000 4 4) AP 0 "j 0ooOCD00 0 Mt MOcvH Or 0 S4JU no o O MoM  a ,00^ '.r i 'ooo N ai Or100 0 0Aa) A 4)O C C u %D 4 % r 0 0 0>, > *H 4 0 >1 dd V Vd () w% 0 0C C 4 04f Z *> 0 0r (0IP P O V o >O.Q44. a rv (a 34 00 k W 0 O) C0 >0 0 i 0 c au 3 :O O +3 c 1 u0 * e O .Cd C 0000 0 M m ## # a, a A , nOd rOH o 4 ( 00J00M* 0 000 MU^ ic g^= 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 65636159575553 o Liquidated Firms 514947454341393735333129272523211917151311 9 7 5 3 1 Months before Bankruptcy (Chapter 11) + Reorganized Firms Figure 1. Risk Premia Curves Comparison Risk premia trends for companies that filed for Chapter 11 and later reorganized versus those that filed and were later liquidated. Table 4. TTest of Risk Premia Trends Time MeanI Mean2 16.70 11.46 10.38 6.08 8.31 7.12 6.80 6.80 6.86 5.98 7.42 7.33 6.73 6.19 6.14 6.42 4.73 5.10 5.04 4.88 5.74 4.49 4.23 4.32 4.32 4.46 4.54 3.99 4.04 3.95 3.33 3.50 3.80 3.80 3.83 3.82 3.44 3.51 3.70 3.50 3.56 3.32 2.56 1.87 1.72 1.89 1.71 2.08 11.18 8.08 7.43 7.11 6.22 5.68 5.55 4.89 4.78 4.65 4.47 4.41 4.45 4.42 4.23 4.00 4.04 3.81 3.74 3.66 3.49 3.73 3.49 3.58 3.58 3.57 3.77 3.75 3.49 3.48 3.53 3.34 3.34 3.30 3.29 3.25 3.72 3.53 3.39 3.49 3.46 3.45 3.49 3.20 3.26 3.12 2.89 3.08 Diff. 5.51858 3.37600 2.94731 1.02914 2.08476 1.43333 1.25468 1.90249 2.08516 1.32662 2.94818 2.92675 2.28420 1.77084 1.90900 2.42500 0.68789 1.28795 1.30813 1.22106 2.25051 0.76234 0.74654 0.74654 0.74759 0.88553 0.77331 0.24753 0.55032 0.46810 0.19686 0.16256 0.45914 0.50408 0.53727 0.56812 0.28775 0.01832 0.30900 0.01545 0.10248 0.12621 0.93164 1.32963 1.53593 1.22093 1.17630 0.99972 ttest 5.969257 3.651703 3.188007 1.113180 2.255015 1.550387 1.357147 2.059800 2.255444 1.434954 3.188950 3.165763 2.470741 1.915457 2.064899 2.623039 0.744070 1.393130 1.414961 1.320781 2.434302 0.824601 0.807508 0.807508 0.808646 0.957843 7.588362 2.428966 5.400186 4.593351 1.931730 1.595207 4.505502 4.946421 5.272179 5.574928 2.823640 0.179790 3.032172 0.151591 1.005648 0.897810 6.627130 9.458170 10.925600 8.684910 8.367450 7.111410 s.l. 0.5% 0.5% 0.5% 2.5% 10% 10% 5% 2.5% 10% 0.5% 0.5% 2.5% 5% 5% 2.5% 10% 10% 10% 2.5% 0.5% 2.5% 0.5% 0.5% 5% 10% 0.5% 0.5% 0.5% 0.5% 1% 1% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% Table 4continued. 1.68 1.97 1.74 1.80 1.84 1.84 1.80 1.74 1.88 2.08 2.49 2.00 2.45 1.83 2.45 2.49 2.72 2.79 2.52 2.79 2.68 2.89 2.73 2.93 2.86 2.76 2.77 2.50 2.57 2.62 2.73 3.04 2.91 2.87 "MeanI and Mean." are the risk premia means for the later liquidated and later reorganized firms, respectively. "Diff." is their difference. "ttest" is the value of the ttest, and "s.l." is the significance level. 1.10180 0.55000 1.04960 0.87340 1.04792 0.88565 10.14058 1.11917 0.87986 0.69457 0.10409 0.57091 0.17650 0.89842 0.58684 0.42263 0.14889 7.837530 3.912360 7.466210 6.212830 7.454230 6.299980 7.996630 7.961060 6.258740 4.940710 0.100230 4.061090 1.255510 6.390810 4.174430 3.006340 1.059100 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5% 1% a)0* 0 IA a) 41 (I .r4 $4 I 90 44 rO44 Cd V I A 0 ) 0 ro >o ooowo ooomo N ooN0 W P N 0 w o0 w H o0 O0 N N N H N N N 0O N O r4 4 N 4J oooooooooooooooo 4 > omon In o i N iiio r m ."u C (U rq 0 0) m+ 0+ m mOl+UO CM .M 0 H HmUUM UAUUMa 04 0 0 Y . c +r c O Lo IV o T3 I + % c. m u o UH 9H 4 NI + 4 mo o mmmm o so r o o o+++ r.), 0 0om E 0 0 COP 03 0 0 o o a 0 CI m emem aCoD mCm%3 o S0 r N v de %Do ;r1, iN cO 0 oko CA %0 oiCho I do 0 0 Si r> 0 0 MC o iia N r r ( 0 H O N r \ mM O0 oOm o O N  NH := NH NNro He ( 'gd0 SN CD O % ~N P~ N o W. 00 0HAv AdH JAHn D14 A A 0 HN 'q 4CM (AoA o u I( r oNI QM wQ in H ON zz0 in g 4) to 4 .1. .AAO ,4 .Q. OQ 0 4. 0 4 * C U U H0 SH. k H* V 4>1 0 I1 C O .4 0 H <04 U 4 #) Va)* Sa) 4 p r I*to o >4 OHH *0o 00 0'dO 4 CO CO O4 I4) 0 (l l4 ( 4) 4a H4OCU40) 01 V ( 0 rO.) 0 IC 4 HIUC*IO. La)OU U OH p 01.i 0 H 0 or H.a) .4 4 4 r4 4) (d 00I 000 g W (O M01 0 )4 4 A P4 iZ .0 $4 > 44 4) OO U 9 r. 0)opr.A uV4J 0 V 9 a1 r. 44 4 U U o ^ 1 1 o a " .01 i Q .r a) r. rQ U >1 00 r M 44 0 4 P r4 4) r V 0P4 E4 4) 0 rn r 0 ) tP'o V 0) 4) (0 V W C D 0 V %0 r, 0C% 0 i t to.to r H H H C N N N N N N m m m m m m 0 H4P= c CM^ uca^fwitin om oh Io U1^'~tIM ~ M N M ~ n Q HNSd o w 00 0a 0 00 O 0 0 ewo00NoA Con0C v4o W) Uw Cj 000 N CN rI o CO co 0% r. cn 000 ocoo o\ m CM 0NN Ln ri CO00WD HlPo el a1m I 4+ + + CQOUU00 mIU 4mAm~uommUU~mMEU m co r DLn o 000000 L r Ln o r Ln 00 0O 00 00 00 CO U00 II UU CQCp + I I Ir I CQ ll+++ C i Co 4 O NI 0 in 0 0 Nri o n N o co Lo n On o oC in i co n N oH * DA A C 1 AO A a) p *N n H4 N A n in 4n \) n Q l n in In In a W0 P l l W) rw p 0 0 O n ri 0 AJQK4J4Ar W z4 mawmsQ~a0 (U Q U QUQUQ )Z NCA J^  ON N CD rl M ooCN Or I Cl scOOH m a m 0 V L C r DO 4 4n H rU u E 0 (a c to Q)U O MU C U in ci m m M< 0 o 0 ti o 0 HP $4 r4 )W ) Q 0 0 r. 9 V N 00) U n4 t u C A 0 O mO 0mHQuO CQMSfflKHhUP 00 00 01 CM CO  n Hl r I I dp 1I 0 0 U) 0) 0 p p 3 zUM W E coo C 0n o o 0A ri an  C  0 dp M NM co CM n dp r 4J (U il 4) a) t 4) S) U3 QU) U} JM r 4 k 3 0 p www)wwwU)U)UO ONO 00co co Lo rN O~crlA. to 14 H O OH O H 0O as r m 00 *0 a) m i0 Ln rlA NNN2C a\I rI O C0 0 0 a mr VCOH I o 0 0utU 0000 o o 04 01 00 0 0o H4) CO rHNmo0NmVoowrmoH I M NiHHr NNNNNNMMMM mmv mow O0O cococ EP 0 *4 U ii' 41 4) 0 *H m *M E1 14 o *H a 0 (0 0E )U 4 UC 0 a 4 :0 0 Cu rc C 0'0 zNH o NMM Nn Ln r q'r Table 7. Ttest for Chapter 11 (bankrupt) and Matching Samples: Event Study Results Chapter 11 Sample Matching Sample E1(0) Std. 0.03199700 0.00687700 H0: E,(0) =,0, tI = 21.98 (d.f. = 499, significant at 0.5%) E2(0) Std. 0.00203900 0.00645500 Ho: E2(0) = 0, tg = 1.45 (d.f. = 499, significant at 10%) HO: E1(0) = E2(0) ttest = 15.545 (d.f.= 42) (significant at 0.5%) Table 8. Ttest for SubGroups of Chapter 11 Companies: Those which were Liquidated and those which Reorganized Liquidated Group E,(0) 0.03293800 Std. 0.01980400 Ho: E,(0) = 0, t, = 4.98 (d.f.: 499, significant at 0.5%) Reorganized Group E2(0) 0.02922600 Std. 0.00694700 H0: E2(0) = 0, t2 = 26.94 (d.f.: 499, significant at 0.5%) Ho: E,(0) = E2(0) ttest = 0.32 (d.f.: 9) Table 9. Disturbance Resulting from Bond Downgrade on Chapter 11 (Bankrupt Sample) and Statistical Analysis Event Day CE m% avg E(t) Ml} 0.006464 0.007603 0.001908 0.001019 0.016982 0.001227 0.002338 0.005651 0.007840 0.009647 0.031997 0.018805 0.022623 0.002346 0.002065 0.008776 0.034234 0.014345 0.029843 0.021802 0.008666 Variable E(l) E(0) CE(10,0) CE(5,0) CE(3,0) CE(1,0) CE(+1,0) CE(+3,0) CE(+5,0) CE(+10,0) CE(10,10) Value(%) 0.009674 0.031997 0.090222 0.056246 0.055135 0.041644 0.013192 0.011777 0.005066 0.031530 0.089755 tstatistic 1.41 4.65 3.38 2.11 2.06 1.56 0.49 0.44 0.19 1.18 3.36 10.0% 1.0% 0.5% 2.5% 2.5% 10.0% * 0.5% The ttest for CE is: t = CE*(N/2)/(Std(CE)* (T12)) 0.006464 0.014067 0.015975 0.016994 0.033976 0.032749 0.035087 0.040738 0.048578 0.058225 0.090222 0.071417 0.048794 0.046448 0.044383 0.053159 0.087393 0.073048 0.102891 0.081089 0.089755 10  9  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8 9 10 Table 10. Disturbance Resulting from Bond Downgrade on Matching Sample and Statistical Analysis Event Day CE IAm avg E(t) Xll 0.012418 0.022204 0.018645 0.003892 0.010662 0.004340 0.013230 0.005412 0.010702 0.002165 0.002039 0.007029 0.000817 0.019285 0.001402 0.003376 0.000191 0.001111 0.005467 0.004831 0.004599 Variable E(1) E(0) CE(10,0) CE(5,0) CE(3,0) CE(1,0) CE(+1, 0) CE(+3, 0) CE(+5, 0) CE(+10,0) CE(10,10) Value (%) 0.002165 0.002039 0.010983 0.012406 0.005164 0.000126 0.004990 0.015112 0.017086 0.010467 0.002555 tstatistic 0.34 0.32 1.13 1.28 0.53 0.01 0.51 1.56 1.76 1.08 0.26 * 10.0% * 5.0% The ttest for CE is: t = CE*(N"1)/(Std(CE)* (T12)) 0.012418 0.034622 0.015977 0.012085 0.001423 0.002917 0.016147 0.021559 0.010857 0.013022 0.010983 0.018012 0.017195 0.002090 0.000688 0.004064 0.004255 0.003144 0.002323 0.007154 0.002555 10  9  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8 9 10 0.03 0.02 0.01 0 0.01 0.02 0.03 0.04 0.05 0.06  0.07  0.08  0.09 0.1 0.11 I 10 9 8 7 6 0 Chapter 11 Sample 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Day Surrounding Event + Matching Somple Figure 2. Disturbance Due to Bond Downgrade This graph compares the disturbance caused by a bond downgrade on companies in the sample which filed for Chapter 11 and in the sample which did not file for bankruptcy. CHAPTER 5 EMPIRICAL MODEL OF BANKRUPTCY The evidence that bond rating downgrades provide new information to the market suggests that proper analysis of fundamental corporate factors, such as the ones presumably used by S&P's and Moody's, can give an early warning of impending financial difficulties. Even so, there are at least four problems with using bond downgrades as the sole or primary indicator of bankruptcy risk. First, many firms whose bonds are downgraded never experience significant financial stress. In fact, a company may simply be trying to modify its riskreturn balance and better reposition itself in the market place to capitalize on future opportunities. Second, although our event study identified a differential effect between the companies that eventually filed for protection under Chapter 11 of the bankruptcy code and those which did not have to seek protection, that does not mean we can easily tell between the two before the fact. In other words, how much of a difference is "significant?" Third, S&P's and Moody's sometimes give conflicting signals, and there have been cases where the downgrade either does not predate the bankruptcy filing by 49 very much time or there is no downgrade at all. Finally, it appears that consistent signals start appearing only approximately two years ahead of the Chapter 11 filing, assuming, of course, that they can be correctly interpreted. Thus, bond downgrades give us about as much forewarning as the ZETA model of Altman et al., and the latter model is probably more a practical predictor of bankruptcy than bond downgrades. Hence, we believe that proper analysis of fundamental corporate characteristics would provide us with a more effective empirical model which could determine bankruptcy risk. What we would need is an indicator which can alert investors and managers of developing circumstances that would normally lead to increased probabilities of bankruptcy long before it actually becomes necessary to file for protection under Chapter 11. Such an indicator would allow investors to make more informed portfolio allocation decisions, and it would signal to corporate managers that corrective actions need to be taken before financial difficulties become serious. We believe that if such an indicator can be found and used to predict financial distress and possible bankruptcy up to five years ahead of potential bankruptcy, then the scarce resources in the economy can be better allocated. Current bankruptcy prediction models, however, have not shown that they can reliably forecast bankruptcy risk more than two years ahead of filing of Chapter 11. In fact, there is very little evidence to date that it is even possible to 50 detect the roots of financial distress up to five years ahead of an actual crisis. Our main purpose in this part of the dissertation, then, is to explore this issue: can a bankruptcy prediction model be designed that maintains significant forecasting powers up to five years ahead of the date of Chapter 11 filing? While we would also like to develop a model that can surpass the predictive powers of the ZETA model in the shortrun while also preserving that power over five years, we do not, in this dissertation, intend to search specifically for such a "best" model. That task will be left for future research after we have shown that it is possible to maintain high levels of accuracy over the longrun. Presentday finance literature does not provide us with many works that have looked at the relationship between various types of risk, such as bankruptcy risk, and companies' fundamental characteristics. Zavgren (1985) provides some evidence that asset efficiency is an important indicator which may be of use to us, but we believe that other variables would also be needed. Derkinderen and Crum (1988) developed a framework known as the Potential and Resilience Evaluation (PARE) model on the issues of longterm riskreturn balance. This framework suggests some possible variables which can be used to assess the fundamental and strategically crucial characteristics of a company. Basing our views from such a fundamental perspective, as suggested by Derkinderen and Crum (1988) and Zavgren (1985), we have arrived at a list of eight 51 variables which can assess both the short and longrun dimensions of the bankruptcy problem. We now turn to a discussion of these variables and the roles they would play in our study of longterm bankruptcy risk. Variable Definitions We selected our eight variables out of many potential candidates. In selecting them, we aimed to find the minimum number of factors that together provide signals about both short and longrun aspects of the companies, in isolation as well as relative to other companies in their core industry. Our reasons for selecting these variables were also partially based on the availability of data, although these variables are considered to be good indicators of differences between the more successful companies and those with lackluster performance records. These variables can roughly be divided into two groups: 1). those which assess company operating and profitability characteristics (which will be referred to as "the Group I variables"), and 2). those which assess fundamental company characteristics (which will be referred to as "the Group II variables.") Existing bankruptcy prediction models focus mostly on relationships that would be included in the first group. Although these factors are obviously important to bankruptcy, particularly in the short run, we contend that the second group must also be considered if the model is to have adequate longterm predictive powers. 52 Four variables are included in Group I to measure the company's financial and operating positions. The first is return on assets, or ROA, defined as EBIT/TA. This is the basic earning power ratio and is a strong signal of profitability. We consider that it is a particularly good representation of the company's performance in implementing growth in the past. The second variable in this category is the fixed charge coverage ratio, FCC. This ratio measures simultaneously a company's level of debt and how well its cash flow covers the servicing requirements of debt. It is one of the most important indicators of the ability of the firm to survive adversity in the shortrun. The third variable is the markettobook ratio. The markettobook ratio measures investors' confidence in the firm and, as a direct result, how well the company can tap into the equity market for capital. In other words, this ratio indicates the extent to which investors believe that the firm has good growth opportunities for the future. A ratio greater than one indicates that the return from reinvested earnings is expected to exceed the required rate of return. Finally, the balance ratio of income and sales, defined as the difference between the growth rates of income and sales, focuses on the profitability of incremental sales. It measures whether the company is boosting sales at the expense of profits and, therefore, may be heading into financial problems even as it continues to expand market share. 53 To assess the second category of difference indicators, the Group II variables which measure company fundamental characteristics, four additional variables are used. First, ownership assesses the agency effects of the company's management. According to the agency theory literature, such as Jensen and Meckling (1976), when the shareholders contract with the management for the latter to serve the former as agents, some cost is inevitably involved, including a dead weight loss. This cost occurs because management and shareholders in most corporations (particularly the larger ones) are usually distinctly separate groups, and they likely have differing, even conflicting, interests. For example, management of America's top 200 firms own only 0.1 percent of their companies' stock, and nearly one out of ten Fortune 500 Chief Executive Officers own no stock at all in their companies. Because of such low ownership stakes, many scholars have questioned whether such managements really serve the shareholders' interests. As a result of questions such as this, management ownership has become a topic of interest and discussion in recent years. We agree that this topic is important and relevant to our needs in this dissertation. We believe, however, that absolute ownership measures are not as significant as the net transfer of ownership, which measures whether management, as a whole, increased or decreased its ownership share of the corporation during a period of time. Assuming that management has information the average 54 shareholder does not, then whether a management is a net purchaser or a net seller of the company's stock shows management's confidence in its own projects. Further, it also shows whether management is committed to the success of the company or whether it is simply "grabbing for parachutes." To incorporate these ideas into the model, we include the net rate of management stock acquisitions as a variable, defined as the difference between management purchases and sales of the company's stock, measured in percentages of total equity. The second variable in this category is the capital intensity ratio, defined as total assets divided by sales. This ratio measures how much a company must invest in assets to expand its sales. Thus, it indirectly tells us both the structure of the industry and how much the company will have to rely on fresh capital to fuel growth. In this dissertation, though, we do not follow the traditional definitions of industry as given by COMPUSTAT or Dun & Bradstreet. Rather, developing from the ideas of Tse (1987), we regroup the COMPUSTAT SIC codes so as to define 24 lines of industry by the nature of the business. These definitions of industry, along with the growth rate and bankruptcy rate of each industry, are presented in Table 11. As Table 11 and Figure 3 show, a company's line of business does impact significantly on bankruptcy. While the specialty manufacturing industry (code #19) had a 13% cumulative bankruptcy rate during the 19681987 period, the chemicals 55 (code #4) and utilities (code #20) industries suffered only about a 1% cumulative bankruptcy rate during the same period. Expanding on the information about competitiveness contained in the industry characteristics, and to assess a company's position within its industry, we employ the relative sales growth ratio. This ratio is the difference between the sales growth rate for the primary or core industry in which the company competes and the rate of growth of the company's sales. It indicates the competitiveness of the company within its major industry in terms of its ability to gain market share. It also complements the balance ratio of income and sales, the Group I variable that measures whether the company has gained market share at the expense of profit margins. The final variable in the Group II variables set is the relatedness ratio, as described by Rumelt (1982). This variable assesses a company's diversification program in that it indicates the extent to which the company focuses its efforts on a portfolio of related businesses that could be expected to have synergistic interdependencies. It is calculated as: (% of assets in related segments) x (number of segments 1) (number of segments) and determines whether a company is a "single business" (a value of zero), "unrelated diversified" (a low positive value), or "related diversified" (a high positive value). As Rumelt (1980) points out, different strategies of 56 diversification can strongly affect a company's longterm prospects, and the degree of relatedness should assess the benefits of those diversifications. According to Rumelt, the higher the relatedness ratio the greater the chances of good performance. The eight variables described above cover the two broad categories and also collectively address the various dimensions of the PARE framework, which are: 1) the extent to which the firm has good growth opportunities available; 2) whether or not the market perceives that the company can exploit the growth opportunities successfully; 3) the degree to which the fortunes of the firm are subject to foreseeable adversities in the future; 4) whether or not the firm has the ability to survive such adversities. Role of Variables in the Model The model of bankruptcy risk developed in this dissertation includes the eight variables discussed above and uses them to derive a summed probability of bankruptcy. Using Logist Analysis, which will be discussed in Chapter 6, a probabilistic function of a cumulative score of z is derived which, in turn, is composed of these eight factors: P = f(z), where f' > 0. z = ao + biX, + b2X2 + ... + bSX8, where bl.. are coefficients, X1 is ROA (EBIT/TA), X2 is FCC, X3 is Balance Ratio, X4 is Market/Book Ratio, X5 is Relatedness Ratio, X6 is Net Rate of Management Stock Acquisitions, X7 is Relative Sales Growth Rate, X8 is Capital Intensity. Hypotheses Because the methodology used in this dissertation, Logist Analysis (discussed in Chapter 6), develops a model in which the coefficients can reveal the role each variable plays, we can hypothesize about how each factor in the model affects overall assessment of bankruptcy risk. Specifically, according to our model, a negative beta means that the larger the variable, the less the chance of bankruptcy. Similarly, a positive beta means that the larger the variable, the greater the chance of bankruptcy. If any of the variables are able to take on negative values, the rules given above about the sign of the coefficient should be reversed. We hypothesize that all coefficients bi through b8 should be negative. The coefficients for return on assets, fixed charge coverage, and the markettobook ratio should be obvious. In principle, the salesincome balance ratio's coefficient is negative because if income is growing more briskly than sales, then the company is experiencing widening profit margins, which would inevitably lead to higher profitability and even more growth in the future. Since longterm considerations sometimes make it necessary to sacrifice shortrun profitability to drive out the competition and gain market 58 share, however, even good, solid companies may have negative values for this ratio. Hence, our confidence about the sign of this particular coefficient is less than for those of the first three variables. More important than the sign, though, is the idea that the balance ratio for the bankrupt companies should be significantly different than the ratio for non bankrupt companies. The relatedness ratio's coefficient is negative because a larger relatedness ratio indicates that a company is diversified into related lines of business, which means, as Rumelt (1982) shows, that the company will be able to achieve real product synergy and countercyclicality. The net rate of stock acquisition is also expected to be negative because that signals net purchase of stock by management. This is a signal that management expects the firm to be profitable in the longrun. The coefficient for by, relative sales growth, is negative because we expect that companies with good relative sales growth rate will have a negative value for the variable, and a negative coefficient is needed to reverse the impact on the chances of bankruptcy. Finally, the sign of the coefficient for capital intensity is negative because, as Ohlson (1980) points out, larger capital intensity is associated with larger company size, and larger industrial companies do not go bankrupt as easily as smaller ones. On the other hand, though, to the extent that the reciprocal of 59 the capital intensity ratio is an indicator of asset efficiency, the negative sign would be counter to the findings of Zavgren (1985). Table 11. Industry Classification, Growth and Bankruptcy Rates Industry Number Industry Food Clothing & Textiles Paper & Publishing Chemicals Drugs Petroleum Refining Rubber & Leather Glass & Cement Metals COMPUSTAT Growth SIC Rate 20002199 8.94% 22002399 5.41% 26002799 9.51% 28002839, 28402899 10.84% 28302839 11.42% 29002999 12.82% 30003199 5.33% 32003299 7.45% 33003499 6.28% 10 Industrial Machinery 35003569, 35803599 6.33% 11 Office Machinery & 35703579, Electronic Equipment 36503679 8.71% 12 Electrical Equipment 36803699 14.38% 13 Motor Vehicles 37003799 7.96% 14 Scientific & Surveying Equipment 38003899 8.58% 15 Transportation 40004599, Agriculture Extractive Construction Specialty Manuf. Utilities Wholesale Consumer Products Services Financial 47004799 11.20% 01000999 10.42% 10001499 10.48% 15001799, 24002499 9.93% 39003999 7.02% 48004899 14.37% 50005199 10.51% 52005999 8.78% 70008999 12.39% 60006799 19.00% Bankruptcy Rate 2.3622% 8.1633% 3.9130% 1.1062% N/A 1.6393% 0.9788% 2.5000% 3.3898% 2.3490% 6.8452% 8.7805% 6.2201% 3.9474% 11.2245% 2.6316% 5.4217% 5.2239% 13.0435% 1.3245% 6.5421% 4.4983% 3.7516% 2.5097% Growth Rate is the average annual growth rate of the industry between 1968 and 1987. Bankruptcy Rate is the percentage of businesses that failed during that period. I I I I I II III I II I I III II 1 3 5 7 9 11 13 15 17 19 21 23 2 4 6 8 10 12 14 16 18 20 22 24 Industry Code Industry and Bankruptcy Rate 14, 12 10 8 Ku i6 ps________^ _____ &____ \ ^ \ ^ ^ $ G n ^   Cum. % Figure 3. CHAPTER 6 METHODOLOGY TO TEST EMPIRICAL MODEL The Logist Analysis Methodology The methodology used in this dissertation to build the empirical bankruptcy model is logist analysis. Logist analysis is a statistical method that computes the conditional probability that a given observation belongs to a particular class of observations if certain variables about the observation are known. Based on a cumulative probability function, this model does not require that independent variables be multivariate normals or that the classes have equal covariance matrices. Instead, the model is solved using the maximum likelihood method. Thus, logist analysis reduces the fundamental bankruptcy estimation problem to the following: given that a company belongs to some prespecified population, what is the probability that this company will fail within some prespecified period of time? Ohlson (1980), which was discussed earlier in the Literature Review section, was probably the first work on bankruptcy to use logist analysis. Although the research did 63 not produce a significantly viable model, the work nevertheless provided some interesting insights into the use of logist analysis for empirical studies of bankruptcy. In Ohlson's model, Xi denoted a vector of predictors for company i, p denoted a vector of unknown parameters, and P(Xi, 8), where P is a probability function (0 P < 1), denoted the probability of bankruptcy for a given set of vectors Xi and P. The logarithm of the likelihood of any specific outcome, as reflected by the binary sample space of bankruptcy versus non bankruptcy, is given by: L(3) = Z log P(Xi, P) + E log (1 P(Xj, P)), where i, j are elements of the S1 index set of bankrupt companies and S2 index set of nonbankrupt companies, respectively. For any specified function P, the maximum likelihood estimates of P1, P21, ** Pn are obtained by solving: max, L(P). Because we do not as yet have a full theory of bankruptcy, however, we cannot easily find an appropriate class of functions P. As a practical matter, therefore, we can only select a function for the sake of computational and interpretative simplicity. One such function is the logistic function: P = (1 + exp{yi))', where y, = EZ jXij = P'Xi. This formula has two implications. First, P is increasing in y. Second, y is equal to log (P / (1 P)). 64 Like discriminant analysis, logist analysis weights the independent variables and creates a score for each company. The Z score obtained may be used to determine the probability of membership in a group where: Probability of bankruptcy = 1 / (1 + exp(z)) = 1 / (1 + exp(a + blX + ... + bpXp)). The b coefficients are weighted so as to maximize the joint probability of bankruptcy for the known bankrupt companies and the probability of nonbankruptcy for those companies that did not go bankrupt. Unlike the coefficients derived from discriminant analysis, these coefficients tell us the role that each individual variable plays in the overall empirical model. Therefore, we can use them to analyze which factors are the most significant in longterm bankruptcy forecasts. Loqist versus Discriminant Analysis Much previous bankruptcy work, most significantly Altman et al. (1977), has employed the traditional linear discriminant analysis, although both the linear and the quadratic forms have been used. For our dissertation, though, we consider that logist analysis can yield a superior model because logist analysis does not share many of the problems faced by discriminant analysis. First, linear discrimination is basically a multivariate technique that assigns a score to each element in a sample 65 using a linear combination of independent variables. The multivariate approach is very appealing because it reduces several financial dimensions of a problem to a single score. In general, such reductions have been quite successful. The bankruptcy models derived from discriminant analysis tend to have high classification accuracies, at least in the short to mediumterms. Serious questions, however, have been raised about whether so many factors and dimensions of a complex financial problem like bankruptcy can validly be reduced to a single score, or whether crucial information would be lost during the process of such a reduction. Second, discriminant analysis has several statistical requirements that are difficult to meet for most samples. For discriminant analysis to work, the independent variables must be multivariate normals, and the covariance matrices of the original and holdout groups must be equivalent. In practice, satisfying both assumptions is difficult. The requirement that the independent variables have multivariate normal distributions, for example, is frequently violated. It will be violated whenever a dummy independent variable, such as the time variable t, is used. Although some remedial measures, such as log transformations, square root transformations, and elimination of outliers can be used, such methods have unclear economic implications which are often too easily ignored. Further, in many cases the requirement that covariance matrices be equal is also violated. This means 66 that the group covariances are not statistically equivalent, as indicated by Box's F statistic. A way to avoid the latter problem of unequal covariances is to use quadratic discriminant analysis. Unlike linear discrimination, the quadratic form does not require that covariances must be equal. Instead, quadratic discriminant analysis assesses the covariance of each group independently as it builds a model. The problem, however, is that quadratic discriminant analysis is not nearly as widely used as linear discriminant analysis, and there are also questions about its modelbuilding powers. Altman et al. (1977) and Marks and Dunn (1974) both reported that linear discriminant analysis could achieve greater classification success than quadratic discriminant analysis. The Marks and Dunn paper reached this conclusion for samples where the group variances are similar, the group means are far apart, the sample sizes are small, and the number of variables is small. Although these two papers do not conclusively show that linear discriminant analysis is superior to quadratic discriminant analysis, they suggest that there are significant problems with using the latter to build an empirical model of bankruptcy. We use the logist analysis method because it resolves both major problems of discriminant analysis. First, unlike discriminant analysis, it does not reduce all the financial dimensions of bankruptcy to a single cutoff score. Rather, it assesses each relevant independent variable and comes up 67 with a probability of bankruptcy, so that, given that a company belongs to a certain sample, logist analysis provides the probability of failure. Second, unlike linear discriminant analysis, logist analysis does not require that the independent variables be multivariate normals or that groups have equal covariance matrices. Harrell and Lee (1985) reported that even when all the assumptions of discriminant analysis are met, logist analysis is at least as effective as discriminant analysis. Hence, our results should be much more significant than under discriminant analysis. Furthermore, unlike the quadratic version of discriminant analysis, logist analysis is a sound, proven technique that can provide good classification accuracy. Therefore, we believe that the logist analysis methodology is significantly superior to discriminant analysis for our research. For this reason, we employ it to build our empirical model of bankruptcy. Sample Design Logist analysis in our research requires two groups of companies, a bankrupt and a matching sample. Companies that were on the COMPUSTAT Research Tape and which filed for Chapter 11 between 1968 and 1987 are used as our bankrupt companies sample. We select a matching sample of companies in the same industries and with similar asset sizes but that avoided bankruptcy. 68 Our data come from several sources. We use the COMPUSTAT Research Tape and Industry Tape for basic data on financial variables of both our samples. The COMPUSTAT Research Tape provides such data for the bankrupt sample, while the Industry Tape provides such data for our matching sample. We use the Ownership Reporting System Tape, published by the National Archives and Record Services, to obtain data on the management acquisition of company stock. Next, we use the COMPUSTAT Segments Information Tape to find the segments of our companies and to compute their degree of diversification. Finally, we use the COMPUSTAT Research and COMPUSTAT Industry tapes again to calculate industry growth and bankruptcy rates. At the start, we had 315 bankrupt companies that were deleted from the COMPUSTAT Industry Tape and moved to the COMPUSTAT Research Tape between 1968 and 1987 by a deletion code of 02, which indicates bankruptcy. We could not, however, find 5 years of continuous data for all 315 companies because the information we needed was on several different tapes, each of which had information on different time periods. The COMPUSTAT Business Segments Information Tape, for example, has data only from 1975 onward, as does the Ownership Reporting System. The Master Current Tape of Ownership Reporting System, however, offers data from January 1980 to August 1987, and the Master History Tape offers data from January 1975 to April 1982. Even though we used every available tape and even calculated several variables by hand, 69 we still could keep only 59 observations in our sample of bankrupt companies. Most of the companies were "lost" because we could not find ownership data about management purchase and sale of stock or segment information about their lines of business. After determining the composition of the bankruptcy sample, we matched the sample by industry and asset size and selected 63 companies that did not go bankrupt and had the data we needed. Table 12 presents the companies in our original bankrupt and matching samples. Orthodox logist analysis requires that samples be selected randomly from a population of bankrupt and non bankrupt companies. In almost all studies on bankruptcy which have used the logist analysis methodology, however, the sample has been selected using nonrandom, statebased criteria. Therefore, the probability of bankruptcy derived by logist analysis for any firm i is actually the probability in the specific sample, not the general population. The relationship between the probability of bankruptcy based on the population and the probability of bankruptcy based on the sample depends on how the sample of bankrupt companies was selected from the population in general as well as how the sample of non bankrupt companies was selected. Because of this, the probabilities from logist analysis must be adjusted for the effects of the sample selection, or else they would become meaningless because by selecting a sample differently, we can derive completely different results. In the following 70 chapter, we explain how we adjusted our results and discuss in greater detail how the selection process actually affects the results of logist analysis. Table 12. Original (Bankrupt) and Matching Sample for Deriving Empirical Bankruptcy Model Original Sample MI CNUM Company Name To IndDNUM Asset 1 2073 ATI Inc. 84 237399 12.40 2 13900 Aldebaran Drilling Co. Inc. 87 171381 5.83 3 14419 Aldon Industries Inc. 87 22272 9.48 4 25909 American Fuel Technologies 86 42860 1.20 5 37460 Apache Energy & Minerals 84 246792 5.40 6 40150 Argonaut Energy Corp. 86 171311 15.47 7 77266 Beker Industries 85 42870 267.90 8 124187 Buttes Gas & Oil Co. 87 171311 389.52 9 140556 Capitol Air Inc. 84 154511 34.75 10 141602 Cardis Corp. 87 215013 195.20 11 159620 Chargit Inc. 87 237399 19.00 12 163742 Chemical Investors Inc. 83 32640 20.60 13 202666 Commodore Resources Corp. 82 171311 0.09 14 208106 Conner Corp. 87 182451 71.83 15221241 Cosmetic Sciences Inc. 86 238091 1.50 16 225015 Crawford Energy Inc. 85 171381 26.95 17 228885 Crutcher Resources Corp. 86 171389 99.80 18 232827 Cytox Corp. 85 215161 1.30 19 234230 Dakota Minerals Inc. 84 171311 4.70 20 236280 Danker Labs Inc. 85 143851 1.90 21238136 Datatron Inc. 85 215080 7.30 22 254674 Discovery Oil Ltd. 86 171311 15.16 23 278902 Econo Therm Energy Systems 86 93443 22.88 24 292009 Empire Oil & Gas Co. 83 171381 31.34 25 292666 Energy Exchange 85 171311 55.43 26 292935 EndLase Inc. 86 215080 12.50 27 293799 Enterprise Technologies Inc. 85 215170 33.30 28 364652 Gamex Industries Inc. 82 193990 2.00 29 402274 Gulf Energy Corp. 84 171311 5.05 30 423276 Helionetics Inc. 86 123621 27.90 31 456704 Information Displays Inc. 84 123686 37.00 32 460380 Intl Stretch Prods 84 22200 5.88 33 460468 Intl Teldata Corp. 85 246794 0.65 34 461027 Interstate Motor Freight 84 154210 82.28 35 552813 MGF Oil Corp. 84 171311 342.92 36559150 Magic Marker Industries Inc. 86 193950 8.10 37 585163 Mego International 82 193944 46.00 38 595215 MidAmerica Petroleum Inc. 86 171381 22.47 39 628300 Mutual Oil of America Inc. 86 171311 29.97 40 635080 National Business Comm. Corp. 85 225900 5.55 41 638777 NATPAC Inc. 86 225411 25.90 42 654048 Nicklos Oil & Gas Co. 85 171381 96.78 43 682121 OmniMedical 84 237600 9.00 44 712221 People's Restuarants Inc. 86 225812 41.79 45 747623 Quanta Systems Corp. 85 113664 2.40 Table 12continued. 46 748379 47 761049 48 765361 49 771044 50 795872 51802828 52 805567 53 816068 54 817910 55 925523 56 929073 57 984010 58 984126 59 989875 QuikPrint of America Inc. Reser's Fine Foods Inc. Richmond Tank Car Co. Roblin Industries Sambo's Restaurants Santec Corp. Saxon Industries Seiscom Delta, Inc. Servamatic Systems Inc. Viable Resources Inc. Vuebotics Corp. Xenerex Corp. Xonics Inc. Zytrex Corp. Matching Sample M# CNUM Company Name 1204682 2 866055 3 550819 4 524038 5255264 6870738 7 628850 8 136420 9443784 10 480827 11 205477 12 878504 13 69689 14 674098 15 872625 16 209705 17 786629 18 847660 19 192108 20 914802 21239133 22 971889 23 208258 24 739647 25 666416 26 46357 27 6351 28 250568 29 131069 30 458683 31 369032 Comptek Research Inc. Summit Energy Inc. Lydall Inc. Lee Pharmaceuticals Diversified Industries Inc. Swift Energy Co. NCH Corp. Canadian Occidental Petroleum Hudson General Corp. Jorgensen (Earle M.) Co. Computer Task Group Inc. Technical Tape Inc. BaruchFoster Corp. Oakwood Homes TRC Cos Inc. Consolidated Oil & Gas Sage Energy Co. SpeedOPrint Business Machines Coeur D'Alene Mines Corp. University Patents Inc. Davis Water & Waste Wilshire Oil of Texas Conquest Exploration Co. Prairie Oil Royalties Co. Ltd. Northgate Exploration Ltd. Astrex Inc. Adams Resources & Energy Inc. DesignCraft Industries Callahan Mining Corp. InterGraph Corp. General Automation T. IndDNUM Asset 237372 171311 22200 42844 246200 171311 42842 171311 154580 215051 237372 32640 171311 182451 238911 171311 171311 215081 171040 143851 215051 171311 9480 171311 171040 215065 215172 193911 171040 123686 123681 12.44 28.80 50.14 6.50 68.23 12.60 272.10 317.94 48.30 197.11 29.92 31.00 18.10 56.00 3.04 123.23 139.40 7.65 22.58 18.18 36.48 64.04 17.19 32.75 117.60 25.30 35.58 7.62 55.97 28.90 38.60 246794 12013 133743 93312 225812 123688 32600 171382 175900 171311 237391 171311 143861 113674 2.30 9.70 101.30 32.13 220.94 2.90 486.60 23.36 26.36 6.25 2.10 30.95 15.40 6.50 Table 12continued. 32 732852 Pope, Evans & Robbins Inc. 84 22330 4.89 33 647072 New Mexico & Arizona Land 85 246519 36.49 34 893552 Transcon Inc.California 84 154213 79.30 35960878 Westmoreland Coal Co. 84 171211 376.30 36 55716 BSN Corp. 86 193949 22.24 37 43147 Artra Group Inc. 82 193960 51.91 38 553748 MSR Explorations Ltd. 86 171311 26.90 39 655555 Nord Resources Corp. 86 171090 66.10 40204909 Computer Factory Inc. 85 225995 13.88 41885539 Three D Department 86 225700 21.15 42 379355 Global Natural Resources Inc. 85 171311 105.80 43 29429 American Science Engineering 84 237391 13.97 44 362232 G R I Corp 86 225961 49.34 45 362360 GTI Corp 85 113679 13.05 46 170819 Christiana Companies 83 246552 44.48 47 208093 Connelly Containers Inc. 86 12030 18.50 48 879369 TeleFlex Inc. 83 133714 109.30 49 707389 Penn Engineering & Mfg Corp. 85 93452 39.01 50476502 Jerrico Inc. 81 225812 238.50 51238085 Datametrics Corp. 85 123688 3.80 52 313693 Federal Paper Board Co. 82 32631 472.83 53 212576 Convest Energy Partners 86 171311 34.49 54 658136 North Canadian Oils Ltd. 86 171311 182.00 55 427879 Hershey Oil Corp. 84 171311 30.38 56 27258 American List Corp. 84 237331 2.39 57 208285 Conquest Exploration Co. 84 171311 123.16 58 942622 Watsco Inc. 84 143822 19.97 59 590262 Merrimac Industries Inc. 84 113663 9.34 "M#" is the matching number, which is used to match the observations in the bankrupt and matching samples. "CNUM" and "DNUM" are the company and industry classifications. "To" is the year during which the company filed for Chapter 11 for companies in the bankrupt sample, or the last year data was collected for our research for companies in the matching sample. "Ind." is the industry code according to our definitions. "Asset" is the company's asset size. CHAPTER 7 RESULTS OF EMPIRICAL MODELS OF BANKRUPTCY Using the sample data described in Chapter 6, we were able to derive five probabilistic models, designated P1 through P5. All of them are based on the factors described in Chapter 5, and they assess bankruptcy risk one through five years ahead of time corresponding to the subscription Pn. The only difference among these distinct models is in their coefficients: they all assume the form discussed in Chapter 5. Table 13 shows the signs of the coefficients of the variables for each model P,. Most of these coefficients conform to our expectations as explained in Chapter 5, but others show significant differences. The signs for the coefficients of the balance ratio and the net rate of management stock acquisitions seem to vary randomly but lean towards being positive, while we expected both to be negative. Both of these variables can be positive or negative, and our expectation was stated for the "normal" case for which the expected value of the variable is positive. Looking at the raw data, a significant number of the values in both samples were negative, so we would have to 75 reverse the coefficient sign convention. Hence, the positive signs give the expected signal and it is only our view of "normal" values for the variables that could not be verified empirically. We suspect that this result can be explained in large part by the way the matching sample was constructed. The match was made by industry and asset size, and it is evident that many of the pairs came from "troubled" industries. It is an empirical question, but we suspect that a random sample from all industries would conform to the original expectations. The other sign anomalies are not as troubling. The first four variables (Group I) are expected to be most significant close to bankruptcy, and three of the four have the correct signs in the first three years. Also, the last four variables (Group II) are expected to be most significant in earlier years, and three of the four have the correct sign in the last four years. We believe that this pattern confirms the validity of our expectations. Logist analysis provides a technique that allows us to find the most significant variables in any predictive model. A variable is "most significant" if, by ChiSquare Qstatistic and MLE's statistic, they meet the requirements of entry and stay significance levels prespecified for the model. Our entry and stay significance levels were set at 0.05. Table 14 shows the most significant variables in each of our models. Capital intensity is significant in all periods. This means 76 that the nature of a company's line of business always plays a significant role. When bankruptcy is far into the future, our data indicate that this factor plays the largest role of the eight variables used in our model. As we approach bankruptcy, especially one year ahead of bankruptcy, however, ROA, FCC, and Market/Book Ratio become increasingly significant. This confirms our view that in the shortterm, variables in the company operating and profitability indicators group that are weighted toward a company's current financial data would play significant roles. Other factors, such as relative sales growth, balance ratio of income and sales growth, and management stock acquisition, have also played increasingly larger roles near the time of bankruptcy. To investigate this timing phenomenon further, we built and tested separate predictive models based on the groups defined in Chapter 5. Group I was composed of company operating and financial indicators and included ROA, market tobook ratio, FCC, and balance ratio. Group II was composed of fundamental company characteristics indicators and included the net rate of management stock acquisitions, the relative sales growth rate, the relatedness ratio, and capital intensity. We then compared the predictive power and effectiveness of the main models built with all eight variables with those of the Group I and Group II models. Table 15 shows the predictive powers and effectiveness of all three sets of models. Figure 4 shows the predictive power of 77 our main model, and Figure 5 compares the Group I and Group II models. We then investigated into the classification powers of our model by examining the empirical probability density functions for bankrupt and nonbankrupt firms. We divided the range of probability of bankrupt from 0 to 1.0 into ten equal intervals. The percentage of bankrupt and nonbankrupt firms relative to the total number of firms that they present which fall within each of these intervals for the five different time periods ti through t5 are tabulated and shown in Tables 16 and 17. The percentages are plotted against the midvalue of the interval to obtain the discrete approximation of the distributions of the bankrupt and nonbankrupt probabilities in Figures 6 to 15. The probabilities of the two groups are shown to diverge significantly by their respective bar graphs. The bankrupt group is clearly skewed toward the higher probabilities of failure that our model derived, while the nonbankrupt group is clearly skewed toward the lower probabilities of failure. These results are similar to those of Zavgren (1985). Her paper, however, only presented original probabilities, while we present both the original probabilities and those probabilities adjusted for sample selection (as discussed below). As mentioned in the previous chapter, because we selected our data with nonrandom, statebased criteria, we must adjust the probabilities derived from logist analysis. 78 For any given firm i in the general population with a probability P of bankruptcy, logist analysis would give a probability P' of bankruptcy for that company in our specific sample. We must find ways of finding a relationship between P and P' and also between the structures of our samples. Assuming that there are N, bankrupt and N2 nonbankrupt firms in the general population and n, bankrupt and n2 nonbankrupt firms in our bankrupt and nonbankrupt samples, P', according to Bayes' formula for conditional probability, is equal to: P' = P (n,/N1) / {P (n,/N,)+ (lP) (n2/N2)) (1) Previous work, such as Palepu (1986), which tried to predict merger targets using logist analysis models, have partially explored this relationship, but he only gave a formula for P' in the special case when n,=N,. We, however, derived a general formula for P' for cases when nI is not equal to N1, and n2 is not equal to N2: Let al = n,/N,, a2 = n2/N2, Then formula (1) can rewritten as P' = (a, P)/{(al*P) + (lP) a2)} (2) Substituting P = (1 + exp(Yj))"' into (2), we derive the formula for any value of a, and a2: P' = (1 + exp{lg(a2/a1)Yj}) 1. (3) This formula implies the following relationships between the samples and P' and P: If aI = a2: P' = P, Type I error will not change, Type II error will not change. If a, > ag: P' > P, Type I error will increase, Type II error will decrease. If al < a., P' < P, Type I error will decrease, Type II error will increase. According to this formula, without adjustments, we can derive a model with an artificially high or artificially low type I error by settling for an artificially low or artificially high type II error, or vice versa, simply by selecting the right samples. After adjustments, artificial type I and II errors are still possible because, even then, a, and a2 are part of the model. Therefore, to have meaningful probability models with the logist analysis methodology, we must always first adjust for al and a2 and then report their values along with our type I and type II errors. Table 18 presents such data for our sample. Since a, > a2 in our samples, type I error increased after adjustments were made, while type II error decreased. We can observe this same phenomenon by comparing Figures 6 through 10 with Figures 11 through 12, respectively. Our data lead to some interesting conclusions. First, we have succeeded in building a model whose predictive power does not fall precipitously as time before bankruptcy increases. Whereas Altman's ZETA model, under optimal conditions, is 96% accurate one year before bankruptcy but only 60% accurate five years before bankruptcy, our model's 80 predictive power, based on data from one experimental sample, is relative stable. It is most effective one year before bankruptcy, with 96.0% accuracy (as measured by the CIndex of logist analysis), but even at its lowest point, three years before bankruptcy, it still has 89.0% accuracy, and five years before bankruptcy it is 95.1% accurate. Second, we have found that during different periods before bankruptcy, different groups of variables become important in predicting bankruptcy. When close to bankruptcy, the Group I financial variables have very high predictive power. As we move farther back in time and try to predict bankruptcy farther ahead of time, we found that these variables' predictive powers started to wane. The Group II fundamental variables became increasingly more powerful as we moved farther back in time. This demonstrates that there is a time relationship between our fundamental variables and the future financial position of the company. Table 13. Signs of Coefficients Model bI b2 b3 b4 b5 b6 b7 b_ P + + + P2 + + P3 + +  P4 + +  P5 +  PI through P5 are models for predicting bankruptcy one to five years ahead of time. bI through b8 are coefficients of the following variables: b,: ROA (EBIT/TA) b2: FCC b3: Balance Ratio b4: Market/Book Ratio b: Relatedness Ratio b: Net Rate of Management Stock Acquisitions b7: Relative Sales Growth Rate b8: Capital Intensity. Table 14. Most Significant Variables in Forecasting Bankruptcy Model Most Significant Variables P, ROA, FCC, Balance Ratio, Capital Intensity, Market/Book Ratio P2 Relative Sales Growth, FCC, Capital Intensity P3 ROA, Net Rate of Management Stock Acquisitions, Relative Sales Growth, Capital Intensity P4 Capital Intensity P5 Capital Intensity P through P5 are models for forecasting bankruptcy one through five years ahead of time, respectively. Table 15. Predictive Power and Effectiveness of Different Models Years: EightVariable Models: CIndex: 0.960 X2 59.75 (SL with 8 DF) 0.50% L.H. Ratio Index 0.5969 Group I Models: CIndex: 0.929 X2 49.63 (SL with 4 DF) 0.50% L.H. Ratio Index 0.4958 Group II Models: CIndex: 0.819 X2 16.45 (SL with 4 DF) 0.50% L.H. Ratio Index 0.1643 0.957 69.31 0.50% 0.6133 0.873 39.88 0.50% 0.3529 0.770 27.43 0.50% 0.2427 0.892 48.48 0.50% 0.4135 0.771 16.33 0.50% 0.1365 0.835 35.19 0.50% 0.3001 0.909 44.51 0.50% 0.4819 0.740 10.33 5.00% 0.1074 0.863 35.31 0.50% 0.3823 5 0.951 45.94 0.50% 0.5980 0.598 3.83 50.00% 0.0460 0.889 32.47 0.50% 0.4227 The CIndex comes from logist analysis and indicates the classification accuracy of the model. X2 (or ChiSquare) is the 2 log likelihood ratio chisquare statistic of the model. IUU 80  60 40 20 1 2 3 4 5 Yeors before Bankruptcy Figure 4. Classification Accuracy of Empirical Model of Bankruptcy Accuracy Group I Group II 1 2 3 4 5 Years before Bankruptcy Figure 5. Classification Accuracy of Models Based on Group I and Group II Variables s 86 i3 dPe doPdP dPOP O dPdP dOde 00 icoto O n c co H 00 n com w0 i00 0 0 0 N 0 0 0v 0 0 m 0 d (0 o uI eq 000 0HO NHH < 0000 O 0 N 0,4 r.dp dodP dp ef dpdP do C r O cn c* eqtn no 0 ~ n rOc Oqq> r o w o '44 0 *** ** co ion toGo Ln N qeqm N r oo ooe oM ON O' o wp ap de do dp do d dP dp de > in oo mn mo m J .** , r4 dP P dpoo dP or0 p 4Q tnocr IC A 000 oA V o Lf *. .* ** " *I ,. il H S HO do doPdP doO dEdp0 dfd 0M rq8 ino4mcn onoc oOm>Dw om w $o 4j w 8M 4M Al C; C M.0 0 0q i 0 d c 0cow ioo o0o 0I0 .oo 0 Sdpd d0 dP dPd 0 p Op dP dP 0 10 Ln in oo 1n0Ln inwO in %o 4 0%M 000 HOM 0m 0  H f 0MO ei OP df 0M e Ov Ov a *o0 Io 0 own N 0 HI 4 'M dpg dpdp edpd d dp d > ) 1) 1m 1 9 0) 1 1 w Eo r. ra rCt 1 0 cJ 0 "q 0 f o rin 0 t go o q inq 0 to zC o O't 0 M 00 ON or * * dP d 0 c Octo 0 ,.4 4P H muI 'iq .l uI c0 .o A 0 0cl S41 (0 to OON rlOW OH d 00C0 0 N r dp dp mn o o Sdp \o o # 0 c ;oo 0ooo H 0 dkp dp nmoo ** * dp dP c10O dP dP In oo dp dp Ln in o de 0 (M fM cL LA de 0\ U) O..J0 Oi N 0p\ d * MM LOO Co rmo d dP 0 N N ONN ** * 0000 ocoo0 U)I rI o 0 w 0 0 C (n 0) 0 DH >QM >AH I 0 I I 0) 1 1 4 ) 0 o 4 r HO *H 0 o rI S Z CO E4 Zn m E dOe d i\ in in ** * OaCO LOLN N do tO CM OOILA CMM w Ln r S* * LNA ,0 L> N LOCm * * O 0 ino * * . 0 )O * * No% **ro * * %00 O 0 coo de dp r 0 H 0 O * 00 0 dP d * O~rl dP dp 0c.O (no e 0 dPdP \00 NO * * n u? W r Ln w 0 o tn o *~o** 000D SNO Os 0 00 co in NO LA 0 8 : * 44 4J :0 1)4 .0 '.4 ato 4) C 0 4. 0 l 0 r 4J V 4J 4.)4.) rH 0 3 aaa LO to M4 > 4a >1ai Oi C O E C 00 '. ' 0 r0 S: 2;o 2 sam = I? 0d d omo o c4 c4 rl dp do a n o ** * 0H U)mo Hoo ONO dpdP H 0 0 LO C o C; * * 0.25 0.45 0.15 0.35 0.65 0 85 0.75 0.95 Probability Interval MidVolues Figure 6. Unadjusted Empirical Probability Density Function, 1 Year Before Bankruptcy Nonbkpt Bankrupt 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 mnnIJinl J Nonbkpt Bankrupt 0.05 0.25 0.45 0.65 0.85 0.15 0.35 0.55 0.75 0.95 Probability Interval MidValues Figure 7. Unadjusted Empirical Probability Density Function, 2 Years Before Bankruptcy Nonbkpt 3arkrupt 0.05 0.25 0.45 0.65 0.85 0.15 0.35 0.55 0.75 0.95 Probability Interval MidValues Figure 8. Unadjusted Empirical Probability Density Function, 3 Years Before Bankruptcy Nonbkpt Bankrupt 0.05 0.25 0.45 0.65 0.85 0.15 0.35 0.55 0.75 0.95 Probability Interval MidValues Figure 9. Unadjusted Empirical Probability Density Function, 4 Years Before Bankruptcy 0.8 0.7Nonbkpt Bankrupt 0.6 c 0 a 0.5 o 0.4 0 C 0 0.3 U 0.2 0.1  0 0.05 0.25 0.45 0.65 0.85 0.15 0.35 0.55 0.75 0.95 Probability Interval MidValues Figure 10. Unadjusted Empirical Probability Density Function, 5 Years Before Bankruptcy 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.25 0.15 7 urJ l~a 0.65 0.85 0.55 0.75 Prob'atlitly Interval MidValues Figure 11. Adjusted Empirical Probability Density Function, 1 Year Before Bankruptcy Nonbkpt Bankrupt Y 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Probability Interval MidValues Figure 12. Adjusted Empirical Probability Density Function, 2 Years Before Bankruptcy 15 0.25 0 45 0.65 0.85 0.15 0.35 0.55 0.75 0.95 Nonbkpt Bankrupt Nonbkpt Bankrupt 0.05 0.25 0.45 0.65 0.85 0.15 0.35 0.55 0.75 0.95 Probability Interval MidValues Figure 13. Adjusted Empirical Probability Density Function, 3 Years Before Bankruptcy 