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Bankruptcy : a proportional hazard approach Betton, Sandra Ann 1987

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BANKRUPTCY: A PROPORTIONAL HAZARD APPROACH By SANDRA ANN BETTON B. Comm., McMaster U n i v e r s i t y , 1985 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Commerce and Business A d m i n i s t r a t i o n ) We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September 1987 © S a n d r a Ann Betton, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Commerce end Business A d m i n i s t r a t i o n The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date September 29, 198? ABSTRACT The r e c e n t dramatic i n c r e a s e i n the c o r p o r a t e bankruptcy r a t e , coupled with a s i m i l a r r a t e o f i n c r e a s e i n the bank f a i l u r e r a t e , has re-awakened i n v e s t o r , lender and government i n t e r e s t i n the area of bankruptcy p r e d i c t i o n . Bankruptcy p r e d i c t i o n models are of p a r t i c u l a r v a l u e to a f i r m ' s c u r r e n t and f u t u r e c r e d i t o r s who o f t e n do not have the b e n e f i t of an a c t i v e l y t r aded market i n the f i r m ' s s e c u r i t i e s from which to make i n f e r e n c e s about the debtor's v i a b i l i t y . The models commonly used by many experts i n an endeavour to p r e d i c t the p o s s i b i l i t y of d i s a s t e r are o u t l i n e d i n t h i s paper. The p r o p o r t i o n a l hazard model, pioneered by Cox [1972], assumes t h a t the hazard f u n c t i o n , the r i s k of f a i l u r e , given f a i l u r e has not a l r e a d y o c c u r r e d , i s a f u n c t i o n of v a r i o u s e x p l a n a t o r y v a r i a b l e s and estimated c o e f f i c i e n t s m u l t i p l i e d by an a r b i t r a r y and unknown f u n c t i o n of time. The Cox P r o p o r t i o n a l Hazard model i s u s u a l l y a p p l i e d i n medical s t u d i e s ; but, has r e c e n t l y been a p p l i e d to the bank f a i l u r e q u e s t i o n [Lane, Looney & Wansley, 1986]. The model performed w e l l i n the narrowly d e f i n e d , h i g h l y r e g u l a t e d , banking i n d u s t r y . The p r i n c i p a l advantage of t h i s approach i s that the modi i n c o r p o r a t e s both the s u r v i v a l times observed and any c e n s o r i n g of data thereby u s i n g more of the a v a i l a b l e i n f o r m a t i o n i n the a n a l y s i s . U n l i k e many bankruptcy p r e d i c t i o n models, such as l o g i t and p r o b i t based r e g r e s s i o n models, the Cox model est i m a t e s the p r o b a b i l i t y d i s t r i b u t i o n - i i i -of s u r v i v a l times. The p r o p o r t i o n a l hazard model would, t h e r e f o r e , appear to o f f e r a u s e f u l a d d i t i o n to the more t r a d i t i o n a l bankruptcy p r e d i c t i o n models mentioned above. T h i s paper e v a l u a t e s the a p p l i c a b i l i t y o f the Cox p r o p o r t i o n a l hazard model i n the more d i v e r s e i n d u s t r i a l environment. In order to t e s t t h i s model, a sample of 109 firms was s e l e c t e d from the Compustat I n d u s t r i a l and Research I n d u s t r i a l data tapes. F o r t y one of these f i r m s f i l e d p e t i t i o n s under the v a r i o u s bankruptcy a c t s a p p l i c a b l e between 1972 and 1985 and were matched to 67 f i r m s which had not f i l e d p e t i t i o n s f o r bankruptcy d u r i n g the same p e r i o d . In view of the dramatic changes i n the bankruptcy r e g u l a t o r y environment caused by the Bankruptcy reform a c t of 1978, the l e g a l framework of the bankruptcy process was a l s o examined. The performance o f the estimated Cox model was then e v a l u a t e d by comparing i t s c l a s s i f i c a t i o n and d e s c r i p t i v e c a p a b i l i t i e s t o those o f an estimated d i s c r i m i n a n t a n a l y s i s based model. The r e s u l t s of t h i s study i n d i c a t e t h a t while the c l a s s i f i c a t i o n c a p a b i l i t y of the Cox model was l e s s than t h a t o f d i s c r i m i n a n t a n a l y s i s , the model pr o v i d e s a d d i t i o n a l i n f o r m a t i o n beyond t h a t a v a i l a b l e from the d i s c r i m i n a n t a n a l y s i s . - i v -T A B L E O F C O N T E N T S ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i I. INTRODUCTION 1 I I . BANKRUPTCY A. DEFINITION 5 B. LEGAL ENVIRONMENT 7 C. THE BANKRUPTCY RECORD 17 I I I . MODELS COMMONLY USED A. STOCK-PRICE BASED MODELS 19 B. UNIVARIATE RATIO ANALYSIS 2 0 C. STATIC MULTIVARIATE ANALYSIS 21 D. REGRESSION AND TIME BASED MODELS 25 IV. PLAN OF ANALYSIS A. RATIO SELECTION 29 B. THE DATA SET 31 V. SAMPLE CHARACTERISTICS A. SAMPLE STATISTICS 3 8 B. RATIO DISTRIBUTION 41 C. CHANDLER AND REFORM ACTS 4 2 VI. DISCRIMINANT ANALYSIS A. THEORY 4 8 B. ONE YEAR RESULTS 52 -v-V I I . THE COX MODEL A. SURVIVAL THEORY 5 5 B. THE COX PROPORTIONAL HAZARD MODEL 57 C. ONE YEAR PRIOR ESTIMATION 6 2 D. FOUR YEARS PRIOR ESTIMATION 70 E. "TIED" OBSERVATIONS 7 5 V I I I . MODEL COMPARISON 79 IX. SUMMARY AND CONCLUSION 8 6 FOOTNOTES 89 BIBLIOGRAPHY 9 4 APPENDIX I. SURVIVAL PLOTS 97 APPENDIX I I . NORMAL PROBABILITY PLOTS 101 APPENDIX I I I . STRATIFIED COX ESTIMATES 106 - v i -ii I S T O F T A B L E S 1 MAJOR CORPORATIONS F I L I N G CHAPTER XI 14 2 L I S T OF RATIOS USED 29 3 W. T. GRANT SALES 3 3 4 CHARACTERISTICS OF INCOMPLETE DATA 34 5 SUMMARY ST A T I S T I C S 3 8 6 TESTS OF GROUP SIMILARITY 46 7 CLASSIFICATION FUNCTION 5 3 8 CLASSIFICATION FUNCTION (4 YEARS PRIOR) 54 9 COX MODEL ESTIMATION 6 3 10 CORRELATION MATRIX 64 11 COX MODEL ESTIMATION (4 YEARS PRIOR) 7 0 12 CORRELATION MATRIX (4 YEARS PRIOR) 7 2 13 COX MODEL, RE-ESTIMATION 73 14 "TIED" OBSERVATIONS 7 6 15(a) MODEL PERFORMANCE (DISCRIMINANT MODEL) 80 15(b) MODEL PERFORMANCE (COX MODEL) 81 16 LINEAR DISCRIMINANT FUNCTION SCORES 84 - V I 1 -L I S T O F F I G U R E S 1 ANNUAL FAILURE RATE 17 2 RATIO PROFILE OF BANKRUPT AND SURVIVING FIRMS 39 3 DISCRIMINANT ANALYSIS (GRAPHICALLY) 4 8 4 LOG MINUS LOG SURVIVAL FUNCTION 68 5 GOODNESS OF FIT 6 9 6 GOODNESS OF FIT (4 YEARS PRIOR) 74 7 GOODNESS OF FIT ("TIED" OBSERVATIONS) 7 8 APPENDIX I: SURIVIAL PLOTS 8 SURVIVAL FUNCTION #0 42078 9 7 9 SURVIVAL FUNCTION #564402 98 10 SURVIVAL FUNCTION #868168 99 11 SURVIVAL FUNCTION #297882 100 APPENDIX I I : NORMAL PROBABILITY PLOTS 12 CURRENT ASSETS / SALES (4 YEAR PRIOR) 101 13 WORKING CAPITAL / ASSETS (4 YRS. PRIOR) 102 14 WORKING CAPITAL / ASSETS (1 YR. PRIOR) 103 15 NET INCOME / SALES (4 YEARS PRIOR) 104 16 NET INCOME / SALES (1 YEAR PRIOR) 105 - v i i i -APPENDIX I I I : STRATIFIED SURVIVAL FUNCTIONS 17 CASH FLOW / TOTAL DEBT 106. 18 NET INCOME / SALES 107. 19 TOTAL CLAIMS / ASSETS 108. -1-I . INTRODUCTION On a v e r a g e a U.S. b u s i n e s s f i r m f a i l e d e v e r y f o r t y - n i n e m i n u t e s d u r i n g 1970. T h i r t e e n y e a r s l a t e r , i n 1983, a f i r m *1 f a i l e d , on a v e r a g e , e v e r y s i x t e e n m i n u t e s . T h i s s t a r t l i n g i n c r e a s e i n t h e c o r p o r a t e b a n k r u p t c y r a t e , c o u p l e d w i t h a s i m i l a r r a t e o f i n c r e a s e i n t h e bank f a i l u r e r a t e , h as r e -awakened i n v e s t o r , l e n d e r and government i n t e r e s t i n t h e a r e a o f b a n k r u p t c y p r e d i c t i o n . The e a r l y i d e n t i f i c a t i o n o f a p o t e n t i a l b a n k r u p t would be i n v a l u a b l e t o i n v e s t o r , c r e d i t o r and management a l i k e . B a n k r u p t c y p r e d i c t i o n m o d e ls a r e o f p a r t i c u l a r v a l u e t o a f i r m ' s c u r r e n t and f u t u r e c r e d i t o r s who o f t e n do n o t have t h e b e n e f i t o f a a c t i v e l y t r a d e d m a r k e t i n t h e f i r m ' s s e c u r i t i e s f r o m w h i c h t o make i n f e r e n c e s a b o u t t h e d e b t o r ' s v i a b i l i t y . One w o u l d hope t h a t a s u c c e s s f u l " P r e d i c t i o n M o d e l " would a l l o w a f i r m ' s management t o a c t on t h e s i g n a l o f i m p e n d i n g doom and by t a k i n g c o r r e c t i v e m e a s ures a v o i d t h e f i l i n g o f p e t i t i o n s f o r b a n k r u p t c y . I n t h i s way, a 'good' p r e d i c t o r o f b a n k r u p t c y w o u l d , i n e f f e c t , become a s e l f - d e f e a t i n g p r o p h e s y . The m o d e l s commonly u s e d by many e x p e r t s i n an e n d e a v o u r t o p r e d i c t t h e p o s s i b i l i t y o f d i s a s t e r w i l l be o u t l i n e d i n t h i s p a p e r . _ On a v e r a g e i n 1970, a f i r m was i n c o r p o r a t e d e v e r y two m i n u t e s w h i l e on a v e r a g e i n 1983, one was i n c o r p o r a t e d e v e r y f i f t y - t w o s e c o n d s . -2-Altman's Z Score model, based on d i s c r i m i n a n t a n a l y s i s , i s one of the most commonly a p p l i e d bankruptcy p r e d i c t i o n models. T h i s type o f model has been a p p l i e d i n many d i f f e r e n t i n d u s t r i e s and s i t u a t i o n s and has, on average, performed w e l l . Joy and T o l l e f s o n [1975] found t h a t Altman's Z Score performed s i g n i f i c a n t l y b e t t e r than a p r o p o r t i o n a l chance model. Any new model should, t h e r e f o r e , o f f e r s i m i l a r "general purpose" a p p l i c a b i l i t y and r e l i a b i l i t y . Many other models have been developed i n an e f f o r t t o improve on the d i s c r i m i n a n t a n a l y s i s based Z Score model. While these l a t t e r models have added to our understanding of the bankruptcy c o n d i t i o n , they have not been as widely used as the Z Score. Altman's model appears to be one of the most g e n e r a l l y a p p l i c a b l e bankruptcy p r e d i c t i o n model and, t h e r e f o r e , a c t s as the standard by which a l l o t h e r s must be judged. Among the l a t t e r are Beaver's [1966] U n i v a r i a t e a n a l y s i s of f i n a n c i a l r a t i o s , l o g i t models [Martin, 1977], f a c t o r a n a l y t i c models [West, 1985], and F i r s t Passage Time [Santomero and Vi n s o , 1977]. The Cox P r o p o r t i o n a l Hazard model i s u s u a l l y a p p l i e d i n medical s t u d i e s ; but, has r e c e n t l y been a p p l i e d to the bank f a i l u r e q u e s t i o n [Lane, Looney & Wansley, 1986]. The model performed w e l l i n the narrowly d e f i n e d , h i g h l y r e g u l a t e d , banking i n d u s t r y . The p r i n c i p a l advantage of the Cox model i s t h a t more of the a v a i l a b l e i n f o r m a t i o n i s used i n the a n a l y s i s . The model i n c o r p o r a t e s both the s u r v i v a l times - 3 -observed and any c e n s o r i n g of d a t a . Censoring of data occurs when the study terminates before every f i r m has f a i l e d . U n l i k e many bankruptcy p r e d i c t i o n models, such as l o g i t and p r o b i t based r e g r e s s i o n models, the Cox model estimates the p r o b a b i l i t y d i s t r i b u t i o n of s u r v i v a l times. The Cox model would, t h e r e f o r e , appear to o f f e r a u s e f u l a d d i t i o n t o the more t r a d i t i o n a l bankruptcy p r e d i c t i o n models mentioned above. T h i s paper seeks to e v a l u a t e the a p p l i c a b i l i t y of the Cox P r o p o r t i o n a l hazard model i n a more d i v e r s e i n d u s t r i a l environment. In order to t e s t t h i s model, a sample of 109 f i r m s was s e l e c t e d from the Compustat I n d u s t r i a l and Research I n d u s t r i a l data tapes. F o r t y one of these f i r m s f i l e d p e t i t i o n s under the v a r i o u s bankruptcy a c t s a p p l i c a b l e between 1972 and 1985. In view of the dramatic changes i n the bankruptcy r e g u l a t o r y environment caused by the Bankruptcy reform a c t of 1978, the l e g a l framework of the bankruptcy process was a l s o examined. The Cox model was estimated on a sample of 41 f i r m s which f i l e d f o r bankruptcy between 1972 and 1985. These f a i l u r e s were matched to 67 f i r m s which had not f i l e d p e t i t i o n s f o r bankruptcy d u r i n g the same p e r i o d . The performance of the estimated Cox model was then e v a l u a t e d by comparing i t s c l a s s i f i c a t i o n and d e s c r i p t i v e c a p a b i l i t i e s to those of an estimated d i s c r i m i n a n t a n a l y s i s based model. The r e s u l t s of t h i s study i n d i c a t e t h a t while the c l a s s i f i c a t i o n c a p a b i l i t y of the Cox - 4 -m o d e l was l e s s t h a n t h a t o f d i s c r i m i n a n t a n a l y s i s , t h e C o x m o d e l p r o v i d e s i n f o r m a t i o n b e y o n d t h a t p r o v i d e d b y t h e d i s c r i m i n a n t a n a l y s i s . - 5 -I I . BANKRUPTCY A. DEFINITION The terms " b u s i n e s s f a i l u r e " , " i n s o l v e n c y " and " b a n k r u p t c y " a r e o f t e n u s e d i n t e r c h a n g e a b l y . However, t h e s i t u a t i o n s d e s c r i b e d by t h e s e t e r m s and t h e c o n s e q u e n c e s o f e a c h a r e v e r y d i f f e r e n t . B u s i n e s s f a i l u r e d e s c r i b e s t h e e c o n o m i c c o n d i t i o n i n w h i c h t h e r e t u r n r e a l i z e d on a s s e t s i s l e s s t h a n t h e o p p o r t u n i t y c o s t s . 1 I n s u c h a c a s e t h e f i r m ' s e a r n i n g s a r e o f t e n m i n i m a l b u t s u f f i c i e n t t o c o v e r v a r i a b l e c o s t s . Such a f i r m i s n o t n e c e s s a r i l y g o i n g t o become b a n k r u p t , i t may e v e n become f i n a n c i a l l y p r o f i t a b l e i n t h e n e a r f u t u r e . I n s o l v e n c y e s s e n t i a l l y r e f e r s t o l i q u i d i t y p r o b l e m s . T e c h n i c a l i n s o l v e n c y o c c u r s when a f i r m c a n n o t meet i t ' s 2 c u r r e n t o b l i g a t i o n s and i s n o t i n i t s e l f a s u f f i c i e n t c o n d i t i o n f o r b a n k r u p t c y as t h e i n a b i l i t y t o meet c u r r e n t o b l i g a t i o n s c a n be a t e m p o r a r y c r i s i s t o an o t h e r w i s e h e a l t h y f i r m . Such s i t u a t i o n s a r e l i k e l y t o o c c u r i n h i g h l y s e a s o n a l i n d u s t r i e s . B a n k r u p t c y i s by f a r t h e most s e r i o u s f i n a n c i a l c r i s i s a f i r m h a s t o f a c e . The major d i f f e r e n c e between t h i s c o n d i t i o n and t h e p r e v i o u s l y d i s c u s s e d c r i s e s i s t h a t a t h i r d p a r t y , t h e B a n k r u p t c y C o u r t s , h a s now e n t e r e d t h e p r o c e e d i n g s . Any f i r m w h i c h becomes e m b r o i l e d i n b a n k r u p t c y p r o c e e d i n g s i s u n l i k e l y t o emerge uncha n g e d : i t w i l l e i t h e r be r e o r g a n i z e d -6-and emerge as a new f i r m o r i t w i l l be l i q u i d a t e d and d i s a p p e a r . N e i t h e r t h e owners ( s t o c k h o l d e r s ) n o r t h e o r i g i n a l management r e t a i n f u l l c o n t r o l t h e f i r m ' s d e s t i n y , c o n t r o l h a s l a r g e l y been r e l i n q u i s h e d t o t h e C o u r t s who w i l l , a c t i n g i n t h e b e s t i n t e r e s t s o f t h e c r e d i t o r s , d e c i d e whether t h e f i r m i s r e - o r g a n i z e d o r i s l i q u i d a t e d . Of t h e t h r e e " d i s t r e s s " c o n d i t i o n s o u t l i n e d , b u s i n e s s f a i l u r e i s t h e h a r d e s t t o i d e n t i f y a s i t i n v o l v e s d e t e r m i n i n g t h e r a t e o f r e t u r n p o s s i b l e i n an a l t e r n a t i v e u s e o f a f i r m ' s a s s e t s and c o m p a r i n g t h i s r a t e t o t h e a c t u a l r a t e o f r e t u r n b e i n g r e a l i z e d . T h i s c o m p a r i s o n r e q u i r e s a d e t e r m i n a t i o n o f t h e t r u e m a r k e t v a l u e and m a r k e t r a t e o f r e t u r n on t h e f i r m ' s a s s e t s . Such a v a l u a t i o n i s v e r y d i f f i c u l t t o a r r i v e a t p r a c t i c a l l y i n t h e c a s e o f a f i r m w i t h o u t an a c t i v e m a r k e t f o r i t ' s s e c u r i t i e s . I f t h e f i r m ' s s e c u r i t i e s a r e a c t i v e l y t r a d e d , t h e m a r k e t d a t a c a n be u s e d t o compare t h e s e r e l a t i v e m a r k e t r a t e s o f r e t u r n . The f i n a n c i a l " d i s t r e s s " c o n d i t i o n s o f i n s o l v e n c y and b a n k r u p t c y a r e u s u a l l y e a s i e r t o i d e n t i f y . I n s o l v e n c y r e q u i r e s a c o m p a r i s o n o f t h e r e l a t i v e v a l u e s o f t h e c a s h f l o w s and c u r r e n t o b l i g a t i o n s , b o t h o f w h i c h c a n o f t e n be d e t e r m i n e d f r o m t h e f i r m ' s f i n a n c i a l s t a t e m e n t s . B a n k r u p t c y i s t h e most e a s i l y i d e n t i f i a b l e c o n d i t i o n as i t i s a l e g a l s t a t e and o nce e n t e r e d , a f i r m c a n n o t h i d e t h e f a c t t h a t t h e p e t i t i o n h a s b e en f i l e d . -7-T h i s p a p e r w i l l , t h e r e f o r e , c o n c e n t r a t e on t h e p r e d i c t i o n o f t h e f i l i n g o f a b a n k r u p t c y p e t i t i o n a s i t i s an o b j e c t i v e l y v e r i f i a b l e c o n d i t i o n . B. LEGAL ENVIRONMENT BACKGROUND; The need f o r l e g a l r e c o u r s e i n a c a s e o f b a n k r u p t c y was f i r s t r e c o g n i z e d by t h e E u r o p e a n m e r c a n t i l e s t a t e s o f t h e l a t e m i d d l e a g e s . As e a r l y b a n k r u p t c y law was p r i m a r i l y aimed a t t h e m e r c h a n t who was p l a n n i n g t o remove e i t h e r h i s a s s e t s o r h i m s e l f f r o m t h e a r e a , i t was an i n v o l u n t a r y p r o c e d u r e and e s s e n t i a l l y r e t a l i a t o r y i n n a t u r e . The s o l v e n c y o f t h e " b a n k r u p t " was r a r e l y i f e v e r q u e s t i o n e d , t h e l a w ' s p u r p o s e was t o e n s u r e t h a t d e b t s were p a i d b e f o r e l e a v i n g a j u r i s d i c t i o n . " ^ As t h e e c o n o m i c e n v i r o n m e n t became more complex, t h e need f o r a l e g a l mechanism f o r t h e management o f i n s o l v e n c y c a s e s a r o s e i n B r i t a i n . T h e s e c a s e s , u n l i k e t h e " b a n k r u p t c y " c a s e s , g e n e r a l l y i n v o l v e d i n s o l v e n c y r a t h e r t h a n f l i g h t and c o n s e q u e n t l y , were o f a more c o - o p e r a t i v e n a t u r e . The B r i t i s h i n s o l v e n c y l a w s were v o l u n t a r y i n n a t u r e and were b a s e d on t h e n o t i o n o f g i v i n g a b a s i c a l l y h o n e s t " u n f o r t u n a t e " a means o f d i s t r i b u t i n g h i s a s s e t s e q u i t a b l y among h i s c r e d i t o r s . U n l i k e t h e b a n k r u p t c y l a w s , t h e i n s o l v e n c y l a w s a l l o w e d and e n c o u r a g e d n e g o t i a t i o n between d e b t o r and c r e d i t o r f o r t h e i r m u t u a l b e n e f i t . I f an i n s o l v e n t s a t i s f i e d t h e c o u r t s , he c o u l d be d i s c h a r g e d f r o m h i s d e b t s -8-and begin a g a i n with a c l e a n s l a t e which was not p o s s i b l e 4 under the bankruptcy laws. A l l modern bankruptcy l e g i s l a t i o n has developed from these opposing p h i l o s o p h i e s of r e t a l i a t i o n and c o - o p e r a t i o n . THE CHANDLER ACT: The C o n s t i t u t i o n of the U n i t e d S t a t e s v e s t s the s o l e j u r i s d i c t i o n over bankruptcy laws with the 5 F e d e r a l Government. The aim i s to e s t a b l i s h uniform and f a i r treatment of a l l bankrupts and t h e i r c r e d i t o r s . In 1898, the U.S. Congress passed the Bankruptcy A c t , and e s s e n t i a l l y i t served the United S t a t e s u n t i l the 1930's when the Great Depression focussed p u b l i c and government a t t e n t i o n on the f u n c t i o n i n g of the Bankruptcy A c t . In 1938 the U.S. Congress responded t o the massive s o c i a l and economic upheaval caused by the d e p r e s s i o n by p a s s i n g an exte n s i v e amendment t o the Bankruptcy A c t . The amendment sponsored by Chandler, although t e c h n i c a l l y o n l y an amendment, made such wide sweeping changes t o the o r i g i n a l a c t , t h a t the Bankruptcy Act became known as the Chandler Ac t . S e v e r a l f e a t u r e s of the a c t deserve s p e c i a l mention. F i r s t l y , while any f i r m may become i n s o l v e n t , not a l l f i r m s may d e c l a r e bankruptcy. The A c t does not allow b u i l d i n g and l o a n a s s o c i a t i o n s and insurance and banking c o r p o r a t i o n s to e i t h e r v o l u n t a r i l y or i n v o l u n t a r i l y f i l e under the Chandler A c t , r a t h e r t h e i r l i q u i d a t i o n or r e h a b i l i t a t i o n i s l e f t to 6 s t a t e a u t h o r i t y . The h i s t o r i c a l b a s i s of t h i s exemption i s a - 9 -b a s i c d e f e r e n c e t o s t a t e a u t h o r i t y . I n v o l u n t a r y b a n k r u p t c y i s a l s o d e n i e d t o t h e c r e d i t o r s o f f e d e r a l and s t a t e g o v e r n m e n t s and f a r m e r s . R a i l r o a d s r e c e i v e s p e c i a l t r e a t m e n t under t h e A c t . P r i o r t o 1933, t h e o n l y c o u r s e open t o a f i n a n c i a l l y d i s t r e s s e d r a i l w a y was t o e n t e r e i t h e r f e d e r a l o r s t a t e r e c e i v e r s h i p . S e c t i o n 77, d e a l i n g w i t h r a i l r o a d r e o r g a n i z a t i o n , was e n a c t e d i n 1933 w i t h t h e a i m o f f a c i l i t a t i n g and s t r e a m l i n i n g t h e r e o r g a n i z a t i o n p r o c e s s w h i l e t a k i n g i n t o a c c o u n t " t h e p u b l i c 7 i n t e r e s t " . I t i s i n t e r e s t i n g t o n o t e t h a t w h i l e t h e C h a n d l e r A c t made e x t e n s i v e r e v i s i o n s t o t h e B a n k r u p t c y A c t , i t made no c h a n g e s t o S e c t i o n 77. The C h a n d l e r A c t c a n be a p p l i e d t o a d e b t o r e i t h e r v o l u n t a r i l y o r i n v o l u n t a r i l y . The o n l y r e q u i r e m e n t s f o r a v o l u n t a r y p e t i t i o n f o r b a n k r u p t c y a r e t h a t t h e p e t i t i o n e r has d e b t s , p a y t h e f i l i n g f e e , and n o t be one o f t h e exempt i n s t i t u t i o n s . The s o l v e n c y o f t h e p e t i t i o n e r i s i r r e l e v a n t , t h e o n l y r e l e v a n t m a t t e r i s t h a t a t l e a s t one c r e d i t o r e x i s t s . A p e t i t i o n f o r r e o r g a n i z a t i o n c a n o n l y be e n t e r e d v o l u n t a r i l y . ^ E x c e p t i n c e r t a i n c i r c u m s t a n c e s an i n v o l u n t a r y p e t i t i o n c a n be f i l e d a g a i n s t any d e b t o r whose t o t a l d e b t s e x c e e d g $1000. The p e t i t i o n must be s i g n e d by a t l e a s t t h r e e c r e d i t o r s w i t h $500 i n d e b t s ( i n a g g r e g a t e ) i f more t h a n t w e l v e e x i s t , o t h e r w i s e o n l y one c r e d i t o r ' s s i g n a t u r e i s r e q u i r e d . " ^ However, a b a n k r u p t c y p e t i t i o n c a n n o t be f i l e d on -10-a whim; r a t h e r , t h e d e b t o r must have c o m m i t t e d an " a c t o f b a n k r u p t c y " . T h e s e " a c t s " c a n be summarized a s : h i d i n g a s s e t s , g i v i n g p r e f e r e n t i a l t r e a t m e n t t o c e r t a i n c r e d i t o r s , a l l o w i n g a l i e n o r a s s i g n m e n t o f a s s e t s t o o c c u r w h i l e 12 i n s o l v e n t o r a d m i t t i n g an i n a b i l i t y t o p a y . U n l i k e a v o l u n t a r y p e t i t i o n w h i c h u s u a l l y r e s u l t s i n an immediate a d j u d i c a t i o n o f b a n k r u p t c y , an i n v o l u n t a r y p e t i t i o n c a n be c o n t e s t e d i n t h e B a n k r u p t c y C o u r t s . I f t h e c r e d i t o r s a r e u n a b l e t o p r o v e i n s o l v e n c y and t h e c o m m i s s i o n o f a t l e a s t one o f t h e " A c t s o f B a n k r u p t c y " , t h e p e t i t i o n w i l l be d i s m i s s e d . I n a s t r a i g h t b a n k r u p t c y , under C h a p t e r V, t h e b a n k r u p t emerges w i t h a " c l e a n s l a t e " f i n a n c i a l l y ; b u t , g e n e r a l l y , w i t h no a s s e t s a s t h e y have been l i q u i d a t e d i n o r d e r t o s a t i s f y c r e d i t o r s ' c l a i m s . U n f o r t u n a t e l y t h e s e p r o c e e d i n g s impose s e r i o u s c o s t s on d e b t o r and c r e d i t o r a l i k e . An A r r a n g e m e n t , under C h a p t e r XI o f t h e A c t , a t t e m p t s t o b o t h r e d u c e t h e c o s t o f b a n k r u p t c y and a l l o w t h e b u s i n e s s t o c o n t i n u e a c t i v i t y . An a r r a n g e m e n t i s a p r o c e e d i n g p u r s u a n t t o w h i c h an e m b a r r a s s e d d e b t o r , by agreement w i t h h i s c r e d i t o r s and s u b j e c t t o c o u r t a p p r o v a l , r e m a i n s i n b u s i n e s s b u t s e c u r e s e i t h e r a n e x t e n s i o n on t i m e fojj^payment o r p a y s them o f f on a p r o r a t a b a s i s , o r b o t h . C h a p t e r X o f t h e A c t a l l o w s c o r p o r a t i o n s t o r e f i n a n c e and r e o r g a n i z e , change c o r p o r a t e s t r u c t u r e , w i t h o u t i n t e r r u p t i o n o f b u s i n e s s a c t i v i t y . W h i l e R e o r g a n i z a t i o n and A r r a n g e m e n t b o t h i n v o l v e n e g o t i a t i o n between d e b t o r and c r e d i t o r s w i t h t h e c o u r t s a c t i n g as i n t e r m e d i a r y , t h e r e e x i s t -11-c o n s i d e r a b l e d i f f e r e n c e s between Chapters X and XI i n the areas of c o n t r o l , r e p r e s e n t a t i o n , and f a i r n e s s . C o n t r o l of a Chapter XI proceeding i s vested i n the debtor. Only the debtor can f i l e the p e t i t i o n and only the debtor can propose a p l a n . The major weakness i n a Chapter XI proceeding i s t h a t independent v e r i f i c a t i o n of f i n a n c i a l i n f o r m a t i o n d i s c l o s e d by the debtor i s o f t e n not undertaken as the A c t makes no p r o v i s i o n f o r i n v e s t i g a t i o n . T h i s i n f o r m a t i o n problem f o r unsecured c r e d i t o r s i s compounded by two other f e a t u r e s of the Chapter: the " f r i e n d l y " c r e d i t o r s 13 committee and the expense reimbursement p r o v i s i o n . The c r e d i t o r s ' committee, t h e o r e t i c a l l y , i s the unsecured c r e d i t o r s r e p r e s e n t a t i v e . However, i n p r a c t i c e , i t i s made up of major c r e d i t o r s who o f t e n have a c l o s e a s s o c i a t i o n with the debtor. The problems of inadequate r e p r e s e n t a t i o n are compounded by the Chapter's reimbursement p r o v i s i o n t h a t the expenses i n c u r r e d by the committee may not be reimbursed i f the debtor's arrangement p l a n i s not 14 confirmed. Consequently, most debtors are s u b j e c t to only a c u r s o r y i n v e s t i g a t i o n as acceptance of the proposed p l a n i s o f t e n b e t t e r f i n a n c i a l l y than f o r c i n g l i q u i d a t i o n as a f a i r p l a n under Chapter XI i s r e q u i r e d t o p r o v i d e g e n e r a l c r e d i t o r s with more than would be p r o v i d e d i n l i q u i d a t i o n . " ^ Chapter X, i n c o n t r a s t , v e s t s c o n t r o l i n an independent t r u s t e e r a t h e r than e i t h e r c r e d i t o r or e q u i t y owners. The c o u r t appointed t r u s t e e has wide i n v e s t i g a t i v e powers and has -12-th e f i r s t o p p o r t u n i t y t o propose a p l a n o f r e o r g a n i z a t i o n . A l l other i n t e r e s t e d p a r t i e s , except the debtor, may a l s o f i l e p r o p o s a l s . The debtor may o n l y f i l e a f t e r the t r u s t e e ' s time t o f i l e has e x p i r e d . 1 * ' R e p r e s e n t a t i o n requirements are s i g n i f i c a n t l y d i f f e r e n t between Chapters X and XI. Chapter XI o f f i c i a l l y d e a l s only with unsecured c r e d i t o r s and has no r e g u l a t i o n s r e g a r d i n g the appointment or s e l e c t i o n o f c r e d i t o r s r e p r e s e n t a t i v e s . Chapter X, i n c o n t r a s t , d e a l s with a l l c r e d i t o r s and r e q u i r e s t h a t the t r u s t e e and h i s at t o r n e y be t r u l y " d i s i n t e r e s t e d " p a r t i e s who are f r e e of any c o n f l i c t s of i n t e r e s t . The Chapter a l s o r e q u i r e s f u l l d i s c l o s u r e and imposes f i d u c i a r y standards on any r e p r e s e n t a t i v e s . There are no fee 17 reimbursement r e s t r i c t i o n s s i m i l a r t o those i n Chapter XI. F a i r n e s s of the p l a n i s another area i n which Chapters X and XI d i f f e r markedly. As o r i g i n a l l y enacted i n 1938, Chapter XI pl a n s had to be i n the bes t i n t e r e s t s of c r e d i t o r s , f a i r and e q u i t a b l e and f e a s i b l e . Chapter X p l a n s , on the 5|her hand, had t o be f a i r and e q u i t a b l e and f e a s i b l e . A f a i r p l a n under Chapter XI r e q u i r e s t h a t g e n e r a l c r e d i t o r s r e c e i v e more than they would i n a l i q u i d a t i o n . Chapter X i n c o n t r a s t f o l l o w s the p r i n c i p l e s of a b s o l u t e p r i o r i t y . The j u n i o r c r e d i t o r s have no i n t e r e s t s under the p l a n u n t i l more 19 s e n i o r c r e d i t o r s are p a i d i n f u l l . A major problem i n u s i n g Chapter X and XI i s t h a t the Act makes no d i s t i n c t i o n between who may apply. Chapter XI was intended f o r use by sm a l l e r c l o s e l y h e l d c o r p o r a t i o n s and -13-non-business i n d i v i d u a l s . There have been s e v e r a l attempts by the S e c u r i t i e s and Exchange Commission t o f o r b i d the use of Chapter XI t o any p u b l i c c o r p o r a t i o n with more than one 20 hundred stock h o l d e r s . These moves have not been s u c c e s s f u l . Given a c h o i c e between f i l i n g under Chapter X or XI, a debtor, i n g e n e r a l , would p r e f e r Chapter XI as he maintains c o n t r o l o f the busi n e s s and the proceedings. While the c o n t r o l and r e p r e s e n t a t i o n problems may not be major i n a sma l l f i r m these weaknesses can o f f e r l i t t l e p r o t e c t i o n t o the c r e d i t o r s who a r e n ' t " f r i e n d l y " . Chapter XI case law has evolved t o the p o i n t t h a t although the chapter o n l y d e a l s with unsecured c r e d i t o r s , there i s s u f f i c i e n t precedent and procedure t o d e a l with secured c r e d i t o r s w i t h i n a Chapter XI bankruptcy a c t i o n . A ra t h e r d i s t u r b i n g t r e n d of l a r g e c o r p o r a t i o n s u s i n g the more i n f o r m a l proceedings of Chapter XI r a t h e r than the more a p p r o p r i a t e Chapter X has developed and i s i l l u s t r a t e d by Table 1. THE BANKRUPTCY REFORM ACT OF 1978; By the l a t e 1960's and e a r l y 1970's i t had become obvious t h a t the Chandler Act was no longer f u n c t i o n i n g i n i t s intended manner. The bankruptcy c o u r t s were faced with an ever i n c r e a s i n g number of b a n k r u p t c i e s as more and more consumers and businesses made use of the pr o c e s s . The annual case l o a d o f a t y p i c a l -14-+ + Table 1 MAJOR CORPORATIONS FILING CHAPTER XI 1971 - 1973 Name Date Debt A r l a n ' s Dept. S t o r e s Harvard MDS FAS I n t e r n a t i o n a l Famous Schools F e d e r a l ' s Inc. King Modular Housing Topper Toys Botany I n d u s t r i e s DCA Development 5/73 1/72 2/7 2 2/72 8/7 2 2/73 2/73 4/7 2 2/73 na 81. OM 5 0. 3M 40. 7M 4 0. OM 37.OM 3 4. 8M 33. OM 32.8M 28. 2M 2 0. OM I from: Report of the Commission on the Bankruptcy Laws I I Page 261 I + + r e f e r e e was 132 cases i n 1947; by 1967, i t had r i s e n t o 1074 21 cases. . . . i t i s c l e a r t h a t i n r e c e n t y ears the bankruptcy system has been p r o c e s s i n g a f a r h e a v i e r case l o a d than was contemplated e i t h e r a t the time of enactment of the Bankruptcy Act i n 1898 or a t the t i m e 2 ^ f i t s complete r e v i s i o n by the Chandler Act i n 1938. In an e f f o r t t o s t r e a m l i n e and modernize the bankruptcy procedure, the Bankruptcy Reform Act, or Bankruptcy Code as i t i s commonly r e f e r r e d t o , was enacted i n 1978. The Chandler Act was o f f i c i a l l y r e p e a l e d on October 1, 1979. The two chapters of i n t e r e s t i n the Code are Chapters 7 ( l i q u i d a t i o n ) and 11 ( r e o r g a n i z a t i o n ) . In order t o f i l e an i n v o l u n t a r y p e t i t i o n , the c r e d i t o r s must show t h a t the debtor i s g e n e r a l l y not paying h i s debts as they become due or t h a t w i t h i n 120 days p r i o r t o f i l i n g , a c u s t o d i a n took p o s s e s s i o n -15-or was appointed. T h i s s e c t i o n e l i m i n a t e s the more cumbersome "Acts of Bankruptcy" and r e p l a c e s them with a more reasonable solvency type o f t e s t . The amount of debt h e l d by f i l i n g c r e d i t o r s has been i n c r e a s e d to $5000. Chapter 11 of the Code c o n s o l i d a t e s and r e f i n e s the Arrangement and R e o r g a n i z a t i o n chapters (X and XI) of the o l d Act. Under the r e v i s e d Chapter, a debtor may f i l e h i s p l a n of r e o r g a n i z a t i o n a f t e r f i l i n g h i s p e t i t i o n . A f t e r t h i s p e r i o d , i f a t r u s t e e has been appointed by the c o u r t s , any i n t e r e s t e d p a r t y may f i l e a p l a n as w e l l . C o n f i r m a t i o n r e q u i r e s t h a t the p l a n be accepted by two t h i r d s i n amount and one h a l f i n number of each c l a s s of c r e d i t o r s and by two t h i r d s i n amount, r e g a r d l e s s of number, of s h a r e h o l d e r s . The c o u r t may con f i r m a p l a n even i f a c l a s s of c r e d i t o r s o b j e c t i f the c o u r t f i n d s t h a t the i n t e r e s t s of t h a t c l a s s are not impaired by the p l a n . Chapter 11 permits the debtor t o continue running h i s business u n l e s s the c o u r t f i n d s i t i n the best i n t e r e s t s of c r e d i t o r s and/or the owners or i f "cause" can be shown. Cause i s g e n e r a l l y c l a s s e d as f r a u d , incompetence or gross mismanagement."^ One of the major goals of the Bankruptcy Reform Act of 1978 was t o speed up the process as the longer a f i r m spends i n the bankruptcy system, the higher the c o s t s t o debtors, c r e d i t o r s and s o c i e t y i n g e n e r a l . A c c o r d i n g t o the Bankruptcy Commission [1973], the average time spent i n 1971 by c o u r t -16-o f f i c i a l s on Chapter X cases was 243.2 hours. The average time spent on Chapter XI cases ranged from 29 to 57 hours, 2 6 depending on the s i z e o f the f i r m i n q u e s t i o n . The average c o s t s a t t r i b u t a b l e t o the c o u r t s i n a Chapter X case was 27 $7660 while i n a Chapter XI case the c o s t s were $1207. These c o s t s are among the d i r e c t c o s t s o f bankruptcy, however, a major component i n the t o t a l c o s t s i s l i k e l y t o be the i n d i r e c t c o s t s of bankruptcy such as l o s t s a l e s and 2 8 foregone o p p o r t u n i t i e s . In an e f f o r t t o reduce the time spent i n the bankruptcy system, the Act l a y s down s e v e r a l time l i m i t s and g e n e r a l l y makes i t e a s i e r t o enter the bankruptcy p r o c e s s . However, r e c e n t l y concern has been v o i c e d t h a t bankruptcy i s too easy; f i r m s were u s i n g i t t o escape r a t h e r than as a l a s t r e s o r t . There were s e v e r a l p r o p o s a l s before Congress i n 1983 to not on l y make going i n t o bankruptcy more hazardous and l e s s easy; but, a l s o t o d e a l with the problems caused by the r e c e n t Supreme Court r u l i n g t h a t the powers of the Bankruptcy Courts are 29 u n c o n s t i t u t i o n a l . I t i s un c l e a r e x a c t l y what the r e p e r c u s s i o n s of the C o n g r e s s i o n a l p r o p o s a l s and the Supreme Court r u l i n g w i l l be fo r the bankruptcy p r o c e s s . -17-C. THE BANKRUPTCY RECORD Fi g u r e 1 i l l u s t r a t e s the dramatic changes which have occu r r e d i n the bankruptcy r e c o r d s i n c e the passage of the Bankruptcy Reform a c t . F i g u r e 1 ANNUAL FAILURE RATE (Number of f a i l u r e s per 10,000 concerns) +-75 + + 100 + + + + +-50 + + + + + + + + + • I •-+ +-25 I + + + + | I I I I I I I I I +- 0 + + + + + + + + + + + 74 75 76 77 78 79 80 81 82 83 Source: " General Business I n d i c a t o r s " , Business S t a t i s t i c s , 1984. The primary area of concern i n t h i s s i t u a t i o n , i s whether the new Bankruptcy A c t has caused the d e c i s i o n making p r o c e s s o f a f i r m a p p r o a c h i n g b a n k r u p t c y t o change. I n o t h e r w o rds, a r e some f i r m s now f i l i n g f o r b a n k r u p t c y w h i c h under t h e same c i r c u m s t a n c e s w o u l d n o t have f i l e d u n der t h e o l d a c t . A major i s s u e i s whether t h i s change i s s t a t i s t i c a l l y s i g n i f i c a n t , and what a r e t h e i m p l i c a t i o n s o f t h e change i n t h e A c t f o r B a n k r u p t c y P r e d i c t i o n m o d e l s w h i c h do n o t t a k e i n t o a c c o u n t t h i s c hange. - 1 9 -I I I . MODELS COMMONLY USED The p u r p o s e o f b a n k r u p t c y p r e d i c t i o n m o d e l s i s two f o l d : t o c l a s s i f y o r i d e n t i f y f i n a n c i a l l y t r o u b l e d b u s i n e s s e s and t o p r e d i c t t h e i r f u t u r e f a i l u r e on t h e b a s i s o f c u r r e n t and p a s t d a t a . The d a t a and t h e t e c h n i q u e s u s e d o f t e n r e f l e c t t h e d i f f e r i n g v i e w s o f ma r k e t e f f i c i e n c y . M o d e l s o f b a n k r u p t c y o r f a i l u r e c a n t y p i c a l l y be i d e n t i f i e d by t h e t y p e o f d a t a t h e y a n a l y z e . The more modern a p p r o a c h o f s t o c k p r i c e b a s e d m o dels s e e k s t o u s e t h e e f f i c i e n c y o f t h e ma r k e t t o e v a l u a t e t h e u n d e r l y i n g s o l v e n c y o f t h e f i r m , w h i l e t h e more t r a d i t i o n a l m o d e l s , w h i c h i m p l i c i t l y assume t h a t m a r k e t d a t a i s e i t h e r u n a v a i l a b l e o r does n o t f u l l y r e f l e c t a v a i l a b l e i n f o r m a t i o n , u t i l i z e f i n a n c i a l d a t a i n one o f t h r e e ways: c o m p a r i s o n t o a p e e r g r o u p , s t a t i c m u l t i v a r i a t e a n a l y s i s and t i m e s e r i e s b a s e d r e g r e s s i o n a n a l y s i s . A major drawback o f t h e common s t a t i s t i c a l m o d e l s o f b a n k r u p t c y i s t h e i r l a r g e l y a t h e o r e t i c n a t u r e . T h e s e m o d e l s may p r e d i c t an e v e n t , o r d e s c r i b e t h e d a t a v e r y w e l l ; b u t , c a n n o t e x p l a i n t h e phenomenon u n d e r e x a m i n a t i o n a s t h e y a r e n o t b a s e d on any u n d e r l y i n g f i n a n c i a l t h e o r y . A. STOCK-PRICE BASED MODELS S t o c k - p r i c e b a s e d m o d e l s o f b u s i n e s s f a i l u r e a r e t h e most t h e o r e t i c a l l y a p p e a l i n g a s , a c c o r d i n g t o t h e e f f i c i e n t -20-c a p i t a l markets h y p o t h e s i s , the s e c u r i t i e s o f an i n s t i t u t i o n are c o n t i n u a l l y and f a i r l y p r i c e d based on a l l a v a i l a b l e i n f o r m a t i o n . The data r e q u i r e d f o r these models can u s u a l l y be a c q u i r e d with minimal e f f o r t and time d e l a y . In g e n e r a l , these models begin by e s t i m a t i n g an "expected r e t u r n " f u n c t i o n , u s u a l l y based on an a s s e t p r i c i n g model such as the C a p i t a l A s s e t p r i c i n g model. The r e s i d u a l s from such a r e g r e s s i o n a n a l y s i s , t h e r e f o r e , r e f l e c t any "unusual" r e s u l t s which may be due t o the market's p e r c e p t i o n of the company's long term s o l v e n c y . These models have g e n e r a l l y y i e l d e d very promising r e s u l t s . Shick and Sherman [1980] found t h a t from 1967-1974 stock p r i c e s began a downward t r e n d b e f o r e bank examiners r e c o g n i z e d an adverse change i n the bank's condition.''" S t o c k - p r i c e based b a n k r u p t c y / f a i l u r e models o f f e r many advantages on both t h e o r e t i c and p r a c t i c a l grounds, over the more t r a d i t i o n a l f i n a n c i a l r a t i o based models, they do, however, depend on the e x i s t e n c e of a reasonably a c t i v e market f o r the stock i n q u e s t i o n . U n f o r t u n a t e l y , many cases of bankruptcy and weakness occur i n s m a l l , c l o s e l y h e l d i n s t i t u t i o n s which haven't the necessary a c t i v e market f o r t h e i r s t o c k s . B. UNIVARIATE RATIO ANALYSIS One of the o l d e s t technique f o r p r e d i c t i n g f a i l u r e or f i n a n c i a l d i s t r e s s i s based on Peer Group comparison. In -21-t h i s t e c h n i q u e f i n a n c i a l r a t i o s a r e c a l c u l a t e d and t h e n compared t o Pe e r Group r e s u l t s . The m a j o r s t a t i s t i c a l w e a k n e s s e s o f t h i s p r o c e d u r e a r i s e f r o m t h e s e l e c t i o n o f t h e Pee r Group and t h e r a t i o c o m p a r i s o n t e c h n i q u e s . P e e r Group s e l e c t i o n i s a v i t a l p a r t o f t h i s t y p e o f a n a l y s i s a s t h e o b s e r v e d v a l u e o f a f i n a n c i a l r a t i o depends n o t o n l y on t h e u n d e r l y i n g s o l v e n c y o f t h e f i r m , b u t a l s o on 2 o t h e r f a c t o r s u n i q u e t o t h a t t y p e o f b u s i n e s s . F o r example, t h e r a t i o s o f a t o y m a n u f a c t u r e r a r e n o t c o m p a r a b l e t o t h o s e o f a j e w e l r y r e t a i l e r . P e e r g r o u p m o d e l s t y p i c a l l y make u s e o f s e v e r a l key f i n a n c i a l r a t i o s and t h e c o m p a r i s o n o f t h e s e r a t i o s t o t h e p e e r g r o u p norms c a u s e s many s t a t i s t i c a l p r o b l e m s as one i s e s s e n t i a l l y a t t e m p t i n g t o do u n i v a r i a t e a n a l y s i s on m u l t i v a r i a t e d a t a . I n f a c t , s e e m i n g l y i n s i g n i f i c a n t or u n i m p o r t a n t r a t i o s on a u n i v a r i a t e b a s i s c a n become v e r y 3 i m p o r t a n t i n c o m b i n a t i o n w i t h o t h e r r a t i o s . T h i s t y p e o f f a i l u r e m o del c a n c o n s e q u e n t l y y i e l d v e r y c o n f u s i n g r e s u l t s , e s p e c i a l l y i f t h e f i r m i n q u e s t i o n i s above s t a n d a r d i n 4 c e r t a i n a r e a s and s u b s t a n d a r d i n o t h e r s . C. STATIC MULTIVARIATE ANALYSIS T h i s t y p e o f f a i l u r e model s e e k s t o d i s t i l l t h e i n f o r m a t i o n f o u n d i n t h e many f i n a n c i a l r a t i o s a v a i l a b l e i n t o a c o m p o s i t e s c o r e o r v a l u e . T h i s a p p r o a c h was p i o n e e r e d by -22-A l t m a n who a p p l i e d d i s c r i m i n a n t a n a l y s i s t o f i n a n c i a l r a t i o s i n an e f f o r t t o p r e d i c t b a n k r u p t c y . ^ A l t m a n examined f i n a n c i a l r a t i o s f r o m 66 m a n u f a c t u r i n g f i r m s t o d e t e r m i n e a f u n c t i o n w h i c h b e s t d i s c r i m i n a t e d b e tween b a n k r u p t and n o n - b a n k r u p t f i r m s . The v a l i d i t y o f t h i s was e v a l u a t e d i n two ways: f i r s t t h e a b i l i t y t o c l a s s i f y c o r r e c t l y was e v a l u a t e d u s i n g a s e c o n d d a t a s e t drawn f r o m t h e same p o p u l a t i o n a s t h e i n i t i a l s a m p le. The f u n c t i o n was f o u n d t o c l a s s i f y f i r m s e x t r e m e l y w e l l . A s e c o n d t e s t was u n d e r t a k e n t o d e t e r m i n e how w e l l t h e model c l a s s i f i e d p o t e n t i a l b a n k r u p t s by e v a l u a t i n g d a t a f r o m two y e a r s p r i o r t o b a n k r u p t c y . A l t m a n f o u n d t h a t t h e model p e r f o r m e d w e l l j u s t p r i o r t o f a i l u r e , and i t ' s c l a s s i f i c a t i o n a c c u r a c y was s t i l l g o o d two y e a r s p r i o r t o f a i l u r e . However, t h e d i s c r i m i n a t o r y a b i l i t y d e c l i n e d s i g n i f i c a n t l y as t h e t i m e t o f a i l u r e i n c r e a s e d . * * T h i s t y p e o f f i n a n c i a l r a t i o a n a l y s i s h a s been c r i t i c i z e d on s e v e r a l f r o n t s . S t a t i s t i c a l l y , c o n c e r n s have b e e n r a i s e d r e g a r d i n g t h e v a l i d i t y o f t h e u n d e r l y i n g a s s u m p t i o n s i n t h e a n a l y s e s . The p r i m a r y c o n c e r n s i s s u e d c o n c e r n i n g t h e d i s t r i b u t i o n s o f t h e v a r i a b l e s , a s n o n -n o r m a l i t y c a n c a u s e s i g n i f i c a n t p r o b l e m s r e g a r d i n g i n f e r e n c e , e v a l u a t i o n o f t h e c o s t s o f e r r o n e o u s c l a s s i f i c a t i o n and t h e 7 e s t i m a t i o n o f e r r o r r a t e s o f t h e s e m o d els among o t h e r s . M u l t i v a r i a t e a n a l y s i s o f f i n a n c i a l r a t i o s h a s b e e n e x t e n d e d i n t h e hope o f d e v e l o p i n g more u s e f u l t o o l s f o r t h e e a r l y - 2 3 -i d e n t i f i c a t i o n o f a t r o u b l e d f i r m . M a r t i n [1977] e x t e n d e d t h e a p p r o a c h by a p p l y i n g a L o g i t R e g r e s s i o n a n a l y s i s t o t h e g p r o b l e m , w h i l e West [1985] has u s e d f a c t o r a n a l y s i s i n c o n j u n c t i o n w i t h L o g i t e s t i m a t i o n t o a n a l y z e t h e bank 9 c o n d i t i o n p r o b l e m . B a n k r u p t c y o r f a i l u r e m o d e l s w h i c h r e l y on f i n a n c i a l r a t i o s and u s e e i t h e r d i s c r i m i n a n t o r f a c t o r a n a l y s i s a r e s u b j e c t t o s e v e r a l m a j o r t h e o r e t i c a l c r i t i c i s m s . Any m odel o f a b u s i n e s s e n t i t y w h i c h r e l i e s on f i n a n c i a l d a t a i s s u s p e c t , due t o t h e v e r y n a t u r e o f f i n a n c i a l r e p o r t i n g and a c c o u n t i n g t e c h n i q u e s . F i n a n c i a l d a t a , e v e n i f r e p o r t e d h o n e s t l y and a c c u r a t e l y , i s g e n e r a l l y o u t o f d a t e by t h e t i m e i t h a s b e e n c o l l e c t e d and p r e s e n t e d . The d a t a may be a c c u r a t e i n t h e s e n s e t h a t a l l t h e v a l u e s a r e i n d e p e n d e n t l y v e r i f i a b l e , and a r e c o r r e c t f o r t h e p e r i o d i n q u e s t i o n b u t i f t h e s t a t e m e n t s a r e p u b l i s h e d a c o n s i d e r a b l e t i m e a f t e r t h e p e r i o d i n q u e s t i o n , t h e v a l u e o f t h e d a t a i s l i m i t e d f o r c u r r e n t d e c i s i o n m a k i n g . The b a s i c t e n a n t o f a l l a c c o u n t i n g s y s t e m s i s t h a t a l l r e p o r t e d v a l u e s must be i n d e p e n d e n t l y v e r i f i a b l e , c o n s e q u e n t l y , most p u b l i c l y d i s c l o s e d f i n a n c i a l d a t a a r e r e p o r t e d on an h i s t o r i c a l c o s t b a s i s . Not o n l y i s t h e t i m e l i n e s s o f t h e f i n a n c i a l d a t a h i g h l y s u s p e c t ; b u t t h e d a t a i t s e l f i s a l s o h i g h l y s u s c e p t i b l e t o m a n i p u l a t i o n . The p r e v a l e n c e o f r e c o r d m a n i p u l a t i o n i s v e r y e v i d e n t i n t h e bank f a i l u r e r e c o r d s . I n a s t u d y o f t h e 57 F e d e r a l D e p o s i t I n s u r a n c e C o r p . i n s u r e d banks c l o s e d due t o f i n a n c i a l d i f f i c u l t i e s between 1960 and 1972, i t was f o u n d t h a t n e a r l y - 2 4 -30% o f t h e f a i l u r e s were due t o f r a u d , embezzlement and m a n i p u l a t i o n . The r a t i o b a s e d m o d e l s o u t l i n e d t h u s f a r a r e a l s o s u b j e c t t o c r i t i c i s m f o r t h e i r e s s e n t i a l l y s t a t i c n a t u r e . R a t h e r t h a n o b t a i n i n g e v i d e n c e c o n c e r n i n g t h e banks l i k e l y e x p o s u r e t o f a i l u r e i n i t s o p e r a t i o n s , t h e s e r a t i o s q u e s t i o n t h e a b i l i t y o f t h e bank t o a v o i d - ^ r e s e n t f a i l u r e w i t h i t ' s p r e s e n t a s s e t c h a r a c t e r i s t i c s . A m a j o r c o n c e r n w i t h a l l s t a t i s t i c a l m o d e l s i s t h e i r l a r g e l y a t h e o r e t i c n a t u r e . I n o r d e r f o r a model o f b a n k r u p t c y o r f a i l u r e t o h ave e c o n o m i c m e a n i n g , t h e v a r i a b l e s s h o u l d be d e d u c e d f r o m a t h e o r y o f t h e u n d e r l y i n g e c o n o m i c 1 2 and d e c i s i o n p r o c e s s e s f a c e d by t h e company management. The p r i n c i p a l r e a s o n f o r i n c l u d i n g s p e c i f i c r a t i o s i n many o f t h e f a i l u r e s t u d i e s i s t h a t t h e y a p p e a r t o d i s c r i m i n a t e w e l l b e tween f a i l u r e and n o n - f a i l u r e , n o t f o r any p a r t i c u l a r t h e o r e t i c a l r e a s o n . W h i l e t h e a t h e o r e t i c n a t u r e o f a p u r e l y s t a t i s t i c a l m o del i s o f l i t t l e c o n c e r n i f t h e s o l e p u r p o s e o f an a n a l y s i s i s t o p r e d i c t b a n k r u p t c y ; however, one i s o f t e n i n t e r e s t e d i n m o d e l s w h i c h c a n o f f e r i n s i g h t i n t o why b a n k r u p t c i e s o c c u r as w e l l as p r e d i c t i n g t h e i r o c c u r r e n c e . The major drawback o f t h e t r a d i t i o n a l m o d e l s o f b a n k r u p t c y o r f a i l u r e i s t h a t t h e y y i e l d a p r o b a b i l i t y t h a t a p a r t i c u l a r f i r m w i l l f a i l w i t h i n one p e r i o d . Such a p r o b a b i l i t y i s n o t v e r y u s e f u l i n e i t h e r i n v e s t m e n t a n a l y s i s o r i n management d e c i s i o n m a k i n g . A n o t h e r drawback o f t h e d i s c r i m i n a n t a n a l y s i s b a s e d m o dels i s t h a t d a t a f r o m one y e a r -25-p r i o r t o f a i l u r e cannot be mixed with data from two years p r i o r t o f a i l u r e . Consequently, these models are very data s p e c i f i c i n t h a t a l l the a v a i l a b l e data i s not used, r a t h e r o n l y s p e c i f i c subsets are anal y z e d . D. REGRESSION AND TIME BASED MODELS In an e f f o r t t o model the dynamics of f a i l u r e , Santomero & Vinso [1977] apply time s e r i e s techniques which had been q u i t e commonly used i n m o d e l l i n g insurance r i s k exposure. E s s e n t i a l l y t h e i r model i s d e r i v e d from the premise t h a t the f i r m ' s c a p i t a l a c t s as a b u f f e r a g a i n s t f u t u r e l o s s e s and tha t v a r i a t i o n s i n t h i s b u f f e r occur s t o c h a s t i c a l l y . The two tec h n i q u e s , known as F i r s t Passage Time or Gambler's Ruin and Maximum Risk exposure are used t o model the bank c a p i t a l b u f f e r . Santomero & Vinso c o n c e n t r a t e on a p p l y i n g the maximum r i s k exposure technique as the Gambler's Ruin technique r e l i e s on the u n p a l a t a b l e assumption o f a zero or negative d r i f t i n the c a p i t a l account. T h i s assumption would appear to be more a p p r o p r i a t e f o r n o n - p r o f i t or c h a r i t a b l e 14 o r g a n i z a t i o n s than f o r p r o f i t maximizing i n s t i t u t i o n s . The maximum r i s k exposure model of the banking system was analyzed i n c r o s s s e c t i o n . Santomero & Vins o ' s r e s u l t s i n d i c a t e t h a t the t r a d i t i o n a l c a p i t a l a s s e t r a t i o i s a u s e f u l t o o l i n i d e n t i f y i n g t r o u b l e d banks; but, t h a t a bank's c a p i t a l stock -26-v a r i a b i l i t y i s a l s o a v e r y i m p o r t a n t component i n d e t e r m i n i n g a b ank's s u r v i v a l p o t e n t i a l . S a ntomero and V i n s o , t h e r e f o r e , c o n c l u d e t h a t t h e i r m o d e l , w h i c h t a k e s i n t o a c c o u n t t h i s c a p i t a l s t o c k v a r i a b i l i t y , i n c o n j u n c t i o n w i t h a p r o p o s e d s c r e e n o f f e r s a more e x a c t c l a s s i f i c a t i o n and i d e n t i f i c a t i o n t e c h n i q u e t h a n t h e p r e v i o u s l y a v a i l a b l e methods. 1*' The d a t a r e q u i r e m e n t s o f t h e Santomero and V i n s o model a r e v e r y d i f f e r e n t f r o m t h e more t r a d i t i o n a l " A l t m a n " t y p e o f m o d e l . I n o r d e r t o e s t i m a t e t h e b e h a v i o u r o f a company's c a p i t a l s t o c k o v e r t i m e , t h e Maximum R i s k E x p o s u r e model r e q u i r e s a t i m e s e r i e s o f d a t a . The most d e s i r a b l e d a t a s e t w o u l d be a c o n t i n u o u s r e c o r d o f t h e m a r k e t v a l u e d c a p i t a l l e v e l s ; however, t h e b e s t one c a n do i s t h e w e e k l y r e p o r t s f i l e d by a p p r o x i m a t e l y t h r e e h u n d r e d b a n k i n g i n s t i t u t i o n s w i t h t h e F e d e r a l R e s e r v e . The c a p i t a l v a l u e s r e p o r t e d a r e e s s e n t i a l l y a c c o u n t i n g v a l u e s a s t h e " F e d . " d o e s n o t r e q u i r e 17 m a r k e t v a l u e r e s t a t e m e n t i n t h e s e w e e k l y r e p o r t s . W h i l e e x t e n s i v e t i m e s e r i e s d a t a i s r e q u i r e d , i t i s r e q u i r e d o n l y on t h e f i r m o f i n t e r e s t . The " A l t m a n " b a s e d m o d e l s , i n c o n t r a s t , r e q u i r e c r o s s - s e c t i o n a l d a t a . W h i l e s u c h a r e q u i r e m e n t i s u n l i k e l y t o c o n c e r n a r e g u l a t o r y a g e n c y who i s r e s p o n s i b l e f o r m o n i t o r i n g t h e p o p u l a t i o n o f b u s i n e s s e s w i t h i n an i n d u s t r y , i t i s l i k e l y t o be o f c o n s i d e r a b l e c o n c e r n t o a p o r t f o l i o manager who i s i n t e r e s t e d i n a s m a l l s u b s e t o f an i n d u s t r y . -27-THE COX MODEL; R e c e n t l y , Lane, Looney and Wansley [1986] have extended the "Altman" type o f c r o s s - s e c t i o n a l a n a l y s i s through the a p p l i c a t i o n o f the Cox P r o p o r t i o n a l Hazard Model t o the bank f a i l u r e problem. T h i s model o f f e r s s e v e r a l advantages over the more t r a d i t i o n a l f a i l u r e models i n t h a t i t generates an expected time u n t i l f a i l u r e and has fewer r e s t r i c t i v e u n d e r l y i n g d i s t r i b u t i o n a l assumptions. One of the b a s i c assumptions u n d e r l y i n g the P r o p o r t i o n a l Hazards Model, which w i l l be d i s c u s s e d i n more d e t a i l below, i s t h a t the observed values of the v a r i a b l e s e f f e c t the hazard faced by an average f i r m . The more t r a d i t i o n a l models tend t o c l a s s i f y companies as e i t h e r f a i l u r e or n o n - f a i l u r e and do not take i n t o account t h a t a l l one can say about a n o n - f a i l e d f i r m i s t h a t i t has not f a i l e d as y e t . P r o p o r t i o n a l Hazard models, i n c o n t r a s t , 19 can analyze such censored data samples. Lane, Looney, and Wansley evaluated the Cox model as p a r t o f an e a r l y warning system f o r bank f a i l u r e i n two ways: by a s s e s s i n g the model's accuracy i n p r e d i c t i n g time u n t i l f a i l u r e and by comparing the model's a b i l i t y t o c l a s s i f y i n d i v i d u a l s i n the f a i l u r e / n o n - f a i l u r e c ontext with the more common m u l t i p l e d i s c r i m i n a n t a n a l y s i s approach. Twenty-one r a t i o s were used as p o t e n t i a l p r e d i c t o r s of f a i l u r e . These r a t i o s were s e l e c t e d t o r e p r e s e n t the f i v e CAMEL dimensions of bank o p e r a t i o n s which appear t o measure bank s o l v e n c y , and are used e x t e n s i v e l y by the bank -28-20 e x a m i n e r s . CAMEL i s an acronym r e p r e s e n t i n g C a p i t a l ( l e v e r a g e ) , A s s e t ( l o a n ) q u a l i t y , Management ( l o a n c o m p o s i t i o n , e f f i c i e n c y o r p r i c i n g ) , , E a r n i n g s , and L i q u i d i t y . The r e s u l t s o f t h e Lane s t u d y i n d i c a t e t h a t t h e Cox H a z a r d model i s u s e f u l i n a n a l y z i n g bank f i n a n c i a l c o n d i t i o n . D i s c r i m i n a n t a n a l y s i s and t h e P r o p o r t i o n a l H a z a r d m o dels a p p e a r t o y i e l d s i m i l a r c l a s s i f i c a t i o n r a t e s . T h e r e f o r e , i t a p p e a r s t h a t t h e Cox model o f f e r s t h e e x a m i n e r a d d i t i o n a l i n f o r m a t i o n r e g a r d i n g p r o b a b l e t i m e t o f a i l u r e w i t h o u t l o s i n g 21 s i g n i f i c a n t c l a s s i f i c a t i o n a c c u r a c y . The h a z a r d f u n c t i o n a p p r o a c h , b a s e d on s u r v i v a l - t h e o r y , o f f e r s s e v e r a l a d v a n t a g e s o v e r t h e more t r a d i t i o n a l a p p r o a c h by p r o v i d i n g an e s t i m a t e o f t h e p r o b a b l e t i m e u n t i l f a i l u r e , and by l e s s e n i n g t h e b u r d e n imposed by t h e h i g h l y p a r a m e t r i c n a t u r e o f t h e t r a d i t i o n a l a n a l y s i s . I t w o u l d , t h e r e f o r e , a p p e a r t h a t t h i s a p p r o a c h m e r i t s f u r t h e r e x a m i n a t i o n . -29-IV. PLAN OF ANALYSIS In t h i s paper, the Cox p r o p o r t i o n a l hazard model w i l l be a p p l i e d t o the problem of bankruptcy p r e d i c t i o n i n a d i v e r s e i n d u s t r i a l s e t t i n g and the model's performance w i l l be compared t o the performance of an estimated l i n e a r d i s c r i m i n a n t f u n c t i o n based on Altman [1963]. A. RATIO SELECTION " R a t i o s " were s e l e c t e d on the b a s i s of three c r i t e r i a : p o p u l a r i t y , performance and a v a i l a b i l i t y . P o p u l a r i t y and performance r e f e r t o the frequency of use of the r a t i o and i t ' s performance i n other s t u d i e s . Two s t u d i e s of major s i g n i f i c a n c e f o r t h i s purpose were Beaver [1966] and Altman [1966]. A v a i l a b i l i t y r e f e r s t o data l i m i t a t i o n s as not a l l the f i r m s r e p o r t e d the necessary data. The r a t i o s used are found i n t a b l e 2. 1 Table 2. LIST OF RATIOS USED. 1. Cash flow R a t i o s : 1. Cash flow t o s a l e s . 2. Cash flow to T o t a l A s s e t s . 3. Cash flow to T o t a l Debt. 2. Net Income R a t i o s . 1. Net income / S a l e s . 2. Net income / T o t a l A s s e t s . 3. Net income / T o t a l Debt. -30-4. Retained earnings / T o t a l A s s e t s . 5. Earnings before I n t e r e s t and Tax / t o t a l A s s e t s . Debt t o T o t a l A s s e t s . 1 Long term debt / T o t a l A s s e t s . 2. C u r r e n t + longterm debt + p r e f . shares / T o t a l A s s e t s . 3. I n t e r e s t / long term debt. L i q u i d A s s e t s - Current L i a b i l i t i e s R a t i o s . 1. Working c a p i t a l / T o t a l A s s e t s . 2. Cash / c u r r e n t l i a b i l i t i e s . 3. C u r rent a s s e t s / c u r r e n t l i a b i l i t i e s . 4. Quick a s s e t s / T o t a l A s s e t s . 5. Quick A s s e t s / c u r r e n t l i a b i l i t i e s . Turnover R a t i o s . 1. Inventory / S a l e s . 2. C u r r e n t A s s e t s / S a l e s . 3. Quick A s s e t s / S a l e s . 4. T o t a l A s s e t s / S a l e s . 5. No c r e d i t i n t e r v a l , (quick a s s e t s minus c u r r e n t l i a b i l i t i e s / funds f o r o p e r a t i o n s ) 6. Defensive I n t e r v a l , (quick a s s e t s / funds f o r o p e r a t i o n s ) . 7. Margin. S a l e s / c o s t of goods s o l d . 8. Change i n margin. Market R e l a t e d R a t i o s . 1. C l o s i n g market value of e q u i t y / t o t a l a s s e t s . 2. Change i n Market value of e q u i t y . 3. Invested C a p i t a l / T o t a l A s s e t s . cash flow = income from o p e r a t i o n s b e f o r e d e p r e c i a t i o n p l u s change i n accounts payable minus2change i n accounts r e c e i v a b l e minus change i n i n v e n t o r y . working c a p i t a l = c u r r e n t a s s e t s minus c u r r e n t l i a b i l i t i e s . q u i c k a s s e t s equals cash p l u s accounts r e c e i v e d . funds expen d i t u r e s f o r o p e r a t i o n s equals s a l e s minus o p e r a t i n g income b e f o r e d e p r e c i a t i o n . i n v e s t e d c a p i t a l equals the sum of longterm debt, p r e f e r r e d s t o c k , m i n o r i t y i n t e r e s t s and common sto c k . -31-* change i n market equals c l o s i n g market time (t) d i v i d e d by c l o s i n g v alue time ( t - 1 ) . B. THE DATA SET Data Sources: The p r i n c i p a l data sources f o r t h i s study were the Compustat r e s e a r c h and i n d u s t r i a l tapes f o r 1986. These tapes c o n t a i n f i n a n c i a l statement data on a l a r g e number of f i r m s f o r the p e r i o d 1966-1986. The Compustat Research i n d u s t r i a l tape c o n t a i n s data on f i r m s removed from the Compustat i n d u s t r i a l annual tape. Firms can be e l i m i n a t e d from the i n d u s t r i a l tape f o r a v a r i e t y o f reasons, i n c l u d i n g mergers, i n c o n s i s t e n t r e p o r t i n g , bankruptcy or r e t u r n i n g t o p r i v a t e ownership. Compustat data i s d e r i v e d from the p u b l i s h e d f i n a n c i a l statements and the 10K r e p o r t s f i l e d by f i r m s with the S e c u r i t i e s and Exchange Commission i n the United S t a t e s . Most f i r m s l i s t e d on the Compustat tapes are the l a r g e r p u b l i c l y t r a ded ones r a t h e r than the more common s m a l l e r p r i v a t e f i r m s . Any use of an a n a l y s i s of bankruptcy based on these data must take i n t o account t h i s p o t e n t i a l data b i a s when a p p l y i n g r e s u l t s t o the g e n e r a l p o p u l a t i o n of f i r m s . Sample S e l e c t i o n ; T h i s study excluded r a i l r o a d s , i n s u r a n c e and banking i n s t i t u t i o n s , and sav i n g s and loan a s s o c i a t i o n s due t o t h e i r s p e c i a l treatment under the Bankruptcy A c t s , both the Chandler and Reform A c t s . Real e s t a t e , other f i n a n c i a l companies, other t r a n s p o r t a t i o n f i r m s -32-and s e r v i c e i n d u s t r i e s such as t r a v e l agencies were a l s o excluded as most of the data a v a i l a b l e on bankruptcy and f a i l u r e r a t e s appears t o e i t h e r exclude or separate these i n d u s t r i e s . T h e r e f o r e , the sample was r e s t r i c t e d t o commercial and i n d u s t r i a l f a i l u r e s i n c l u d i n g c o n s t r u c t i o n , manufacturing and mining, and the r e t a i l and wholesale t r a d e s . B ankruptcies were i d e n t i f i e d by examining the c a p i t a l s t r u c t u r e changes of the remaining f i r m s on the r e s e a r c h i n d u s t r i a l f i l e , as r e p o r t e d i n the C a p i t a l Changes Reporter. Of the 618 f i r m s examined, 84 were i d e n t i f i e d as f i l i n g p e t i t i o n s under Chapters X and XI of the Chandler Act or under Chapter 11 of the Reform A c t . In order t o develop a n o n - f a i l u r e sample with s i m i l a r c h a r a c t e r i s t i c s t o the bankruptcy sample, bankrupt and non-bankrupt f i r m s were r e q u i r e d t o have had data r e p o r t e d on the Compustat tape f o r a t l e a s t f i v e y e a rs p r i o r t o f a i l u r e , s i x years was the p r e f e r r e d v a l u e . T h i s time p e r i o d was s e l e c t e d f o r the f o l l o w i n g reason: Beaver's study of f i n a n c i a l r a t i o s as p r e d i c t o r s of f a i l u r e found t h a t a t approximately f i v e y e ars p r i o r t o f a i l u r e i t becomes more d i f f i c u l t t o d i s t i n g u i s h the f u t u r e 3 f a i l u r e from the f u t u r e s u r v i v o r . In t h i s study bankrupt f i r m s were matched t o s i m i l a r non-bankrupt f i r m s f i v e and s i x years p r i o r t o f a i l u r e . The aim of t h i s procedure was t o b e g i n w i t h a sample of s i m i l a r f i r m s b e f o r e the f a i l u r e s -33-began t h e i r f i n a n c i a l s l i d e i n order t o ensure c o m p a r a b i l i t y of the f i n a n c i a l r a t i o s t o be analyzed. The f i v e t o s i x year p r i o r data requirement e l i m i n a t e d 28 f a i l u r e s from c o n s i d e r a t i o n l e a v i n g a sample of 56 f i r m s which f i l e d p e t i t i o n s f o r bankruptcy between 1971 and 1985. Data V a l i d a t i o n . A c c o r d i n g t o the Compustat Codebook, the data does not exceed the F10.6 format, i n other words, the l a r g e s t v alue p o s s i b l e i s 999.999999 m i l l i o n . However, when the data obtained was checked a g a i n s t the format requirement, one f i r m , W. T. Grant, was r e j e c t e d . T h i s r e s u l t was not unexpected. At the time of bankruptcy i n 1975, W. T. Grant had 82,000 employees, 1200 4 s t o r e s and s a l e s o f over $1.6 b i l l i o n . However, when the Compustat s a l e s f i g u r e s were examined, the data appeared q u e s t i o n a b l e . (See t a b l e 3.) + + I Table 3 I I T. GRANT SALES I I ( Tn m i l l i o n s ) I 1969 1970 1971 1972 1973 1974 | P i a t t (p35) 1096 1210 1254 1374 1644 1849 | Compustat 1214 1254 1374 1644 1849 1761 | + + U n f o r t u n a t e l y , W. T. Grant's f i n a n c i a l data were not v e r i f i a b l e through other sources such as Moody's, as the e a r l i e s t Moody's c o r p o r a t e d i r e c t o r y a v a i l a b l e i n the U n i v e r s i t y o f B r i t i s h Columbia Main L i b r a r y was f o r 1977, and due t o the above problem the company was e l i m i n a t e d from c o n s i d e r a t i o n . Data was a l s o examined t o ensure t h a t v i t a l v a l u e s were not m i s s i n g . Seventeen f i r m s were i d e n t i f i e d as missing data immediately p r i o r t o f a i l u r e . The r e s u l t s of f u r t h e r examination are presented i n t a b l e 4. + + Table 4 CHARACTERISTICS OF INCOMPLETE FINANCIAL DATA # of f i r m s C h a r a c t e r i s t i c s s t 7 F i l e d l n d q u a r t e r . 7 F i l e d 2r^ q u a r t e r . 2 F i l e d 3 q u a r t e r . 1 M i s s i n g 3 years of data. + + The above r e s u l t s are a d i r e c t consequence of the problem of t i m e l i n e s s of f i n a n c i a l d a t a . In the m a j o r i t y of s t c a s e s , c l o s i n g stock p r i c e s were r e p o r t e d f o r December 31 of the year p r i o r t o f a i l u r e . In an e f f o r t t o m a i n t a i n an adequate sample s i z e of bankrupts, and i n view of the slow d e l i v e r y o f f i n a n c i a l data, f i r m s which f i l e d p e t i t i o n s i n the f i r s t h a l f o f the year and had mi s s i n g f i n a n c i a l data were i n c l u d e d i n the sample. In these cases, the l a s t f i l e d statement was t r e a t e d as the one year p r i o r d a t a . T h e r e f o r e , one year p r i o r data i s a c t u a l l y between 1 and 18 months p r i o r t o f a i l u r e . C o m p a r a b i l i t y . The data used i n t h i s study were obtained by "matching" bankrupt f i r m s with non-bankrupt f i r m s f o r two -35-reasons. F i r s t , a random sample of f i r m s drawn from the t e s t i n d u s t r i e s ( i n d u s t r i a l and commercial f i r m s e x c l u d i n g f i n a n c e , i n s u r a n c e , r a i l r o a d s and s e r v i c e s ) i s u n l i k e l y to p r o v i d e a s u f f i c i e n t number of bankrupt f i r m s t o enable any i n f e r e n c e s t o be drawn from the r e s u l t s of t h i s study. Between 1972 and 1985, 80 f i r m s w i t h i n the t e s t i n d u s t r i e s f i l e d f o r bankruptcy, however, over 8000 u n - f a i l e d f i r m s were l i s t e d on the Compustat i n d u s t r i a l tape i n 1986. T h e r e f o r e , any random sample drawn from a p o p u l a t i o n such as t h i s would be predominantly u n - f a i l e d f i r m s as the p r o b a b i l i t y of s e l e c t i n g a f a i l u r e i s l e s s than 1%. The second reason f o r t h i s "matching" was t o ensure c o m p a r a b i l i t y of the bankrupt and nonbankrupt samples. The purpose of most s t u d i e s of bankruptcy i s t o i s o l a t e and i d e n t i f y the unique f i n a n c i a l c h a r a c t e r i s t i c s of f i r m s which w i l l f i l e f o r bankruptcy i n the f u t u r e i n the b e l i e f t h a t these unique a t t r i b u t e s can then be used to p r e d i c t f a i l u r e . While i n p r i n c i p l e a c c o u n t i n g data r e f l e c t s the f i r m ' s " a b s o l u t e " f i n a n c i a l c o n d i t i o n , bankruptcy p r e d i c t i o n r e q u i r e s an e s t i m a t i o n of the " r e l a t i v e " f i n a n c i a l c o n d i t i o n of the f i r m . Comparing a f u t u r e bankrupt t o " s i m i l a r " non-bankrupt f i r m s f a c i n g s i m i l a r economic c o n d i t i o n s enables one t o i s o l a t e the d i f f e r e n c e s due t o the pre-bankruptcy s t a t e from those due t o i n d u s t r y or s i z e d i f f e r e n t i a l s . -36-Th e sample of u n - f a i l e d f i r m s was obtained from the Compustat i n d u s t r i a l tape. A n o n - f a i l e d f i r m "matched" a bankrupt i f the f o l l o w i n g c o n d i t i o n s were met: 1. The f i r m s must be i n the same or s i m i l a r i n d u s t r y as represented by the SIC codes. An u n - f a i l e d f i r m ' s SIC code was c o n s i d e r e d "matched" i f i t was w i t h i n p l u s or minus 5 of the u n i t s d i g i t of the f a i l u r e ' s SIC code. 2. Net income bef o r e e x t r a o r d i n a r y items, s a l e s , and net a s s e t s were compared i n the same year which was 5 to 6 years p r i o r t o f a i l u r e . For example i f a f i r m f a i l e d i n 1981, the comparison would be c a r r i e d out on 1975 and 1976 data. A match was accepted i f on a t l e a s t four of these s i x comparisons, the u n - f a i l e d f i r m ' s data was w i t h i n a f a c t o r of t h r e e ( l e s s than 3 times but g r e a t e r than 1/3 times) of the f a i l e d f i r m ' s data. The requirement t h a t f i r m s ' v a l u e s be w i t h i n a f a c t o r of th r e e a r r i v e d a t somewhat a r b i t r a r i l y . A f a c t o r of three was the lowest f a c t o r t h a t p e r m i t t e d most of the f a i l u r e s t o be matched t o a t l e a s t one n o n - f a i l u r e . Net income bef o r e e x t r a o r d i n a r y items and s a l e s were s e l e c t e d as a b a s i s of comparison i n an attempt t o i d e n t i f y f i r m s of s i m i l a r e f f i c i e n c y , as measured by net income, and market power, as i n d i c a t e d by s a l e s . Net a s s e t s were i n c l u d e d i n an e f f o r t t o match f i r m ' s of s i m i l a r s i z e . E s s e n t i a l l y , t h i s paper attempted t o match f i r m s of s i m i l a r 'market power' ( s a l e s ) , ' e f f i c i e n c y ' (net income) and ' s i z e ' (assets) f i v e -37-t o s i x y e a r s p r i o r t o one o f t h e two f i r m s ' f i l i n g a p e t i t i o n f o r b a n k r u p t c y . E a c h f a i l u r e was r e s t r i c t e d t o a t most 2 m a t c h e s i n o r d e r t o e n s u r e s i m i l a r i t y between t h e i n d u s t r i a l c o m p o s i t i o n o f t h e b a n k r u p t and n o n - b a n k r u p t s a m p l e s . The e x c h a n g e c o d e s r e p o r t e d by Compustat i n c l u d e i n f o r m a t i o n s u c h a s e x c h a n g e l i s t e d on and i n c l u s i o n o r e x c l u s i o n i n v a r i o u s i n d i c e s s u c h as t h e S t a n d a r d and P o o r ' s 500 (Compustat C o d e b o o k ) . T h e s e c o d e s were u s e d a s ; a f i n a l m a t c h i n g c r i t e r i a i n t h e c a s e o f m u l t i p l e matches t o e n s u r e f u r t h e r c o m p a r a b i l i t y a s e a c h e x c h a n g e and e a c h S & P i n d e x imposes d i f f e r e n t c r i t e r i a on member f i r m s . A f t e r t h e " m a t c h i n g " p r o c e s s h a d b e e n u n d e r t a k e n , f o r t y -one f a i l u r e s r e m a i n e d and were matched t o s i x t y - s e v e n s u r v i v o r s f o r a t o t a l sample s i z e o f one h u n d r e d and e i g h t f i r m s . -38-V. SAMPLE CHARACTERISTICS A. SAMPLE STATISTICS The sample c h a r a c t e r i s t i c s are i l l u s t r a t e d i n t a b l e 5. Table 5. SUMMARY STATISTICS ' m i l l i o n s 5 years CHANDLER ACT REFORM ACT OVERALL p r i o r F a i l u r e Match F a i l u r e Match F a i l u r e Match T o t a l A s s e t s : mean 36.02 37.22 82.42 75.94 54.80 52.93 s.t.dev. 31.96 43.00 108.72 88.02 75.78 67.31 Sci16 S * mean 57.11 69.01 132.64 115.60 87.68 87.92 s.t.dev 71.80 80.15 157.77 125.69 118.91 102.87 Net Income: mean .65 1.73 2.51 3.02 ' 1.40 2.25 s.t.dev 1.14 2.17 3.87 3.75 2.73 2.96 N 25 41 16 26 41 67 In order t o d e s c r i b e the c h a r a c t e r i s t i c s of the o v e r a l l f a i l u r e and s u r v i v a l samples, a p r o f i l e was c o n s t r u c t e d o f e i g h t r a t i o s . The aim of t h i s a n a l y s i s i s d e s c r i p t i v e , t o pr e s e n t a g r a p h i c a l r e p r e s e n t a t i o n o f the changes which o c c u r r e d i n the two groups over time. The p r o f i l e s are presented i n f i g u r e 2. These p r o f i l e s show t h a t , on a u n i v a r i a t e b a s i s , d i f f e r e n c e s e x i s t between bankrupt and non-bankrupt f i r m s . The s t a t i s t i c a l s i g n i f i c a n c e of the apparent d i f f e r e n c e s -39-between the bankrupt and non-bankrupt f i r m s w i l l be evaluated i n s e c t i o n V I ( b ) . However, any f u r t h e r a n a l y s i s cannot be conducted on a u n i v a r i a t e b a s i s as no s i n g l e f i n a n c i a l r a t i o i s capable of completely r e p r e s e n t i n g the complex i n t e r r e l a t i o n s h i p s which c o n s t i t u t e a f i r m . F i g u r e 2. RATIO PROFILE of BANKRUPT AND SURVIVOR FIRMS . «5Uruioof VDCVCVVH uupt Cash flow / T o t a l Debt •h+ + .1 I I 4 • + 1 Net income / T o t a l A s s e t s + L Long term debt / T o t a l A s s e t s + + •iS+ + 4 3 2 1 years pr i o r Work, c a p i t a l / T o t a l a s s e t s •H+ + I--. • i o + + 4 3 2 1 C u r r e n t R a t i o + M a r g i n i-H+ + 13 1.2 I.I U+ 4 3 2 • + 1 p r i o r y e a r s - 4 1 -B. RATIO DISTRIBUTIONS The n o r m a l i t y o f t h e d i s t r i b u t i o n s o f t h e f i n a n c i a l r a t i o s was e v a l u a t e d i n o r d e r t o e s t a b l i s h t h e v a l i d i t y o f any i n f e r e n c e s drawn f r o m t h e d i s c r i m i n a n t a n a l y s i s . The Cox M o d e l , i n c o n t r a s t , d o e s n o t r e l y on any s u c h d i s t r i b u t i o n a l a s s u m p t i o n s . M u l t i v a r i a t e n o r m a l i t y i s n o t r e q u i r e d f o r t h e d a t a d e s c r i p t i o n and e s t i m a t i o n a s p e c t s o f m u l t i v a r i a t e t h e o r y , i t ' s i m p a c t i s f e l t i n t h e a r e a o f i n f e r e n c e . 1 U n f o r t u n a t e l y , p r a c t i c a l t e s t s o f m u l t i v a r i a t e n o r m a l i t y e s s e n t i a l l y do n o t e x i s t and one g e n e r a l l y i n f e r s m u l t i v a r i a t e n o r m a l i t y f r o m t h e n o r m a l i t y o f t h e u n d e r l y i n g v a r i a b l e s . The n o r m a l i t y o f t h e d i s t r i b u t i o n o f t h e r a t i o s was e v a l u a t e d i n two ways, f i r s t by e x a m i n i n g t h e skewness and k u r t o s i s s t a t i s t i c s and s e c o n d l y , by e x a m i n i n g t h e h i s t o g r a m s and n o r m a l p r o b a b i l i t y p l o t s o f t h e r a t i o s . S e v e r a l c h a r a c t e r i s t i c s o f t h e r a t i o s become a p p a r e n t f r o m t h e n o r m a l p r o b a b i l i t y p l o t s w h i c h showed on a v e r a g e t h a t t h e d i s t r i b u t i o n o f t h e v a r i a b l e s d i d n o t become any l e s s n o r m a l t h e c l o s e r one moved t o w a r d b a n k r u p t c y . A few e x c e p t i o n s t o t h i s were r a t i o s i n v o l v i n g n e t i n c o m e / s a l e s , (see a p p e n d i x I I . ) w h i c h showed t h a t t h e d i s t r i b u t i o n became l e s s n o r m a l a s t h e sample moved c l o s e r t o b a n k r u p t c y . T h i s was n o t s u r p r i s i n g as one would e x p e c t f i r m s matched 5 t o 6 y e a r s p r i o r t o f a i l u r e t o b e g i n t o s p l i t i n t o two g r o u p s as b a n k r u p t c y becomes imminent i f t h e r e does -42-e x i s t a d i f f e r e n c e between t h e n o n - b a n k r u p t and b a n k r u p t g r o u p s . I t i s a p p a r e n t f r o m t h e p r o f i l e s c o n s t r u c t e d p r e v i o u s l y t h a t i m m i n e n t l y b a n k r u p t and s i m i l a r n o n - b a n k r u p t f i r m ' s r a t i o s e x h i b i t e d a v e r y d i f f e r e n t t i m e p a t h f r o m e a c h o t h e r i m m e d i a t e l y p r i o r t o f a i l u r e . I n g e n e r a l t h e n o r m a l p r o b a b i l i t y p l o t s f a l l between t h e e x t r e m e s o f t h e w o r k i n g c a p i t a l t o t o t a l a s s e t s p l o t and t h e v e r y a b n o r m a l p l o t o f c a s h / s a l e s , (see a p p e n d i x I I ) . Due t o t h e n o n n o r m a l i t y o f t h e s e r a t i o s , any i n f e r e n c e s drawn f r o m t h e d i s c r i m i n a n t a n a l y s i s u n d e r t a k e n on t h e u n -t r a n s f o r m e d v a r i a b l e s w o u l d be v e r y s u s p e c t . I t i s o f t e n p o s s i b l e t o t r a n s f o r m a n o n - n o r m a l l y d i s t r i b u t e d v a r i a b l e i n t o a n o r m a l v a r i a b l e by u s i n g a l o g o r power t r a n s f o r m a t i o n . Such t r a n s f o r m a t i o n s were n o t u n d e r t a k e n i n t h i s s t u d y a s t h e p r i m a r y a r e a o f i n t e r e s t was t h e Cox model's p e r f o r m a n c e . The d i s c r i m i n a n t a n a l y s i s was u n d e r t a k e n m e r e l y t o p r o v i d e a c o m p a r i s o n model f o r more d e s c r i p t i v e p u r p o s e s . C. CHANDLER VS. REFORM ACTS A s e c o n d i s s u e t o be a d d r e s s e d was: Does a s i g n i f i c a n t d i f f e r e n c e e x i s t between f i r m s d e c l a r i n g b a n k r u p t c y p r i o r t o t h e Reform a c t and t o t h o s e d e c l a r i n g b a n k r u p t c y a t a l a t e r d a t e ? -43 -As the u n d e r l y i n g r a t i o s were not normally d i s t r i b u t e d , the K r u s k a l - W a l l i s t e s t of group s i m i l a r i t y was undertaken. The formal n u l l h y p o t h e s i s of the K r u s k a l - W a l l i s t e s t i s t h a t the d i s t r i b u t i o n s of the two groups are i d e n t i c a l , but, not 2 n e c e s s a r i l y normal. U n l i k e the more commonly a p p l i e d ANOVA, A n a l y s i s of V a r i a n c e , t e s t o f d i s t r i b u t i o n s i m i l a r i t y , K r u s k a l - W a l l i s t e s t i s l e s s s e n s i t i v e to the b a s i c assumption t h a t the p o p u l a t i o n s are normally d i s t r i b u t e d . The K r u s k a l - W a l l i s t e s t was undertaken to t e s t two hypotheses, f i r s t l y , t h a t no d i f f e r e n c e s e x i s t e d between the d i s t r i b u t i o n s of bankrupt and s u r v i v i n g f i r m s , and secondly, t h a t no d i f f e r e n c e s e x i s t e d between f i r m s f i l i n g f o r bankruptcy before and those f i l i n g a f t e r the passage of the Bankruptcy Reform Act of 1978. U n f o r t u n a t e l y the K r u s k a l -W a l l i s t e s t s undertaken were u n i v a r i a t e , they t e s t e d one v a r i a b l e a t a time and can t h e r e f o r e o n l y g i v e a g e n e r a l i n d i c a t i o n t h a t a d i f f e r e n c e does, or does not, e x i s t . Table 6 g i v e s a summary of the t e s t r e s u l t s comparing bankrupt and non bankrupt f i r m s one year p r i o r to f a i l u r e . S i m i l a r r e s u l t s were obtained f o r data four years p r i o r to f a i l u r e . From the r a t i o p r o f i l e ( f i g u r e 2), i t i s apparent t h a t c e r t a i n v a r i a b l e s are capable of d i s c r i m i n a t i n g between f a i l u r e s and n o n - f a i l u r e s when examined on a u n i v a r i a t e b a s i s . I t would a l s o appear t h a t c e r t a i n r a t i o s such as i n v e n t o r y / s a l e s and c u r r e n t a s s e t s / s a l e s are not good -44-d i s c r i m i n a t o r s on a u n i v a r i a t e b a s i s . However, one cannot form any c o n c l u s i o n s r e g a r d i n g the performance o f these v a r i a b l e s when examined i n a m u l t i v a r i a t e s e t t i n g . R ecently concern has been expressed t h a t the Bankruptcy reform a c t has made i t too easy to d e c l a r e bankruptcy, and, consequently, the process has been abused. In order to e v aluate t h i s concern, the K r u s k a l - W a l l i s t e s t was conducted on the h y p o t h e s i s t h a t a t one year p r i o r to f a i l u r e no d i f f e r e n c e s e x i s t e d between the d i s t r i b u t i o n s of f i r m s f i l i n g f o r bankruptcy under the Chandler and Reform A c t s . The r e s u l t s of these t e s t s are summarized i n t a b l e 6. At the 0.01 s i g n i f i c a n c e l e v e l , a l l the v a r i a b l e s , i n d i v i d u a l l y e v a l u a t e d , i n d i c a t e t h a t there does not appear to be a s i g n i f i c a n t d i f f e r e n c e between the r a t i o d i s t r i b u t i o n s of f i r ms f i l i n g under the Chandler and Reform A c t s . In order to e v a l u a t e the o v e r a l l s i g n i f i c a n c e o f the K r u s k a l - W a l l i s t e s t s undertaken, the B o n f e r r o n i approach was used to a r r i v e a t an o v e r a l l s i g n i f i c a n c e l e v e l . I f K t e s t s are to be undertaken, then the B o n f e r r o n i approach uses a 1 = a / K where a i s the minimum o v e r a l l s i g n i f i c a n c e l e v e l , where a 1 i s the s i g n i f i c a n c e l e v e l f o r each t e s t . At an o v e r a l l s i g n i f i c a n c e l e v e l of 0.01, the i n d i v i d u a l s i g n i f i c a n c e l e v e l was 0.0003. I t i s apparent from the p-v a l u e s ( p r o b a b i l i t y of the observed value or a more extreme value o c c u r r i n g under the n u l l hypothesis) t h a t many of the -45 -v a r i a b l e s i n d i c a t e t h a t a s i g n i f i c a n t d i f f e r e n c e e x i s t s between t h e s a m p l e s o f b a n k r u p t and n o n b a n k r u p t f i r m s . I n c o n t r a s t , a t an o v e r a l l s i g n i f i c a n c e l e v e l o f 0.01, t h e K r u s k a l - W a l l i s t e s t r e s u l t s i n d i c a t e t h a t no s i g n i f i c a n t d i f f e r e n c e e x i s t s b etween t h e r a t i o s o f f i r m s f i l i n g f o r b a n k r u p t c y under t h e C h a n d l e r and R e f o r m a c t s . On t h e b a s i s o f t h e K r u s k a l - W a l l i s t e s t s we c a n c o n c l u d e t h e f o l l o w i n g : A) T h a t a s t a t i s t i c a l l y s i g n i f i c a n t , a t t h e 0.01 l e v e l , d i f f e r e n c e e x i s t s between b a n k r u p t and n o n -b a n k r u p t f i r m s one y e a r p r i o r t o f a i l u r e on an i n d i v i d u a l r a t i o b a s i s . T h i s r e s u l t i s s i m i l a r t o B e a v e r ' s f i n d i n g t h a t f i n a n c i a l r a t i o s were a u s e f u l t o o l i n t h e e v a l u a t i o n o f f i r m v i a b i l i t y . B) T h a t n o t a l l r a t i o s p e r f o r m e q u a l l y w e l l i n i d e n t i f y i n g d i f f e r e n c e s between f i r m s . C) T h a t a l t h o u g h t h e r e h a s been a s t a r t l i n g i n c r e a s e i n t h e number and s i z e o f b a n k r u p t c i e s s i n c e t h e p a s s a g e o f t h e R e f o r m A c t , t h e r e d o e s n o t appear t o be a s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e between t h e one y e a r p r i o r r a t i o s o f f i r m s w h i c h f i l e d under t h e C h a n d l e r A c t and t h o s e t h a t f i l e d under t h e Reform A c t . -46-+ + I Table 6 I I TESTS OF GROUP SIMILARITY I I (using the K r u s k a l - W a l l i s methods) I I of I I H o ^ : n o d i f f e r e n c e between S u r v i v o r and Bankrupt. I ' 2 ' I H_ : no d i f f e r e n c e between Bankrupt be f o r e and a f t e r I | U 1978. I R a t i o p-value p-value H H Cash flow / s a l e s . 0399 . 4705 Cash flow / t o t a l a s s e t s .0236 .7893 Cash flow / t o t a l debt . 0001 .7484 Net income / s a l e s 0 .0 .9361 Net income / t o t a l a s s e t s 0 .0 . 3360 Net income / t o t a l debt 0 .0 .2851 Long term debt / t o t a l a s s e t s .0103 .6496 T o t a l claims / t o t a l a s s e t s 0 .0 .1211 Working c a p i t a l / t o t a l a s s e t s 0 .0 .1416 Cash / c u r r e n t l i a b i l i t i e s 0 .0 .2091 Current a s s e t s / c u r r e n t l i a b i l i t i e s 0 .0 .1814 Inventory / s a l e s .5883 .9361 Current a s s e t s / s a l e s . 8123 . 6689 T o t a l a s s e t s / s a l e s .3875 .4705 Quick a s s e t s / s a l e s .1128 . 8937 Quick a s s e t s / c u r r e n t l i a b i l i t i e s 0 .0 .1211 Quick a s s e t s / t o t a l a s s e t s .0193 .1995 Quick a s s e t s / funds f o r o p e r a t i o n s . 6970 .9361 No c r e d i t p e r i o d 0 .0 .1566 Retained earnings / t o t a l a s s e t s 0 .0 .0215 Earnings before i n t e r e s t and tax / t o t a l a s s e t s 0 .0 .7283 Market value e q u i t y / book v a l . debt 0 .0 . 3924 Margin .0003 .6689 I n t e r e s t / long term debt . 0001 .1277 Invested c a p i t a l / t o t a l a s s e t s 0 .0 .9149 Change i n margin .0555 1.0 Change i n market 0 .0 .6689 -47-D) At an o v e r a l l s i g n i f i c a n c e l e v e l o f 0.01, using the B o n f e r r o n i approach, there appears to be a s i g n i f i c a n t d i f f e r e n c e between the sample of bankrupt and non-bankrupt f i r m s . There does not appear to be a s i g n i f i c a n t d i f f e r e n c e , a t an o v e r a l l s i g n i f i c a n c e of 0.01, between the f i r m s f i l i n g f o r bankruptcy under the Chandler and Reform a c t s (before and a f t e r 1978). In view o f these r e s u l t s , the a n a l y s i s w i l l not be undertaken on the two groups of bankrupt f i r m s , r a t h e r the a n a l y s i s w i l l be c a r r i e d out on the e n t i r e sample o f bankrupts. -48-V I . DISCRIMINANT ANALYSIS A. THEORY D i s c r i m i n a n t a n a l y s i s i s a m u l t i v a r i a t e s t a t i s t i c a l t e c h n i q u e w h i c h s e e k s t o t r a n s f o r m a s e r i e s o f s c o r e s i n t o a s i n g l e v a l u e , and w i l l be u s e d i n t h i s p a p e r as a "benchmark" by w h i c h t o j u d g e t h e p e r f o r m a n c e o f t h e Cox m o d e l . E s s e n t i a l l y , t h i s t y p e o f a n a l y s i s d e a l s w i t h t h e c a s e when one h a s a sample f r o m p o p u l a t i o n A and a sample f r o m p o p u l a t i o n B, and on t h e b a s i s o f t h e s e w i s h t o c l a s s i f y i n d i v i d u a l s drawn f r o m an unknown p o p u l a t i o n . A g r a p h i c a l r e p r e s e n t a t i o n o f t h i s s i t u a t i o n i s f o u n d i n f i g u r e 3. -49 -L i n e a r d i s c r i m i n a n t a n a l y s i s f o r c l a s s i f i c a t i o n i n t o two "a p r i o r i ' g r o u p s r e s u l t s i n one d i s c r i m i n a n t f u n c t i o n o f t h e f o r m : ^ Z = b r t + b.X. + b 0 X „ + . . . b X 0 1 1 2 2 mm fch where: X.. = j a t t r i b u t e o r i n d i v i d u a l v a r i a b l e b^ = d i s c r i m i n a n t f u n c t i o n c o e f f i c i e n t f o r j a t t r i b u t e Z = d i s c r i m i n a n t s c o r e The d i s c r i m i n a n t f u n c t i o n maps t h e m u l t i d i m e n s i o n a l a t t r i b u t e s p a c e (x,y i n f i g u r e 3) o n t o a o n e - d i m e n s i o n a l s p a c e ( l i n e I i n f i g u r e 3) and m a x i m i z e s t h e s e p a r a t i o n between t h e two 3 g r o u p s . The o u t p u t o f t h e BMDP S t a t i s t i c a l p a c k a g e i s i n a somewhat d i f f e r e n t f o r m t h a n t h e more common s i n g l e e q u a t i o n f o r m . I n t h e two g r o u p c a s e BMDP p r o d u c e s two f u n c t i o n s , one f o r e a c h g r o u p . Z. = b n . + b,.X n + . . . + b .X I Oi 1 1 1 m i m where t h e s u b s c r i p t i d e n o t e s w h i c h g r o u p t h e f u n c t i o n i s e v a l u a t i n g . A f i r m i s t h e n c l a s s i f i e d i n t o w h i c h e v e r g r o u p h as t h e l a r g e s t Z^. (See BMDP S t a t i s t i c a l S o f t w a r e ) The major a d v a n t a g e o f t h i s t y p e o f a n a l y s i s i s t h e r e d u c t i o n i n d i m e n s i o n s . R a t h e r t h a n h a v i n g t o e v a l u a t e t w e n t y - s e v e n r a t i o s , one now o n l y e v a l u a t e s a s i n g l e s c o r e . N o n - n o r m a l i t y o f t h e u n d e r l y i n g v a r i a b l e s c a n c a u s e s e v e r e p r o b l e m s i n d i s c r i m i n a n t a n a l y s i s p a r t i c u l a r l y i n -50 -q u a d r a t i c d i s c r i m i n a n t a n a l y s i s . The l i n e a r d i s c r i m i n a n t f u n c t i o n i s an a p p r o p r i a t e a s s i g n m e n t r u l e when t h e f o l l o w i n g 4 a s s u m p t i o n s a r e s a t i s f i e d : A) The u n d e r l y i n g p o p u l a t i o n s a r e m u l t i v a r i a t e n o r m a l l y d i s t r i b u t e d . B) The c o v a r i a n c e m a t r i x i s t h e same f o r t h e two p o p u l a t i o n s . C) The "a p r i o r i ' p r o b a b i l i t i e s o f an i n d i v i d u a l b e l o n g i n g t o e i t h e r p o p u l a t i o n i s known. D) The mean and c o v a r i a n c e m a t r i c e s a r e known. E) The i n i t i a l c l a s s i f i c a t i o n s were done c o r r e c t l y . A m a j o r c o n c e r n i n d i s c r i m i n a n t a n a l y s i s i s t h e e s t i m a t i o n o f an e r r o r r a t e . The most common a p p r o a c h i s t o p a r t i t i o n t h e o r i g i n a l sample i n t o two g r o u p s . The d i s c r i m i n a t i n g f u n c t i o n i s t h e n e s t i m a t e d u s i n g one s u b -sample and p e r f o r m a n c e i s e v a l u a t e d u s i n g t h e o t h e r s u b -s a m p l e . T h i s " p a r t i t i o n i n g " a p p r o a c h h a s been c r i t i c i z e d on s e v e r a l f r o n t s . The b a s i c c r i t i c i s m s a r e t h a t i t w a s t e s d a t a ; n o t a l l t h e a v a i l a b l e d a t a i s u s e d t o d e v e l o p t h e model w h i c h c a n be a s e v e r e p r o b l e m i n a s m a l l s a m p l e ; and s e c o n d , t h a t i t d o e s n o t e v a l u a t e t h e d i s c r i m i n a n t f u n c t i o n w h i c h w i l l be 5 u s e d i n p r a c t i c e . The d i s c r i m i n a n t f u n c t i o n w h i c h w i l l be u s e d t o c l a s s i f y f i r m s i n p r a c t i c e s h o u l d u s e a l l t h e sample d a t a a v a i l a b l e , t o p a r t i t i o n t h e d a t a a n d . t h e n use a f u n c t i o n - 5 1 -d e r i v e d on j u s t one p a r t i t i o n i s n o t e f f i c i e n t a s i t d o e s n o t us e a l l t h e i n f o r m a t i o n a v a i l a b l e i n t h e t o t a l s a m ple. The " l e a v i n g - o n e - o u t " a p p r o a c h e s t i m a t e s t h e e r r o r r a t e i n a s l i g h t l y d i f f e r e n t manner. I n t h i s method, t h e d i s c r i m i n a t i n g f u n c t i o n i s e s t i m a t e d u s i n g N - l f i r m s . The r e m a i n i n g f i r m i s t h e n c l a s s i f i e d on t h e b a s i s o f t h i s g f u n c t i o n . T h i s t e c h n i q u e u s e s most o f t h e sample d a t a , b u t , c a n be v e r y t i m e c o n s u m i n g w i t h a l a r g e sample s i z e . I n t h i s s t u d y , d i s c r i m i n a n t a n a l y s i s was c a r r i e d o u t u s i n g t h e BMDP:7M p a c k a g e . T h i s p a c k a g e u s e s s t e p w i s e d i s c r i m i n a n t a n a l y s i s whereby v a r i a b l e s a r e o n l y i n c l u d e d when t h e y s i g n i f i c a n t l y i m p r o v e t h e p e r f o r m a n c e o f t h e l i n e a r d i s c r i m i n a n t f u n c t i o n . One must keep i n mind t h a t t h e s t e p -w i s e p r o c e d u r e i s n o t n e c e s s a r i l y t h e o p t i m a l p r o c e d u r e f o r i d e n t i f y i n g v a r i a b l e s f o r i n c l u s i o n i n t h e a n a l y s i s . I t i s no t u n l i k e l y t h a t a n o t h e r s u b s e t o f t h e v a r i a b l e s i s t h e o p t i m a l s e t i n t e r m s o f model p e r f o r m a n c e . The BMDP:7M p a c k a g e p r e s e n t s a " j a c k k n i f e " c l a s s i f i c a t i o n m a t r i x . The J a c k k n i f e t e c h n i q u e i s e s s e n t i a l l y t h e " l e a v i n g - o n e - o u t " e r r o r c l a s s i f i c a t i o n method. BMDP:7M y i e l d s two c l a s s i f i c a t i o n f u n c t i o n s , one f o r e a c h g r o u p . O b s e r v a t i o n s a r e c l a s s i f i e d i n t o w h i c h e v e r g r o u p y i e l d s t h e h i g h e r s c o r e . - 5 2 -B. ONE-YEAR RESULTS R e s u l t s o f t h e d i s c r i m i n a n t a n a l y s i s c a r r i e d o u t on t h e one y e a r p r i o r t o f a i l u r e d a t a a r e summarized i n t a b l e 7. A l l t h e v a r i a b l e s i d e n t i f i e d by t h i s s t u d y were s i g n i f i c a n t on a u n i v a r i a t e b a s i s . (See T a b l e 6.) I t i s i n t e r e s t i n g t o n o t e t h a t o n l y a few o f t h e many i n d i v i d u a l l y s i g n i f i c a n t v a r i a b l e s were u s e d i n t h i s m u l t i v a r i a t e d i s c r i m i n a n t a n a l y s i s . T h i s i s p a r t l y due t o t h e s t e p w i s e p r o c e d u r e u s e d i n t h e d i s c r i m i n a n t a n a l y s i s whereby any v a r i a b l e s n o t s i g n i f i c a n t l y i m p r o v i n g p e r f o r m a n c e were n o t i n c l u d e d i n t h e c l a s s i f i c a t i o n f u n c t i o n . I t wo u l d t h e r e f o r e a p p e a r t h a t w h i l e a v a r i a b l e may be s i g n i f i c a n t when c o n s i d e r e d i n i s o l a t i o n , i t ' s e f f e c t becomes l e s s s i g n i f i c a n t when combined w i t h a n o t h e r v a r i a b l e . I n o t h e r words t h e a f f e c t o f one v a r i a b l e becomes subsumed i n t h e e f f e c t o f t h e o t h e r . Most o f t h e v a r i a b l e s i d e n t i f i e d by t h i s a n a l y s i s a r e v e r y d i f f e r e n t t o t h o s e i d e n t i f i e d by A l t m a n ' s Z S c o r e 7 m o d e l . A l t m a n ' s d i s c r i m i n a n t a n a l y s i s i d e n t i f i e d t h e f o l l o w i n g v a r i a b l e s : w o r k i n g c a p i t a l t o t o t a l a s s e t s , r e t a i n e d e a r n i n g s t o t o t a l a s s e t s , e a r n i n g s b e f o r e i n t e r e s t and t a x e s t o t o t a l a s s e t s , m a r k e t v a l u e o f e q u i t y t o book v a l u e o f t o t a l l i a b i l i t i e s and s a l e s t o t o t a l a s s e t s . -53-+ + I t a b l e 7 I I CLASSIFICATION FUNCTION | I Survive Bankrupt I I T o t a l c l a i m s / a s s e t s 17.11449 23.89600 I I No c r e d i t p e r i o d 1.21465 -2.10626 | I Earnings before i n t e r e s t 17.86440 6.92492 | I and taxes / a s s e t s I I Constant -5.75120 -10.44621 I CLASSIFICATION ACCURACY (1 YEAR PRIOR) (J a c k k n i f e technique) Survive Bankrupt Accuracy Survive 61 6 91.0% Bankrupt 8 33 80.5% I 69 39 87.0% I + + When d i s c r i m i n a n t a n a l y s i s was c a r r i e d out on the 'four year p r i o r ' data, s e v e r a l i n t e r e s t i n g f e a t u r e s emerged. As expected, the c l a s s i f i c a t i o n accuracy d e c l i n e d . The r e s u l t s of the d i s c r i m i n a n t a n a l y s i s based on the four year p r i o r data are summarized i n t a b l e 8. However, of more i n t e r e s t was that the d i s c r i m i n a t i n g v a r i a b l e s changed. None o f the v a r i a b l e s used i n the one year p r i o r d i s c r i m i n a n t f u n c t i o n appeared i n the four year p r i o r model. T h i s r e s u l t i s not unexpected. One would expect t h a t the p r e d i c t o r s of long term v i a b i l i t y would not n e c e s s a r i l y be the b e s t p r e d i c t o r s of short-term s u r v i v a l . -54-Table 8 CLASSIFICATION FUNCTION Four Years P r i o r t o F a i l u r e Survive Bankrupt Net income / t o t a l a s s e t s -4.61612 -26.18338 T o t a l a s s e t s / s a l e s 2.60267 4.95144 Invested c a p i t a l / t o t a l 41.57300 36.40367 a s s e t s Constant -15.58192 -13.48379 CLASSIFICATION ACCURACY (4 YEAR PRIOR) ( J a c k k n i f e technique) Survive Bankrupt Accuracy Survive 52 13 80.0% Bankrupt 9 26 74.0% 61 39 78.0% I t would, t h e r e f o r e , appear t h a t Altman's Z score approach y i e l d s u s e f u l r e s u l t s . However, any i n f e r e n c e based on these r e s u l t s i s s u b j e c t t o doubt due to the nonnormality of the d i s t r i b u t i o n s o f the u n d e r l y i n g v a r i a b l e s . -55-V I I . THE COX MODEL A. SURVIVAL THEORY T h e r e a r e t h r e e b a s i c f u n c t i o n s w h i c h d e s c r i b e t h e s u r v i v a l e x p e r i e n c e . The f a i l u r e d e n s i t y f u n c t i o n , f ( t ) , w h i c h d e f i n e s t h e p a t t e r n o f f a i l u r e by d e s c r i b i n g t h e i n s t a n t a n e o u s r i s k o f f i n a n c i a l c o l l a p s e . f (t) = l i m Pr ( t < T < t + At ) Afc-5>0+  At where T i s t h e t i m e o f f a i l u r e . The s u r v i v a l f u n c t i o n , S ( t ) , w h i c h d e s c r i b e s t h e p r o b a b i l i t y o f s u r v i v i n g a t l e a s t a s l o n g a s t . S ( t ) = Pr ( T _> t ) S ( t ) = 1 a t t = 0 F ( t ) = 1 - S ( t ) d i s t r i b u t i o n o f t i m e u n t i l f a i l u r e . The t h i r d f u n c t i o n , t h e H a z a r d f u n c t i o n , H ( t ) , d e s c r i b e s t h e i n s t a n t a n e o u s r i s k o f f a i l u r e p r o v i d i n g f a i l u r e h a s n o t a l r e a d y o c c u r r e d . 1 H ( t ) = l i m P r ( t < T < t + A . t | T > _ t ) Afc-»o+  At As t h e s e t h r e e b a s i c f u n c t i o n s d e s c r i b e t h e same 2 s u r v i v a l p r o c e s s , t h e y a r e c l o s e l y r e l a t e d . f ( t ) = - d S ( t ) / d t S (t ) = exp [ - J* H (u) du ] o H ( t ) = f ( t ) / S ( t ) - 5 6 -C o n s e q u e n t l y , d e s c r i b i n g one f u n c t i o n i m p l i e s t h e o t h e r two. As t h e f a i l u r e and s u r v i v a l f u n c t i o n s a r e v e r y h a r d t o e s t i m a t e o r c h a r a c t e r i z e , one h a s t o c o n c e n t r a t e on t h e h a z a r d f u n c t i o n . S u r v i v a l a n a l y s i s f a c e s two m a j o r c o m p l i c a t i o n s : t h e h a z a r d f u n c t i o n may n o t be c o n s t a n t o v e r t i m e and, s e c o n d l y , t h e d a t a may be c e n s o r e d . The t i m e v a r y i n g h a z a r d f u n c t i o n h a s s e r i o u s i m p l i c a t i o n s f o r s t a t i s t i c a l i n f e r e n c e and t h e i n t e r p r e t a t i o n o f t h e r e s u l t s o f t h e a n a l y s i s . I n an e f f o r t t o e n s u r e t h a t t h e c o v a r i a t e s , w h i c h d e t e r m i n e t h e h a z a r d f u n c t i o n , a r e c o n s t a n t o v e r t i m e , t h e a n a l y s i s was r e s t r i c t e d t o t h e v e r y s h o r t p e r i o d o f j u s t one y e a r p r i o r t o f a i l u r e . The Cox m o d e l , however, c a n e s t i m a t e t h e p r o b a b i l i t y d i s t r i b u t i o n o f s u r v i v a l t i m e s when t h e c o v a r i a t e s a r e t i m e d e p e n d e n t . I n s u c h an a n a l y s i s , one must f i r s t e s t i m a t e t h e r e l a t i o n s h i p b etween t h e c o v a r i a t e and t i m e , and t h e n e s t i m a t e t h e Cox m o d e l . Time d e p e n d e n t c o v a r i a t e s were n o t e s t i m a t e d o r a n a l y z e d i n t h i s p a p e r . I n o r d e r t o make t h e c o n s t a n t c o v a r i a t e s a s s u m p t i o n p a l a t a b l e , a v e r y s h o r t t i m e p e r i o d was a n a l y z e d o v e r w h i c h i t w o u l d seem more r e a s o n a b l e t o assume t h a t t h e r a t i o s d i d n o t change s i g n i f i c a n t l y . The v a l i d i t y o f t h e t i m e i n d e p e n d e n t c o v a r i a t e a s s u m p t i o n was e v a l u a t e d by s t r a t i f y i n g t h e sample on t h e b a s i s o f t i m e , and t h e n o b s e r v i n g i f t h e p r o p o r t i o n a l h a z a r d s a s s u m p t i o n s r e m a i n e d v a l i d . T h e r e was - 5 7 -l i t t l e e v i d e n c e t o s u g g e s t t h a t o m i t t e d t i m e d e p e n d e n t c o v a r i a t e s had a s i g n i f i c a n t i m p a c t on t h e o v e r a l l m o d e l . D a t a a r e c e n s o r e d when t h e sample y i e l d s i n c o m p l e t e s u r v i v a l d a t a , u s u a l l y b e c a u s e t h e e x p e r i m e n t o r s t u d y t e r m i n a t e s b e f o r e a d e s i r e d r e s p o n s e o r e v e n t o c c u r s i n e v e r y s u b j e c t i n t h e s t u d y . I n o r d e r t o a n a l y z e t h e c e n s o r e d s a m p l e s one must assume t h a t c e n s o r i n g and f a i l u r e a r e 3 g e n e r a t e d by i n d e p e n d e n t mechanisms. B. THE COX PROPORTIONAL HAZARDS MODEL The major p r o b l e m r e m a i n i n g i n s u r v i v a l a n a l y s i s i s t h a t t h e f o r m o f t h e h a z a r d f u n c t i o n i s unknown. The Cox P r o p o r t i o n a l H a z a r d M o d e l p r e s e n t s a t e c h n i q u e f o r e s t i m a t i n g t h e h a z a r d f u n c t i o n by a l l o w i n g a s e m i - p a r a m e t r i c a s s e s s m e n t o f t h e r e l a t i o n s h i p s among t h e h a z a r d f u n c t i o n s . The p r o p o s e d m odel i s : ^ ( X' B ) i s an a r b i t r a r y f u n c t i o n , i s a v e c t o r o f c o n c o m i t a n t i n f o r m a t i o n i s a v e c t o r o f p a r a m e t e r s T h i s m odel i s s e m i - p a r a m e t r i c a s i t depends on t h e v e c t o r B o f r e g r e s s i o n p a r a m e t e r s . However, H g ( t ) i s a r b i t r a r y and no d i s t r i b u t i o n a l a s s u m p t i o n s a r e n e c e s s a r y t o e s t i m a t e H g ( t ) „ 5 o r B. H ( t ) = H Q (t) exp where : H Q (t) X B - 5 8 -Cox d e f i n e s t h e " R e l a t i v e H a z a r d F u n c t i o n " a s : H ( t ) / H Q ( t ) = exp ( X' B ) The p r o p o r t i o n a l h a z a r d model assumes t h a t t h e r e l a t i v e h a z a r d f u n c t i o n i s c o n s t a n t t h r o u g h t i m e . I n p r o p o r t i o n a l h a z a r d s , t h e s u r v i v a l d i s t r i b u t i o n f o r t h e d i f f e r e n t X's a r e g r e l a t e d a s powers o f one a n o t h e r . t S ( t ) = exp [ - J H 0 ( u ) e x P ( ! ) du ] = [ S Q ( t ) ]*exp ( X' B ) where S _ ( t ) i s t h e b a s e l i n e s u r v i v a l f u n c t i o n o f t h e a v e r a g e f i r m . S g ( t ) c o r r e s p o n d s t o H g ( t ) . The major a d v a n t a g e o f t h e Cox p r o p o r t i o n a l h a z a r d model a p p r o a c h t o s u r v i v a l a n a l y s i s i s t h a t i n f e r e n c e c a n be r e s t r i c t e d t o t h e e f f e c t o f t h e c o n c o m i t a n t i n f o r m a t i o n w i t h o u t knowledge o f t h e f o r m o f t h e s u r v i v a l d i s t r i b u t i o n . I n o t h e r w ords, we c a n r e s t r i c t our a n a l y s i s t o t h e i m p a c t o f t h e o b s e r v e d v e c t o r X, t h e c o n c o m i t a n t i n f o r m a t i o n , on t h e h a z a r d o r s u r v i v a l f u n c t i o n s w h i l e n o t h a v i n g t o e s t i m a t e t h e f o r m o f t h e s u r v i v a l d i s t r i b u t i o n . A p r o b l e m a r i s i n g i n t h e u s e o f t h e Cox model i s due t o t h e i s s u e o f c o n t i n u o u s v e r s u s d i s c r e t e t i m e . The h a z a r d a p p r o a c h i s b a s e d on c o n t i n u o u s t i m e a n d , t h e r e f o r e , no d e a t h s o r f a i l u r e s c a n o c c u r a t t h e same p o i n t i n t i m e . However, i n p r a c t i c e , one h a s t o u s e d i s c r e t e t i m e p e r i o d s and t h e p r o b l e m o f " t i e d " f a i l u r e t i m e o b s e r v a t i o n s a r i s e s . The t i e d o b s e r v a t i o n s c a u s e d i f f i c u l t y a s t h e h a z a r d model makes u s e o f t h e t e m p o r a l o r d e r i n g o f t h e o b s e r v a t i o n s and, t h e r e f o r e , cannot be d i r e c t l y a p p l i e d t o the case o f t i e d s u r v i v a l times.^ The obvious s o l u t i o n t o the problem i s t o decrease the time p e r i o d i n q u e s t i o n i n a e f f o r t t o ensure t h a t o n l y one death o c c u r r e d per p e r i o d . However, i n many cases t h i s i s not f e a s i b l e or i s e x c e s s i v e l y expensive. Many d i f f e r e n t techniques have been proposed t o d e a l with the i s s u e o f t i e d o b s e r v a t i o n s ranging from e v a l u a t i n g every p o s s i b l e o r d e r i n g of o b s e r v a t i o n s t o randomly and a r b i t r a r i l y b r eaking the 8 t i e s . T h i s study s o l v e s the problem o f t i e d o b s e r v a t i o n s by measuring s u r v i v a l time i n days which, i n t h i s sample, r e s u l t s i n no t i e d s u r v i v a l time o b s e r v a t i o n s . The time u n t i l f a i l u r e , i n t h i s study, was measured, i n days, from January 1 of the year i n which f a i l u r e o c c u r r e d . In other words, i f a f i r m s f a i l e d on January 5, 19xx, the recorded s u r v i v a l time was 4 days. The impact o f the t i e d o b s e r v a t i o n s w i l l be i l l u s t r a t e d by e s t i m a t i n g the Cox model u s i n g a one month time i n t e r v a l which r e s u l t s i n many t i e d o b s e r v a t i o n s . Cox models are u s u a l l y e valuated i n two ways: by t e s t i n g the r e a s o n a b i l i t y o f the p r o p o r t i o n a l hazards assumption and by examining the goodness o f f i t . The p r e d i c t i v e a b i l i t y of 9 the model i s r a r e l y t e s t e d . The assumption o f p r o p o r t i o n a l hazards i s evaluated by s t r a t i f y i n g the o v e r a l l sample on the b a s i s o f a v a r i a b l e , and e s t i m a t i n g a hazard f u n c t i o n based on each s t r a t a . I f -60-p r o p o r t i o n a l hazards i s v a l i d , each s t r a t a c o u l d have i t ' s own base l i n e hazard, but the m u l t i p l i c a t i v e p o r t i o n of the hazard f u n c t i o n would be the same a c r o s s s t r a t a . T h e r e f o r e , i f the p r o p o r t i o n a l hazards assumption i s supported by the d a t a , one would expect the graph of the l o g of the u n d e r l y i n g cumulative hazard f u n c t i o n s or l o g o f - l o g o f the s u r v i v a l f u n c t i o n versus time t o produce p a r a l l e l or near p a r a l l e l G o o d n e s s - o f - f i t i s e v a l u a t e d by examining the ' r e s i d u a l s ' which f o r the Cox model are determined by the t r a n s f o r m a t i o n : 1 1 The r e s i d u a l s used i n the more common r e g r e s s i o n a n a l y s i s are d e f i n e d as the observed value minus the p r e d i c t e d or ' f i t t e d ' v a l u e . T h i s approach i s not v a l i d i n the p r o p o r t i o n a l hazard model as the ' f i t t e d ' v a lue i s a p r o b a b i l i t y d i s t r i b u t i o n while there i s no observed d i s t r i b u t i o n . Consequently, one must, i n e f f e c t , e v a l u a t e the ' f i t t e d ' cumulative p r o b a b i l i t y of f a i l i n g b e f o r e a c t u a l death and comparing i t t o the v a l u e of 1, the a c t u a l cumulative p r o b a b i l i t y of f a i l i n g by the observed f a i l u r e date. These r e s i d u a l s should behave as a random sample drawn from a u n i t e x p o n e n t i a l d i s t r i b u t i o n . I f the Cox model " f i t s " the data w e l l , one would expect the graph o f the r e s i d u a l s l i n e s . 10 e. = exp ( B' X. ) D -61-versus the cumulative hazard o f the r e s i d u a l s t o y i e l d a 12 s t r a i g h t l i n e with an expected slope of 1. The cumulative hazard f u n c t i o n was c a l c u l a t e d u s i n g the 13 formula g i v e n i n the BMDP S t a t i s t i c a l Software appendix, il H(e) = ^ m. / tRj + ( e - e ^ m 1 + 1 / #R 1 + 1 let where: m. = number o f deaths a t time I l #R. = number of s u r v i v o r s a t the 3 beginning o f p e r i o d .. e = r e s i d u a l s and e 1 < e < The Cox p r o p o r t i o n a l hazard model was estimated using the BMDP:2L computer software. T h i s package a l l o w s a stepwise procedure u s i n g the maximum p a r t i a l l i k e l i h o o d v a l u e s t o determine e n t r y and e x i t . Once again , one must bear i n mind, the s u b - o p t i m a l i t y o f the step-wise procedure i n i d e n t i f y i n g v a r i a b l e s f o r i n c l u s i o n . BMDP:2L esti m a t e s the r e g r e s s i o n c o e f f i c i e n t s o f the Cox model by maximizing the l o g of the l i k e l i h o o d f u n c t i o n u s i n g a Newton-Raphson a l g o r i t h m . The asymptotic c o v a r i a n c e matrix i s then obtained by i n v e r t i n g 1(b) where 1(b) i s the i n f o r m a t i o n matrix. The i n f o r m a t i o n matrix i s the negative of the matrix o f second p a r t i a l s o f the l o g l i k e l i h o o d f u n c t i o n . (See BMDP S t a t i s t i c a l Software, Appendix 31 f o r a d i s c u s s i o n of the e s t i m a t i o n techniques used by BMDP:2L) The eigenvalues of the i n f o r m a t i o n matrix r a t h e r than the more commonly used -62-c o r r e l a t i o n matrix should be eva l u a t e d i n order t o determine i f m u l t i c o l l i n e a r i t y i s a p o t e n t i a l problem. In order t o eval u a t e m u l t i c o l l i n e a r i t y , both the estimated asymptotic c o r r e l a t i o n matrix and the common c o r r e l a t i o n matrix w i l l be presented i n order t o i l l u s t r a t e the d i f f e r e n c e s between the two. C. ONE YEAR ESTIMATION The P r o p o r t i o n a l Hazard model was estimated u s i n g the step-wise procedure a v a i l a b l e i n the BMDP S t a t i s t i c a l Software. The o v e r a l l s e t o f f i n a n c i a l r a t i o s e v a l u a t e d are found i n t a b l e 2. The r e s u l t s o f the Cox e s t i m a t i o n are found i n t a b l e 9. The o v e r a l l s i g n i f i c a n c e o f the Cox e s t i m a t i o n f o r the one-year p r i o r data i s very good as i l l u s t r a t e d by the p-value. The p-value measures the p r o b a b i l i t y o f the observed r e l a t i o n s h i p o c c u r r i n g i f there i s no t r u e r e l a t i o n s h i p . T h e r e f o r e , we can r e j e c t the h y p o t h e s i s t h a t a l l the c o e f f i c i e n t s are zero with some c o n f i d e n c e . As the s i g n s o f the c o e f f i c i e n t s are of g r e a t importance, the c o e f f i c i e n t s were t e s t e d t o determine i f the s i g n observed was s i g n i f i c a n t by u s i n g a o n e - t a i l e d t e s t . As the degrees o f freedom of t h i s t - d i s t r i b u t i o n are 102, approximate p-values w i l l be presented f o r 60 degrees o f freedom due t o inadequacies i n the t - t a b l e s . The r e s u l t s of these t e s t s are presented i n t a b l e 9. I t would appear t h a t a t -63-a significance l e v e l of 0.05, each c o e f f i c i e n t ' s sign i s s i g n i f i c a n t when evaluated i n d i v i d u a l l y . + + I Table 9 I I COX MODEL ESTIMATION I I ONE YEAR PRIOR TO BANKRUPTCY SAMPLE LOG LIKELIHOOD = 114.4753 GLOBAL CHI-SQUARE — 99.14 D.F. = 7 P-VALUE =0 .0 * STANDARD VARIABLE COEFFICIENT ERROR COEFF./S.E. EXP(COEF) CLAIM1 1.7504 0.8452 2.0710 5. 7572 DELMKT1 -1.5624 0.8917 -1.7522 0. 2096 INTLTD1 0.1738 0.0770 2.2579 1. 1899 NETYSL1 -2.1242 1.3748 -1.5451 0. 1195 CFTD1 -1.7469 0.7184 -2.4315 0. 1743 QKCL1 -1.3441 0.5804 -2.3159 0. 2608 CASLS1 1.5477 0.7804 1.9833 4. 7008 TEST OF SIGN APPROX. P-VALUE. SIGNIFICANCE 6 0 DEGREES CLAIM1 . 025 DELMKT1 .05 INTLTD1 . 01 NETYSL1 .075 CFTD1 . 01 QKCL1 .01 CASLS1 .05 * CLAIM1 = Current + longterm debt + pref.shares / Total Assets. DELMKT1 = Change i n Market Value of equity. INTLTD1 = Interest / long term debt • NETYSL1 = Net income / Sales. CFTD1 Cash flow / Total debt. QKSL1 Quick assets / Current l i a b i l i t i e s . CASLS1 = Current Assets / Sales. -64-I n t u i t i v e l y , t h e Cox model p r o p o s e s t h a t a b a s e l i n e h a z a r d l e v e l e x i s t s f o r a n a v e r a g e f i r m and any d e v i a t i o n f r o m t h a t a v e r a g e r e s u l t s i n a change i n t h e h a z a r d , i n s t a n t a n e o u s r i s k o f f a i l u r e , f a c e d by t h e n o n - a v e r a g e f i r m . H . ( t ) = H Q ( t ) e x p ( X A ' B ) C o n s e q u e n t l y , any n e g a t i v e c o e f f i c i e n t r e s u l t s i n a d e c r e a s e i n t h e e s t i m a t e d i n s t a n t a n e o u s r i s k o f f a i l u r e g i v e n f a i l u r e h a s n o t a l r e a d y o c c u r r e d . + + T a b l e 10 CORRELATION MATRIX (ONE YEAR PRIOR DATA) CLAIM DELMKT INTLTD NETYSLS CFTD QKCL CLAIM 1 DELMKT - .416 1 INTLTD .05 6 - .068 1 NETYSLS - .570 . 342 - .098 1 CFTD - .488 .709 .018 .325 1 QKCL - . 5 62 .614 - .148 .475 . 477 1 CASL - .010 .111 .195 .029 .095 .213 ESTIMATED ASYMPTOTIC CORRELATION MATRIX (ONE YEAR PRIOR DATA) CLAIM DELMKT INTLTD NETYSLS CFTD QKCL CLAIM 1 DELMKT .276 1 INTLTD .205 .039 1 NETYSLS .124 -.191 - .103 1 CFTD . 347 .049 .079 - .110 1 QKCL .237 - .178 .269 - .199 .326 1 CASL -.101 - .079 -.231 .063 - .024 - .233 + + The p r o b l e m o f m u l t i c o l l i n e a r i t y was e v a l u a t e d by e x a m i n i n g t h e e s t i m a t e d a s y m p t o t i c c o r r e l a t i o n m a t r i x o f t h e -65-v a r i a b l e s . (See t a b l e 10) There does not appear t o be a problem o f e x c e s s i v e c o l l i n e a r i t y among the v a r i a b l e s as most of the c o r r e l a t i o n c o e f f i c i e n t s i n Table 10 are l e s s than .3 and o n l y two are between .3 and .4. There i s q u i t e a remarkable d i f f e r e n c e between the c o r r e l a t i o n matrix and the estimated asymptotic c o r r e l a t i o n m a t r i x . One might have expected m u l t i c o l l i n e a r i t y on the b a s i s o f the c o r r e l a t i o n matrix as s e v e r a l o f the c o r r e l a t i o n c o e f f i c i e n t s are above .6, however, when the estimated asymptotic c o r r e l a t i o n matrix i s examined, the apparent c o l l i n e a r i t y i s reduced. The s i g n s o f the c o e f f i c i e n t s are as expected. One might have expected the s i g n o f the c u r r e n t a s s e t s t o s a l e s r a t i o t o be n e g a t i v e i n d i c a t i n g an improvement i n the hazard r a t e f o r an i n c r e a s e i n the r a t i o . However, c u r r e n t a s s e t s a l s o i n c l u d e the r e l a t i v e l y l e s s l i q u i d a s s e t s o f accounts r e c e i v a b l e and i n v e n t o r y . Accounts r e c e i v a b l e and i n v e n t o r y are g e n e r a l l y l e s s l i q u i d than cash f o r the simple f a c t t h a t i t takes time t o co n v e r t these a s s e t s i n t o cash. c u r r e n t a s s e t s = cash + accounts r e c e i v a b l e i n v e n t o r y s a l e s s a l e s s a l e s s a l e s We would expect t h a t as the accounts r e c e i v a b l e and i n v e n t o r y t o s a l e s r a t i o s i n c r e a s e t h a t the f i r m ' s r i s k s of being i n f i n a n c i a l d i f f i c u l t y would a l s o r i s e . An i n c r e a s e i n these two r a t i o s o f t e n r e f l e c t s an i n a b i l i t y t o c o l l e c t on c r e d i t s a l e s and or an i n a b i l i t y t o s e l l i n v e n t o r y . -66-A c c o r d i n g t o t h e e f f i c i e n t m a r k e t s h y p o t h e s i s , t h e f i r m ' s s t o c k p r i c e , i f a c t i v e l y t r a d e d , f u l l y r e f l e c t s t h e p u b l i c l y a v a i l a b l e i n f o r m a t i o n . T h e r e f o r e , we'would e x p e c t t h e two m a r k e t r e l a t e d r a t i o s , m a r k e t v a l u e t o d e b t and change i n m a r k e t v a l u e , t o be i m p o r t a n t v a r i a b l e s i n t h e i d e n t i f i c a t i o n o f b a n k r u p t s . As e x p e c t e d , t h e change i n m a r k e t v a l u e i s a s i g n i f i c a n t v a r i a b l e i n t h e Cox e s t i m a t i o n . The f a c t t h a t t h e change i n m a r k e t v a l u e i s n o t t h e d o m i n a n t v a r i a b l e i s n o t i n d i c a t i v e o f a f a i l u r e on t h e p a r t o f t h e e f f i c i e n t m a r k e t s h y p o t h e s i s . S t u d i e s o f t h e s t o c k p r i c e b e h a v i o u r o f f i r m s a p p r o a c h i n g b a n k r u p t c y (see S h i c k and Sherman) i n d i c a t e t h a t c h a n g e s i n m a r k e t v a l u e s i g n i f i c a n t l y p r e c e d e o b s e r v a b l e c h a n g e s i n t h e f i n a n c i a l d a t a . As t h e change i n m a r k e t v a r i a b l e a n a l y z e d i n t h i s s t u d y i s t h e o n e - y e a r change c a l c u l a t e d one y e a r p r i o r t o f a i l u r e , we w o u l d e x p e c t t h a t t h e major c h a n g e s i n t h e s t o c k p r i c e w o u l d a l r e a d y have o c c u r r e d o r w o u l d be masked by t h e v e r y l o n g t i m e p e r i o d u s e d . The p r o p o r t i o n a l h a z a r d s a s s u m p t i o n was t e s t e d u s i n g t h e g r a p h i c a l t e c h n i q u e d i s c u s s e d p r e v i o u s l y . F i g u r e 4 i l l u s t r a t e s t h e p l o t o f l o g o f minus l o g s u r v i v a l f u n c t i o n v e r s u s t i m e f o r t h e g r o u p o f f i r m s f i l i n g b a n k r u p t c y under t h e C h a n d l e r A c t and t h e i r m a t c h e s , and t h e s i m i l a r g r o u p f i l i n g under t h e Reform A c t . The r e s u l t s f o r d i f f e r e n t s t r a t a c a n be f o u n d i n A p p e n d i x I I I . T h e s e g r a p h s i n d i c a t e t h a t t h e p r o p o r t i o n a l h a z a r d s a s s u m p t i o n i s n o t i n a p p r o p r i a t e . -67-Th e h i g h degree of s i m i l a r i t y and o v e r l a p i n the comparative p l o t of the Chandler and Reform groups lends support t o the r e s u l t s of the u n i v a r i a t e t e s t of group d i f f e r e n c e s which found t h a t there d i d not appear t o be a s i g n i f i c a n t d i f f e r e n c e between the two groups. The s t r a t i f i c a t i o n o f the data i n t h i s a n a l y s i s a l l o w s each group t o have a d i f f e r e n t b a s e l i n e hazard r a t e ; but, the m u l t i p l i c a t i v e p a r t of the hazard f u n c t i o n should be the same i n each s t r a t a . T h e r e f o r e , i f p r o p o r t i o n a l hazards holds and the groups have d i f f e r e n t base l i n e hazard r a t e s we would expect Kay's p a r a l l e l l i n e s . As we observe l i n e s t h a t e s s e n t i a l l y o v e r l a p , there i s f u r t h e r evidence t h a t there does not e x i s t a s i g n i f i c a n t d i f f e r e n c e between the Chandler and Reform Act groups. G o o d n e s s - o f - f i t of the estimated hazard f u n c t i o n was e v a l u a t e d - g r a p h i c a l l y by p l o t t i n g the r e s i d u a l s a g a i n s t the cumulative hazard o f the r e s i d u a l s (see F i g u r e 5). As can be seen i n t h i s case the " f i t " l i n e was reasonably s t r a i g h t w i t h a slope of approximately 0.30 r a t h e r than the expected value of 1. O v e r a l l , the g o o d n e s s - o f - f i t does not appear t o be unreasonable as the " f i t " l i n e i s r e l a t i v e l y s t r a i g h t and the o v e r a l l r e g r e s s i o n i s s i g n i f i c a n t . As i t i s p o s s i b l e t h a t the very h i g h l e v e l of s i g n i f i c a n c e c o u l d be o v e r s t a t e d due t o an e s t i m a t i o n problem and t h e r e f o r e , the model w i l l a l s o be e v a l u a t e d on the b a s i s of i t s performance on non-sample data. -68-F i g u r e 4 LOG MINUS LOG SURVIVAL FUNCTION Cox P r o p o r t i o n a l H a z a r d M o d e l (1 y e a r p r i o r t o b a n k r u p t c y d a t a ) STRATA SYMBOL CHANDLER A REFORM B . + + + + + + . -1.8 + A*A AAAA*B AA B -2.7 + AAAA BB AAAA BBBB AAA*BBBBBBB A BB BBBB**B -3 .6 -4 .5 -5 .4 -6 .3 + B AAA + - BBBB A -- BB AA -- BB AA -- B A -+ B AA + - B A -- B A -- B AA -- B A -+ BB A + - B A -- B AA -- B A -- B A -+ B A + — BA — 70. 210 350 0.0 140 280 DAYS -69-Figure 5 GOODNESS OF FIT OVERALL SAMPLE, 1 YEAR PRIOR TO FAILURE . + + + + + XY. C u M H A Z R D .45 .36 .27 .18 .09 0.0 11 11 1 2 2 1 Y 1 - 2 -11 + . + . . .+. , . 30 1 1 0.0 . + . , .60 1 1 1 1 11 1 2 11 . + . , .90 R = .9807 P(R) 0.000 RESIDU 1.2 , . + . . 1.5 M E A N ST.DEV. R E G R E S S I O N L I N E RES.MS. X .57752 .46155 X= 3.3445*Y-.19973 .00837 Y .23239 .13534 Y= .28756*X+ .06632 719E-6 XVAR = 2 RESIDU VERSUS YVAR = 1 CUMHAZRD -70-D. FOUR-YEARS PRIOR ESTIMATION The Cox proportional hazards model was also estimated on the basis of the four-year prior data set. The results of the estimation are summarized i n Table 11 while the goodness-of-f i t graphs can be found i n figure 6. + + 1 Table 11. I | COX MODEL ESTIMATION I | 4 YEARS PRIOR TO FAILURE I I LOG LIKELIHOOD = -127.9253 I | GLOBAL CHI-SQUARE = 42.29 D.F.= 6 P-VALUE =0.0000 | | * STANDARD I VARIABLE COEFFICIENT ERROR COEFF./S.E. EXP(COEF) NETYTD4 -12.1462 3.0109 -4.0341 0.0000 INVCTA4 -6.3279 1.4204 -4.4548 0.0018Q NETYSL4 22.4321 6.7332 3.3316 4 * 10 TASLS4 1.6977 0.5012 3.3875 5.4615 DELMKT4 -0.4064 0.2468 -1.6464 0.6660 QKTA4 -3.0010 1.7569 -1.7082 0.0497 * NETYTD4 = Net income / Total debt. INVCTA4 = Invested c a p i t a l / Total assets. NETYSLS4 = Net income / Sales. TASLS4 = Total assets / Sales. DELMKT4 = Change i n market value. QKTA4 = Quick assets / Total assets. As one would expect, the set of predictors of long term v i a b i l i t y are d i f f e r e n t from those i d e n t i f i e d by the short term model. However, despite the high s i g n i f i c a n c e of the model, several of the c o e f f i c i e n t s are somewhat unexpected. -71-I t would seem u n l i k e l y t h a t i n c r e a s i n g net income t o t o t a l debt would have such a dramatic impact on the r i s k of f a i l u r e as the model would suggest. The c o e f f i c i e n t o f net income t o s a l e s i s a l s o very s u r p r i s i n g . One would normally expect t h a t an i n c r e a s e i n net income t o s a l e s would i n d i c a t e i n c r e a s i n g e f f i c i e n c y and t h e r e f o r e , should reduce the r i s k of f a i l u r e . However, a c c o r d i n g t o the r e s u l t s o f the model, t h i s i n c r e a s e net income t o s a l e s would a c t u a l l y i n c r e a s e the r i s k o f f a i l u r e d r a m a t i c a l l y . In an e f f o r t t o i d e n t i f y the source of these "strange" r e s u l t s , the c o r r e l a t i o n matrix and the estimated asymptotic c o r r e l a t i o n matrix of these s i x v a r i a b l e s was examined (See t a b l e 12). As can be seen from t h i s t a b l e there e x i s t s c o n s i d e r a b l e c o r r e l a t i o n between net income t o t o t a l debt and net income t o s a l e s , and t o change i n market va l u e . However, the l a r g e s t c o r r e l a t i o n c o e f f i c i e n t v a l u e s were s i m i l a r to those i n t a b l e 10 where there was a p p a r e n t l y l i t t l e m u l t i c o l l i n e a r i t y . In order t o ev a l u a t e the p o s s i b i l i t y of m u l t i c o l l i n e a r i t y , the estimated asymptotic c o r r e l a t i o n matrix was a l s o examined. The estimated asymptotic c o r r e l a t i o n between net income t o s a l e s and net income t o t o t a l debt i s very h i g h , n e a r l y . 8 i n a b s o l u t e v a l u e . The e s t i m a t i o n was, t h e r e f o r e , r e -c a l c u l a t e d u s i n g the f i v e v a r i a b l e s remaining a f t e r net income t o s a l e s was removed. Net income t o s a l e s was s e l e c t e d f o r e x c l u s i o n because the v a r i a b l e t o t a l a s s e t s to sales i s included. Therefore, with the new set of fi v e variables, no variables use the same components. The re s u l t s of t h i s re-estimation are found i n table 13. + + I Table 12. I I CORRELATION MATRIX (FOUR YEARS PRIOR DATA) | | NETYTD INVCTA NETYSLS TASLS DELMKT QKTA | I NETYTD 1 I j INVCTA .35 3 1 I | NETYSLS .734 .411 1 I | TASLS -.026 .134 .154 1 I I DELMKT .744 .156 .412 .030 1 I I QKTA .155 -.169 .069 .036 -.160 1 | | ESTIMATED ASYMPTOTIC CORRELATION MATRIX | I (FOUR YEARS PRIOR DATA) I | NETYTD INVCTA NETYSLS TASLS DELMKT QKTA | I NETYTD 1 I I INVCTA .237 1 I | NETYSLS -.783 -.408 1 I I TASLS -.170 -.176 .076 1 I | DELMKT .137 .016 -.243 -.213 1 I | QKTA .050 .332 -.043 -.139 .074 1 | + + -73-Table 13. COX MODEL, RE-ESTIMATION 4 YEARS PRIOR TO FAILURE LOG LIKELIHOOD = -153.2074 GLOBAL CHI-SQUARE = 36.90 D.F . = 5 P-VALUE = 0 .0000 * STANDARD VARIABLE COEFFICIENT ERROR COEFF./S.E. EXP (COEF) NETYTD4 -3.7497 2.0162 -1.8598 0 .0235 INVCTA4 -3.7199 1.2784 -2.9099 0 .0242 TASLS4 1.3512 0.5041 2.6804 3 .8622 DELMKT4 -0.2799 0.2248 -1.2453 0 .7558 QKTA4 -2.8003 1.6581 -1.6889 0 .0608 NETYTD4 = Net income / Total debt. INVCTA4 = Invested c a p i t a l / Total assets. TASLS4 = Total assets / Sales • DELMKT4 = Change i n market value. QKTA4 = Quick assets / Total assets. With the variable net income to sales omitted, the variables now have the expected signs and the impact of a change i n each variable i s more reasonable. When the goodness-of-fit was evaluated graphically, there was l i t t l e difference from figure 6. Therefore, i t would appear that c o l l i n e a r i t y between the variables has a serious impact on the c o e f f i c i e n t s of those variables but a r e l a t i v e l y minor impact on the " f i t " of the model. -74-Figure 6 GOODNESS OF FIT 4 YEAR PRIOR . + + + + XY + .45 + 1 1 1 11 1 11 .36 + 1 11 C - 1 U 11 M 1 H .27 + 11 A - 1 Z - 11 R - 2 D - 1 .18 + 11 11 1 11 2 . 0 9 + 1 Y 11 X 1 - 1 -11 0.0 + . + + + + + + . , .30 .90 1.5 0.0 .60 1.2 RESIDU R = .9720 P(R) 0.000 MEAN X .46036 Y .23423 ST.DEV. .37587 .13108 R E G R E S S I O N L I N E X= 2 . 7 8 7 0 * Y - . 1 9 2 4 3 Y= . 3 3 8 9 8 * X + . 0 7 8 1 8 RES.MS. .00802 976E-6 -75 -E. T IED OBSERVATIONS The i m p a c t o f t i e d o b s e r v a t i o n s , f i r m s w i t h i d e n t i c a l t i m e s u n t i l b a n k r u p t c y , on t h e Cox p r o p o r t i o n a l h a z a r d s model was e xamined by e s t i m a t i n g t h e model on t h e same sample b u t now u s i n g t i m e t o f a i l u r e m easured i n months. T h i s change i n t h e t i m e p e r i o d r e s u l t e d i n most o f t h e o b s e r v e d t i m e s u n t i l f a i l u r e b e i n g t i e d . The e s t i m a t i o n was c a r r i e d o u t u s i n g t h e BMDP s t a t i s t i c a l p a c k a g e w i t h no c o r r e c t i o n f a c t o r s f o r t h e t i e d o b s e r v a t i o n s . No c o r r e c t i o n s were u s e d i n o r d e r t o s i m u l a t e t h e e x t r e m e c a s e c a u s e d by t h e t i e d o b s e r v a t i o n s i n o r d e r t o compare t h e s e r e s u l t s t o t h o s e o f t h e " c o r r e c t " no-t i e s m o d e l . Any r e a s o n a b l e c o r r e c t i o n s w o u l d , t h e r e f o r e , r e s u l t i n e s t i m a t e s w h i c h w o u l d f a l l b etween t h e s e two e x t r e m e s . The r e s u l t s o f t h i s u n c o r r e c t e d t i e d o b s e r v a t i o n s e s t i m a t i o n a r e p r e s e n t e d i n T a b l e 14. Once a g a i n , t h e r e g r e s s i o n i s h i g h l y s i g n i f i c a n t and t h e v a r i a b l e c o e f f i c i e n t s a l l h a v e t h e e x p e c t e d s i g n , however, t h e v a r i a b l e s i d e n t i f i e d by t h e s t e p w i s e p r o c e d u r e a r e v e r y d i f f e r e n t f r o m t h o s e i d e n t i f i e d i n t h e more c o r r e c t model w i t h o u t t i e s i n t h e o b s e r v a t i o n s . The p r o p o r t i o n a l i t y a s s u m p t i o n was a l s o e v a l u a t e d , and showed t h a t t h e h a z a r d p r o p o r t i o n a l i t y a s s u m p t i o n was n o t u n r e a s o n a b l e . The p r o b l e m c a u s e d by t h e many t i e d o b s e r v a t i o n s becomes a p p a r e n t when one e x a m i n e s t h e g o o d n e s s - o f - f i t p l o t i n f i g u r e 7. As c a n be s e e n i n t h i s g r a p h , t h e " f i t " l i n e i s f a r f r o m -76-being l i n e a r and i n f a c t appears t o be two l i n e s r a t h e r than one. + + I Table 14. I | "TIED" OBSERVATIONS I RESULTS OF COX ESTIMATION (1 year p r i o r ) LOG LIKELIHOOD = -141.6433 GLOBAL CHI -SQUARE =76. 09 D.F. = 6 P-VALUE =0.0000 STANDARD VARIABLE COEFFICIENT ERROR COEFF./S.E. EXP(COEFF.) CFTD1 -1.8776 0.6206 -3.0255 0.1529 CACL1 -0.9892 0.3075 -3.2172 0.3719 INVSLS1 4.7322 1.0407 4.5470 113.5419 EBIT1 -4.6722 1.5361 -3.0417 0.0094 DELMKT1 -1.8206 0.9886 -1.8416 0.1619 DELMRG1 4.4704 2.2057 2.0268 87.3882 I * I I CFTD1 = Cash flow / t o t a l debt. CACL1 = Current R a t i o I j INVSLS1 = Inventory / s a l e s EBIT1 = Earnings / a s s e t s ! j DELMKT1 = Change i n market v a l u e DELMRG1 = Margin change I + + When compared t o the n o - t i e s model, the t i e d model has r e s u l t e d i n a very d i s t o r t e d e s t i m a t i o n . The v a r i a b l e s i d e n t i f i e d by the stepwise procedure and the g o o d n e s s - o f - f i t r e s u l t s i n d i c a t e t h a t t i e d o b s e r v a t i o n s can cause very d i s t o r t e d e s t i m a t e s and p o o r l y f i t t i n g e stimated hazard f u n c t i o n s . I t would t h e r e f o r e , seem t h a t the Cox model, when c o r r e c t e d f o r t i e d o b s e r v a t i o n s , appears t o model the i n t e r a c t i o n s between d i f f e r e n t components of the f i r m s f i n a n c i a l s t r u c t u r e as they r e l a t e t o bankruptcy. The model -77 -i d e n t i f i e s f i n a n c i a l v a r i a b l e s w h i c h one w o u l d i n t u i t i v e l y e x p e c t t o have an e f f e c t on s h o r t t e r m v i a b i l i t y i n t h e one y e a r p r i o r c a s e , w h i l e a l s o i d e n t i f y i n g more l o n g - t e r m s u r v i v a l r e l a t e d r a t i o s i n t h e f o u r - y e a r p r i o r c a s e . The a d e q u a c y o f t h e Cox p r o p o r t i o n a l h a z a r d s model s u r v i v a l f u n c t i o n e s t i m a t e s w i l l be e x a m i n e d and compared t o t h e r e s u l t s o f t h e d i s c r i m i n a n t a n a l y s i s . -78-Figure 7. GOODNESS OF FIT, TIED OBSERVATIONS , + . . X . . . . + + . . . Y . . . + . 5.6 + 11 12 2 11 4.9 + 141 2111 1 1 1 1 4.2 + 11 2 1 3.5 + 2 C - 1 U M H A 2.8 + Z R D 2.1 + 4 - 1 1.4 + .70 + Y 0.0 +Q77526 2121 1111 11 .+.X + + + + . 0.0 .40 1.2 RESIDU . + + . 2.0 V I I I . MODEL COMPARISON The performance of the Cox model was ev a l u a t e d u s i n g two c r i t e r i a : f i r s t , accuracy o f c l a s s i f i c a t i o n or p r e d i c t i o n and secondly, d e s c r i p t i v e power. The base l i n e l e v e l o f performance was t h a t o f the d i s c r i m i n a n t a n a l y s i s model. The c l a s s i f i c a t i o n and p r e d i c t i o n c a p a b i l i t y of the d i s c r i m i n a n t and Cox models was eva l u a t e d by a p p l y i n g the estimated one year p r i o r f u n c t i o n s t o the data from f o u r , t h r e e , two and one year p r i o r t o f a i l u r e . The r e s u l t s are summarized i n t a b l e 15. As the one year p r i o r d ata s e t was used t o develop the models, the r e s u l t s from t h a t time p e r i o d cannot be used t o make any i n f e r e n c e s about the p r e d i c t i v e power of the models. The one year p r i o r r e s u l t s are presented as they h e l p i l l u s t r a t e the improvement i n model c l a s s i f i c a t i o n as we move c l o s e r to f a i l u r e . U n l i k e d i s c r i m i n a n t a n a l y s i s , the Cox model does not l e n d i t s e l f w e l l t o the problem o f c l a s s i f y i n g f i r m s as bankrupt or non-bankrupt as one i s presented with the problem of how to c l a s s i f y a s p e c i f i c expected time to f a i l u r e as i n d i c a t i v e o f bankruptcy or non-bankruptcy. In t h i s paper, a f i r m was c l a s s i f i e d as bankrupt i f i t s expected time u n t i l f a i l u r e was l e s s than 350 days. The value o f 350 days are a r b i t r a r i l y chosen as a l l but one of the bankrupt f i r m s had f i l e d w i t h i n 350 days of the end of the p r i o r p e r i o d . -80-+ + Table 15 (a) MODEL PERFORMANCE DISCRIMINANT ANALYSIS 4 Years p r i o r C l a s s i f i c a t i o n S u r v i v o r Bankrupt T o t a l S u r v i v o r 66 31 97 Bankrupt 2 10 12 3 Years p r i o r C l a s s i f i c a t i o n S u r v i v o r Bankrupt T o t a l S u r v i v o r 62 27 89 Bankrupt 6 14 20 2 Years p r i o r S u r v i v o r Bankrupt T o t a l C l a s s i f i c a t i o n S u r v i v o r 63 15 78 Bankrupt 5 26 31 1 Year p r i o r S u r v i v o r Bankrupt T o t a l C l a s s i f i c a t i o n S u r v i v o r 61 8 69 Bankrupt 7 33 40 + + -81-+ + Table 15 (b) MODEL PERFORMANCE COX MODEL: 4 Years p r i o r S u r v i v o r Bankrupt T o t a l C l a s s i f i c a t i o n S u r v i v o r 57 21 78 Bankrupt 11 20 31 3 Years p r i o r S u r v i v o r Bankrupt T o t a l C l a s s i f i c a t i o n S u r v i v o r 60 19 79 Bankrupt 8 22 30 2 Years p r i o r S u r v i v o r Bankrupt T o t a l C l a s s i f i c a t i o n S u r v i v o r 58 14 72 Bankrupt 10 27 37 1 Year p r i o r S u r v i v o r Bankrupt T o t a l C l a s s i f i c a t i o n S u r v i v o r 57 3 60 Bankrupt 11 38 49 + + As can be seen from t a b l e 15 (a,b), the a b i l i t y o f both models t o f o r e t e l l bankruptcy d e c l i n e d as the time u n t i l f a i l u r e i n c r e a s e d . I t would appear t h a t both the d i s c r i m i n a n t and Cox models p r e d i c t t h a t bankruptcy w i l l occur before the -82-a c t u a l event o c c u r s . In other words, these models appear to underestimate the time u n t i l bankruptcy. For example, d i s c r i m i n a n t a n a l y s i s c l a s s i f i e d 14 f u t u r e bankrupts as bankrupt, 4 years p r i o r t o the p e t i t i o n being f i l e d while the Cox model gave expected times u n t i l f a i l u r e o f l e s s than 350 days to 20 f i r m s 4 years b e f o r e they f i l e d . The f i l i n g o f a bankruptcy p e t i t i o n i s u s u a l l y the l a s t stage i n a f i r m ' s death t h r o e s . T h e r e f o r e , we would expect that the t r u e f a i l u r e o f the f i r m had o c c u r r e d a t some p o i n t b e f o r e the p e t i t i o n was f i l e d . Consequently, i t i s not s u r p r i s i n g t h a t both the d i s c r i m i n a n t and Cox models tend t o i d e n t i f y bankrupts b e f o r e they become l e g a l bankrupts. In order t o assess the d e s c r i p t i v e power of the Cox model a random sample of four f i r m s (two bankrupt and two s u r v i v o r s ) was drawn from the o r i g i n a l sample. The s u r v i v a l f u n c t i o n of each f i r m was then p l o t t e d a g a i n s t time. In order to see the changes i n the s u r v i v a l f u n c t i o n over time and to e v a l u a t e the v a l i d i t y of the estimated p r o p o r t i o n a l hazard model on data o u t s i d e the data s e t used t o estimated the model, a f u n c t i o n was c a l c u l a t e d a t t h r e e , two and one year p r i o r t o f a i l u r e u s i n g the Cox one year p r i o r estimated c o e f f i c i e n t s . These g r a p h i c a l d e s c r i p t i o n s , found i n f i g u r e s 8 through 11 i n Appendix I, of the f i r m s ' s u r v i v a l f u n c t i o n s were obtained by p l o t t i n g the f i r m s p r o b a b i l i t y o f s u r v i v i n g a t l e a s t as long as ' t ' a g a i n s t ' t ' f o r each year p r i o r to -83 -f a i l u r e . One w o u l d e x p e c t t h e s u r v i v a l f u n c t i o n s o f f i r m s w h i c h were n o n - f a i l u r e s a t t h e t i m e o f a n a l y s i s t o be c l o s e t o one f o r any ' t ' a s t h e s e f i r m s w o u l d have a v e r y h i g h p r o b a b i l i t y o f s u r v i v i n g a t l e a s t a s l o n g a s ' t ' . I n c o n t r a s t , one wou l d e x p e c t t h e s u r v i v a l p l o t o f b a n k r u p t f i r m s t o d e c l i n e a s ' t ' i n c r e a s e s , and p e r h a p s t o d e c l i n e f a s t e r t h e c l o s e r * t ' was t o t h e t i m e o f a c t u a l f a i l u r e . I n g e n e r a l , t h e s e g r a p h s e x h i b i t t h e e x p e c t e d r e s u l t s . They g i v e one a " p i c t u r e " o f how a f i r m ' s p r o b a b i l i t y o f s u r v i v i n g c h a n g e s o v e r t i m e . The d i s c r i m i n a n t a n a l y s i s , i n c o n t r a s t , m e r e l y g i v e s one a s c o r e w h i c h i n d i c a t e s p r o b a b l e g r o u p membership. The most u n e x p e c t e d r e s u l t was t h a t o f f i r m number 297882 ( f i g u r e 11). As t h i s f i r m i s one o f t h e s u r v i v o r s , one woul d n o t e x p e c t t o s e e s u r v i v a l f u n c t i o n s e x h i b i t i n g t h i s t y p e o f b e h a v i o u r w h i c h i s v e r y s i m i l a r t o what one would e x p e c t o f a f a i l u r e . ETZ L a v u d , f i r m number 297882, i s an I s r a e l i f i r m w h i c h i s l i s t e d on t h e A m e r i c a n S t o c k E x c h a n g e . The s u r v i v a l f u n c t i o n s p r e s e n t e d h e r e r e p r e s e n t t h e e a r l y t o mid 1970's, and i t i s p e r h a p s s i g n i f i c a n t t h a t ETZ Lavu d was o n l y l i s t e d o n t h e AMEX i n 1972. F u r t h e r e x a m i n a t i o n f a i l e d t o r e v e a l any o t h e r p o s s i b l e r e a s o n s f o r t h i s somewhat u n e x p e c t e d s u r v i v a l f u n c t i o n b e h a v i o u r . The r e s u l t s o f a p p l y i n g t h e 1-year p r i o r l i n e a r d i s c r i m i n a n t f u n c t i o n t o t h e s e f i r m s a r e p r e s e n t e d i n t a b l e 16. -84-I t would t h e r e f o r e appear, i n the case of these four f i r m s , t h a t the Cox model and the d i s c r i m i n a n t model y i e l d very s i m i l a r r e s u l t s . In both models, the f u t u r e bankrupt f i r m s d i d not appear t o be i n the bankruptcy group u n t i l one year p r i o r to f a i l u r e . The Cox model's graphs show a d e c l i n e i n the p r o b a b i l i t y o f s u r v i v a l beginning u s u a l l y i n the second year p r i o r t o f i l i n g the bankruptcy p e t i t i o n . Both the Cox and D i s c r i m i n a n t models show t h a t f i r m #297882 was i n t r o u b l e over the time p e r i o d i n q u e s t i o n . D i s c r i m i n a n t a n a l y s i s c l a s s i f i e s i t as a member of the bankrupt group i n a l l three p r i o r p e r i o d s , and, the s u r v i v a l f u n c t i o n graphs show t h a t the f i r m was i n t r o u b l e over those same y e a r s . + + Table 16 LINEAR DISCRIMINANT FUNCTION SCORES Firm: #042078 #564402 #868168 #297882 Three years p r i o r S u r v i v o r Score 7.26 3.09 2.43 9.07 Bankrupt Score 4.84 0.93 -3.15 9.99 Two years p r i o r S u r v i v o r Score 8.29 1.46 2.91 10.38 Bankrupt Score 6.70 1.04 -2.56 11.19 One year p r i o r S u r v i v o r Score 4.01 2.64 4.89 11.17 Bankrupt Score 9.50 6.01 1.33 12.24 C l a s s i f y o b s e r v a t i o n i n t o whichever group's score i s the h i g h e s t . + • + -85-T h e r e f o r e , i t would appear t h a t the Cox model i s able to p r o v i d e i n f o r m a t i o n t h a t the l i n e a r d i s c r i m i n a n t model cannot. E s s e n t i a l l y the d i s c r i m i n a n t model p r o v i d e s a s i n g l e benchmark which can be used t o c l a s s i f y f i r m s as e i t h e r bankrupt, non-bankrupt, or indeterminate. The Cox model i n c o n t r a s t , p r o v i d e s a p r o b a b i l i t y d i s t r i b u t i o n of the time u n t i l f a i l u r e from which an expected time u n t i l f a i l u r e can be d e r i v e d . For example, ETZ Lavud, a s u r v i v o r , was i d e n t i f i e d by both models as a problem. Acco r d i n g to the d i s c r i m i n a n t a n a l y s i s , the f i r m i s most probably a bankrupt. However, the Cox e s t i m a t i o n f i n d s t h a t a t the beginning of the one year p r i o r p e r i o d , the company had a p r o b a b i l i t y of s u r v i v i n g longer than 353 days of over 20%. The company went on to s u r v i v e f o r a t l e a s t ten more y e a r s . -86-IX. SUMMARY AND CONCLUSION T h i s paper has eval u a t e d the Cox p r o p o r t i o n a l hazard model's a p p l i c a b i l i t y t o the problem o f bankruptcy p r e d i c t i o n . The Cox model o f f e r s s e v e r a l advantages over the more t r a d i t i o n a l p r e d i c t i o n models. T h i s model does not depend on the very r e s t r i c t i v e d i s t r i b u t i o n a l assumptions of m u l t i v a r i a t e n o r m a l i t y and i t produces an estimated p r o b a b i l i t y d i s t r i b u t i o n o f times u n t i l f a i l u r e from which an expected time o f f a i l u r e can be determined. In g e n e r a l , most t r a d i t i o n a l models o f f a i l u r e o n l y estimate a p r o b a b i l i t y of f a i l u r e w i t h i n a g i v e n time p e r i o d . Two major areas o f concern i n the a p p l i c a t i o n o f the Cox model are m u l t i c o l l i n e a r i t y and " t i e d " s u r v i v a l time o b s e r v a t i o n s . M u l t i c o l l i n e a r i t y appears t o r e s u l t i n s e v e r e l y d i s t o r t e d estimated c o e f f i c i e n t s , but, appears t o have a r e l a t i v e l y minor a f f e c t on the o v e r a l l " f i t " of the model. " T i e d " o b s e r v a t i o n s i n c o n t r a s t cannot be handled by the Cox model as the model makes use o f the temporal o r d e r i n g o f events i n i t s e s t i m a t i o n procedure. U n l i k e m u l t i c o l l i n e a r i t y , an i n c o r r e c t treatment o f " t i e d " o b s e r v a t i o n s r e s u l t s i n a s e v e r e l y d i s t o r t e d model. Consequently, any a p p l i c a t i o n o f the model must take i n t o account these p o t e n t i a l problems. In t h i s paper, the Cox p r o p o r t i o n a l hazard model was a p p l i e d t o a sample of 109 f i r m s , 41 of whom f i l e d p e t i t i o n s f o r bankruptcy between 1972 and 1985. As t h i s time p e r i o d i n c l u d e d a major change t o the bankruptcy a c t , the two -87-groups of bankrupt f i r m s were examined to t e s t the hypothesis t h a t no d i f f e r e n c e e x i s t e d between f i r m s f i l i n g under the two bankruptcy a c t s . The r e s u l t s of the K r u s k a l - W a l l i s t e s t s and the s t r a t i f i e d Cox model t e s t s , i n d i c a t e t h a t there does not appear t o be a s i g n i f i c a n t d i f f e r e n c e between the two groups of bankrupts. D i s c r i m i n a n t a n a l y s i s was performed on the bankrupt and non-bankrupt groups t o e s t a b l i s h a base l i n e l e v e l o f performance. I f the Cox model i s of v a l u e , i t must o f f e r something beyond what i s a l r e a d y a v a i l a b l e . The Cox model was estimated f o r one year and four years p r i o r t o f a i l u r e . The degree of f i t and the p r o p o r t i o n a l hazards assumption appeared t o be s a t i s f i e d . In both the one and four year models, the i d e n t i f i e d v a r i a b l e s had the s i g n one would i n t u i t i v e l y expect. The longer term model (4 year p r i o r ) i d e n t i f i e d d i f f e r e n t v a r i a b l e s from the s h o r t term model as being important f a c t o r s i n the s u r v i v a l e x p e r i e n c e . As one would expect, the p r o p o r t i o n a l hazards model estimated i n t h i s more d i v e r s e i n d u s t r i a l s e t t i n g d i d not perform as w e l l as the model estimated by Lane, Looney, and Wansley [1986]. T h i s d e c l i n e i n performance i s not s u r p r i s i n g as the Lane study ev a l u a t e d performance i n a very narrow i n d u s t r i a l d e f i n i t i o n , o n l y the F e d e r a l Deposit Insurance C o r p o r a t i o n i n s u r e d banks were evaluated where the assumption o f a ' r e p r e s e n t a t i v e ' or average hazard r a t e i m p l i c i t i n the p r o p o r t i o n a l hazards model would seem more p l a u s i b l e . -88-Th e c o n c l u s i o n s drawn f r o m t h i s a n a l y s i s a r e t h a t i f t h e s o l e p u r p o s e o f t h e model i s t o c l a s s i f y f i r m s a s p o t e n t i a l b a n k r u p t s , t h e n t h e d i s c r i m i n a n t a n a l y s i s b a s e d model i s more a p p r o p r i a t e . The c l a s s i f i c a t i o n p e r f o r m a n c e o f t h e d i s c r i m i n a n t a n a l y s i s b a s e d model was shown t o be s u p e r i o r i n a l l p e r i o d s t o t h a t o f t h e Cox m o d e l . T h i s r e s u l t i s n o t s u r p r i s i n g as c e r t a i n v e r y r e s t r i c t i v e a s s u m p t i o n s were made i n e v a l u a t i n g t h e c l a s s i f i c a t i o n a b i l i t y o f t h e Cox m o d e l . I t was shown t h a t t h e u s e o f t h e Cox model p r i m a r i l y f o r c l a s s i f i c a t i o n p u r p o s e s d o e s n o t e x p l o i t t h e m o d e l ' s f u l l p o t e n t i a l . U n l i k e t h e d i s c r i m i n a n t a n a l y s i s model w h i c h y i e l d s a s i n g l e s c o r e and a c l a s s i f i c a t i o n o f e i t h e r s u r v i v o r , b a n k r u p t o r i n d e t e r m i n a t e , t h e e s t i m a t e d Cox model p r o d u c e s t h e d i s t r i b u t i o n o f e x p e c t e d t i m e s u n t i l f a i l u r e . T h e s e s u r v i v a l f u n c t i o n s c a n g i v e a v e r y i n t e r e s t i n g and a u s e f u l p i c t u r e o f t h e f i r m ' s s u r v i v a l p o t e n t i a l o v e r a p e r i o d o f t i m e . The c o n c l u s i o n drawn f r o m t h i s a n a l y s i s i s t h a t t h e Cox m odel i s a p p l i c a b l e i n t h e c a s e o f c o m m e r c i a l and i n d u s t r i a l b a n k r u p t c y . The model p r o v i d e s a d d i t i o n a l and u s e f u l i n f o r m a t i o n t o t h a t p r o v i d e d by t h e commonly u s e d d i s c r i m i n a n t a n a l y s i s b a s e d m o d e l s . The i n t u i t i v e a p p e a l o f t h e Cox m o d e l , i t ' s p e r f o r m a n c e and a p p l i c a b i l i t y t o b a n k r u p t c y p r e d i c t i o n , i n d i c a t e s t h a t f u r t h e r r e s e a r c h i s w a r r a n t e d . -89-F O O T N O T E S I. INTRODUCTION ^ Derived from the Economic Report of the P r e s i d e n t (Transmitted t o Congress, February 1986), p. 359. I I . BANKRUPTCY Harlan P i a t t , Why Companies F a i l (Lexington, Mass. : C Heath Company, 1985), p. 7. 2 P i a t t , p. 8. 3 U. S. Congress, Report of the Commission on the  Bankruptcy Laws of the United S t a t e s , P a r t 1 (Washington, : GPO, 1973) , p. 63. 4 Bankruptcy Commission, p 63. ^ John E. Mulder and Leon S. Forman, Bankruptcy and  Arrangement Proceedings ( P h i l a d e l p h i a : J o i n t Committee on Con t i n u i n g Legal Education, 1964), p. 4. 6 Bankruptcy Commission, P- 183. 7 Bankruptcy Commission, P- 262. 8 Mulder, pp. 16-19. 9 Mulder, p. 16. 10 Mulder, p. 21. 11 Mulder, pp. 22-29. 12 Mulder, p. 143. 13 Bankruptcy Commission, PP. 243-244. 14 Bankruptcy Commission, P- 244. 15 Bankruptcy Commission, P- 245. 16 Bankruptcy Commission, P- 244. 17 Bankruptcy Commission, pp. 244-245. -90-18 Bankruptcy Commission, p. 245. 19 Bankruptcy Commission, p. 245. 20 Bankruptcy Commission, pp. 245-247. 21 Bankruptcy Commission, p. 2. 22 Bankruptcy Commission, p. 3. 23 I n t e r n a t i o n a l Insolvency (K l y n v e l d Main Goerdeler, 1985), p. 154. 2 4 K. M. G., p. 157. 25 Edward I . Altman, Corporate F i n a n c i a l D i s t r e s s (New York: John Wiley & Sons, 1983), p. 28. 2 6 Bankruptcy Commission, p. 136. 27 Bankruptcy Commission, p. 144. 2 8 Altman, Corporate F i n a n c i a l D i s t r e s s , 1983. 29 M a r t i n Edmonds, "Market Ideology and Corporate Power; The United S t a t e s " i n I n d u s t r i a l C r i s e s , Eds. Kenneth Dyson and Stephen W i l k s (New York: S t . M a r t i n ' s P r e s s , 1983), p. 100. I I I . MODELS COMMONLY USED 1 Richard A. Shick and Lawrence F. Sherman, "Bank Stock P r i c e s as an E a r l y Warning System f o r Changes i n C o n d i t i o n " (Journal of Bank Research, Autumn 1980), p. 145. 2 Leon Korobow and David P. Stuhr, "The Relevance of Peer Groups i n E a r l y Warning A n a l y s i s " (Economic Review, F e d e r a l Reserve Bank of A t l a n t a , November 1983) , p. 28. 3 Robert E i s e n b e i s , " P i t f a l l s i n the A p p l i c a t i o n o f D i s c r i m i n a n t A n a l y s i s i n Bus i n e s s , Finance, and Economics" (Journal of Finance, 32, 1977), p. 883. 4 Edward Altman, " F i n a n c i a l R a t i o s , D i s c r i m i n a n t A n a l y s i s and the P r e d i c t i o n o f Corporate Bankruptcy" (Journal of  Finance, 33, 1968), p 591. ^ Altman, " F i n a n c i a l R a t i o s . . .". Altman, " F i n a n c i a l R a t i o s . . .". -91-7 E i s e n b e i s , p. 876-893. g D a n i e l M a r t i n , " E a r l y Warning of Bank F a i l u r e " (Journal  of Banking and Finance, 1, 1977), p 249,276. 9 Robert West, "A F a c t o r - A n a l y t i c Approach t o Bank C o n d i t i o n " (Journal of Banking and Finance, 9, 1985), p. 253-256. Shick and Sherman, p. 137. 1 1 Anthony Santomero and Joseph V i n s o , " E s t i m a t i n g the P r o b a b i l i t y of F a i l u r e f o r Commercial Banks and the Banking System" (Journal of Banking and Finance, 1, 1977), pp. 187 12 C r a i g Johnson, "Ratio A n a l y s i s and the P r e d i c t i o n of Firm F a i l u r e " (Journal of Finance, 25, 1970), p. 1166. 13 Santomero and Vi n s o , pp. 185--189. 14 Santomero and V i n s o , p. 188. 15 Santomero and V i n s o , p. 196, 200- 203. 16 Santomero and V i n s o , p. 203. 17 Santomero and V i n s o , pp. 193--195. 18 W i l l i a m Lane, Stephen Looney and James Wansley, "An A p p l i c a t i o n of the Cox P r o p o r t i o n a l Hazards Model t o Bank F a i l u r e " (Journal of Banking and Finance, 10, 1986), pp. 512-513. 19 Lane e t a l , p. 513. 20 Lane e t a l , p. 516. 2 1 Lane e t a l , pp.528-529. IV. PLAN OF ANALYSIS 1 T h i s c l a s s i f i c a t i o n scheme i s based on Beaver, p. 78. 2 Sidney Davidson e t a l , F i n a n c i a l Accounting (Holt R i n e h a r t , Toronto, 1979), p. 162. 3 W i l l i a m H. Beaver, " F i n a n c i a l R a t i o s as P r e d i c t o r s of F A i l u r e " ( E m p i r i c a l Research i n Accounting, S e l e c t e d S t u d i e s , 1966), pp. 101-102. P i a t t , p.34. V. SAMPLE CHARACTERISTICS 1 Leonard M a r a s c u i l o and J o e l L e v i n , M u l t i v a r i a t e  S t a t i s t i c s i n the S o c i a l S ciences (Brooks Cole P u b l i s h i n g Comapany, Monterey, 1983), p. 203. 2 Lyman Ot t and David K. H i l d e b r a n d , S t a t i s t i c a l T h i n k i n g  f o r Managers (Duxbury P r e s s , Boston, 1983), p. 361. VI. DISCRIMINANT ANALYSIS 1 W i l l i a m Cooley and Paul Lohnes, M u l t i v a r i a t e Procedures  f o r the B e h a v i o u r a l Sciences (John Wiley & Sons, New York, 1962) , p. 117. 2 0. Maurice Joy and John O . T o l l e f s o n , "On The F i n a n c i a l A p p l i c a t i o n s of D i s c r i m i n a n t A n a l y s i s " (Journal of F i n a n c i a l  and Q u a n t i t a t i v e A n a l y s i s 10, 1975), 72~4~. Joy and T o l l e f s o n , 1975. 4 Peter Lachenbruch, D i s c r i m i n a n t A n a l y s i s (Hafner P r e s s , New York, 1975), p. 40. 5 Lachenbruch, p. 33. g Lachenbruch, p. 33. 7 Altman, D i s t r e s s , p.106. VI I . THE COX MODEL 1 Walter C a r t e r , Galen Wampler, and Donald S t a b l e i n , Regression A n a l y s i s of S u r v i v a l Data i n Cancer Chemotheraphy (John Wiley & Sons, New York, 1962), pp. 39-40. 2 C a r t e r e t a l , p. 40. 3 R. Kay, " P r o p o r t i o n a l Hazard Regression Models and the A n a l y s i s of Censored Data" (Applied S t a t i s t i c s , 26, 1977) , p. 227. 4 C a r t e r e t a l , p. 48. -93-5 Lane e t a l , p. 514. C a r t e r e t a l , p. 49. 7 Regina Elandt-Johnson and Norman Johnson, S u r v i a l  Models and Data A n a l y s i s (John Wiley & Sons, New York, 1980), p. 9. g Elandt-Johnson and Johnson, p. 8. 9 Lane e t a l , p. 530. 1 0 Kay, p. 231. 1 1 Kay, p. 230. 1 2 Kay, p. 230-231. 13 W. J . Dixon, BMDP S t a t i s t i c a l Software ( U n i v e r s i t y of C a l i f o r n i a P r e s s , B e r k e l y , 1983), p. 685. B I B L I O G R A P H Y Altman, Edward I. " F i n a n c i a l R a t i o s , D i s c r i m i n a n t A n a l y s i s and the P r e d i c t i o n o f Corporate Bankruptcy". J o u r n a l of Finance, 33 (1968), 589-609. Corporate F i n a n c i a l D i s t r e s s . New York: John Wiley & Sons, 1983. Beaver, W i l l i a m H. " F i n a n c i a l R a t i o s as P r e d i c t o r s o f F a i l u r e " . E m p i r i c a l Research i n Accounting: S e l e c t e d  S t u d i e s 1966. pp. 71-111. Bennett, Spencer and David Bowers. An I n t r o d u c t i o n to  M u l t i v a r i a t e Techniques f o r S o c i a l and B e h a v i o u r a l  S c i e n c e s . New York: H a l s t e d P r e s s , 1977. C a r t e r , Walter H. J r . , Galen L. Wampler and Donald M. S t a b l e i n . R e g r e s s i o n A n a l y s i s of S u r v i v a l Data i n  Cancer Chemotherapy. i n S t a t i s t i c s : Textbooks and  Monographs. V o l 44. Eds: D. B. Owen and R. G. C o r n e l l . New York: Marcel Dekker Inc, 1983. Cooley, W i l l i a m W. and Paul R. Lohnes. M u l t i v a r i a t e Procedures f o r the B e h a v i o r a l S c i e n c e s . New York: John Wiley & Sons, 1962. Cox, D. R. "Regression Models and L i f e - T a b l e s " . J o u r n a l of  the Royal S t a t i s t i c a l S o c i e t y , No. 2 (1972), 187-202. Davidson, Sidney, C.L. M i t c h e l l , Clyde S t i c k n e y , and Roman L. W e i l . F i n a n c i a l A c counting. Toronto: H o l t R i n e h a r t and Winston of Canada L i m i t e d . 1979. Dixon, W. J . , C h i e f E d i t o r . BMDP S t a t i s t i c a l Software. B e r k e l e y : U n i v e r s i t y o f C a l i f o r n i a P r e s s . 1983. Economic Report of the P r e s i d e n t . Transmitted t o Congress, February 1986. Edmonds, M a r t i n . "Market Ideology and Corporate Power: The United S t a t e s " . i n I n d u s t r i a l C r i s e s . Eds. Kenneth Dyson and Stephen W i l k s . New York: S t . Ma r t i n ' s Press, 1983, pp. 67-101. E i s e n b e i s , Robert A. " P i t f a l l s i n the A p p l i c a t i o n of D i s c r i m i n a n t A n a l y s i s i n Business, Finance, and Economics". J o u r n a l of Finance, 32 (1977), 875-900. Elandt-Johnson, Regina C. and Norman L. Johnson. S u r v i v a l Models and Data A n a l y s i s . New York: John Wiley & Sons, 1980. I n d u s t r i a l CompuStat Codebook. Standard and Poor's CompuStat S e r v i c e s , 1986 E d i t i o n . I n t e r n a t i o n a l Insolvency. K l y n v e l d Main Goerdeler, 1985. Johnson, C r a i g J . "Ratio A n a l y s i s and the P r e d i c t i o n o f Firm F a i l u r e " . J o u r n a l of Finance, 25 (1970), 1166-1168. Joy, 0. Maurice and John 0. T o l l e f s o n . "On the F i n a n c i a l A p p l i c a t i o n s of D i s c r i m i n a n t A n a l y s i s " . J o u r n a l of  F i n a n c i a l and Q u a n t i t a t i v e A n a l y s i s , 10 (1975), 723-738. K a l b f l e i s c h , J . D. and Ross L. P r e n t i c e . The S t a t i s t i c a l A n a l y s i s of F a i l u r e Time Data. New York: John Wiley & Sons, 1980. Kay, R. " P r o p o r t i o n a l Hazard Regression Models and the A n a l y s i s of Censored Data". A p p l i e d S t a t i s t i c s , 26, No. 3 (1977), 227-237. K e n d a l l , S i r Maurice. M u l t i v a r i a t e A n a l y s i s . 2nd E d i t i o n . London: C h a r l e s G r i f f i n and Company L t d . , 1980. Korobow, Leon and David P. Stuhr. "The Relevance o f Peer Groups i n E a r l y Warning A n a l y s i s " . Economic Review. A t l a n t a : F e d e r a l Reserve Bank o f A t l a n t a . November 1983, 27-34. . "Performance Measurement of E a r l y Warning Models". J o u r n a l of Banking and Finance, 9 (1985), 267-273. Lachenbruch, Peter A. D i s c r i m i n a n t A n a l y s i s . New York: Hafner P r e s s , 1975. Lane, W i l l i a m , Stephen Looney and James W. Wansley. "An a p p l i c a t i o n of the Cox P r o p o r t i o n a l Hazards Model to Bank F a i l u r e " . J o u r n a l of Banking and Finance, 10 (1986), 511-531. Lee, E l i s a T. S t a t i s t i c a l Methods f o r S u r v i v a l Data A n a l y s i s . Belmont, C a l i f o r n i a : L i f e t i m e L e a r n i n g P u b l i c a t i o n s , 1980. M a r a s c u i l o , Leonard A. and J o e l R. L e v i n . M u l t i v a r i a t e  S t a t i s t i c s i n the S o c i a l S c i e n c e s . Monterey, C a l i f o r n i a : Brooks/Cole P u b l i s h i n g Company, 1983. -96 -M a r t i n , D a n i e l . " E a r l y Warning o f Bank F a i l u r e " . J o u r n a l of Banking and Finance, 1 (1977), 249-276. McWilliams, James D. " D i s c u s s i o n " [of the Z Score Bankruptcy Model]. i n F i n a n c i a l C r i s e s ; I n s t i t u t i o n s and Markets i n a F r a g i l e Environment. Eds. Edward I . Altman and Arno l d W. Sametz. New York: John Wiley & Sons, 1977, pp. 109-129. Mulder, John E. and Leon S. Forman. Bankruptcy and Arrangement Proceedings. P h i l a d e l p h i a : J o i n t Committee on C o n t i n u i n g L e g a l Education, 1964. Ott, Lyman and David K. H i l d e b r a n d . S t a t i s t i c a l T h i n k i n g f o r  Managers. Boston, Massachusetts: Duxbury P r e s s , 1983. P i a t t , H a r l a n D. Why Companies F a i l . L exington, Massachusetts: D C Heath Company, 1985. Santomero, Anthony M. and Joseph D. V i n s o . " E s t i m a t i n g the P r o b a b i l i t y o f F a i l u r e f o r Commercial Banks and the Banking System". J o u r n a l of Banking and Finance, 1 (1977), 185-205. Shick, R i c h a r d A and Lawrence F. Sherman. "Bank Stock P r i c e s as an E a r l y Warning System f o r Changes i n C o n d i t i o n " . J o u r n a l of Bank Research, Autumn (1980), 136-146. U. S. Congress. House. Report of the Commission on the Bankruptcy Laws of the United S t a t e s . P a r t 1. U. S. 93d Congress, 1st S e s s i o n . House Document No. 93-137. Washington, D . C : GPO, 1973. West, Robert C r a i g . "A F a c t o r - A n a l y t i c Approach t o Bank C o n d i t i o n " . J o u r n a l of Banking and Finance, 9 (1985), 253-266. -97-APPENDIX I Figure 8 PLOT OF SURVIVAL FUNCTION FIRM: CUSIP = 042078 (BANKRUPT) PATTERN SYMBOL 1 A ONE YEAR PRIOR TO BANKRUPTCY 2 B TWO YEARS PRIOR TO BANKRUPTCY 3 C THREE YEARS PRIOR TO BANKRUPTCY ESTIMATED SURVIVAL FUNCTION . + . 1.0 +**********CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC - A BBBBBBBBB A BBBBBBBBBBBB AA BBBBB A BBB .80 + A BB A A A A .60 + A AA A A A .40 + A AA AA A A .20 + AA A AA AAA AAAAAA 0.0 + AAAAAAAAAAAAAAAAA . + + + + + + . , 70. 210 350 0.0 140 280 DAYS -98-F i g u r e 9 PLOT OF SURVIVAL FUNCTION FIRM: CUSIP = 564402 (BANKRUPT) PATTERN SYMBOL 1 A ONE YEAR PRIOR TO BANKRUPTCY 2 B TWO YEARS PRIOR TO BANKRUPTCY 3 C THREE YEARS PRIOR TO BANKRUPTCY ESTIMATED SURVIVAL FUNCTION 1.0 +**************CCCCCCCCCCCCCCC A BBBBBBBBBBBBBBB* ***CCCCCCCC A BBBBBBBB AA AAA .80 + A AA A A A .60 + A A AAA A A A AA .40 + AAA AAA AAA AA AA .20 + A AAA A AA 0.0 + . + + + + + + . , 70. 210 350 0.0 140 280 DAYS -99-F i g u r e 10 PLOT OF SURVIVAL FUNCTION FIRM: CUSIP = 868168 (SURVIVOR) PATTERN SYMBOL 1 A ONE YEAR PRIOR TO WITHDRAWAL 2 B TWO YEARS PRIOR TO WITHDRAWAL 3 C THREE YEARS PRIOR TO WITHDRAWAL ESTIMATED SURVIVAL FUNCTION . + + + + + + . . 1.0 +***************************************** + AAAAA .80 + + .60 + + . 40 + + .20 + + 0.0 + + . + + + + + + 70. 210 350 0.0 140 280 DAYS - 1 0 0 -F i g u r e 11 PLOT OF S U R V I V A L FUNCTION F I R M : C U S I P = 297882 (SURVIVOR) P A T T E R N SYMBOL 1 A ONE Y E A R PRIOR TO WITHDRAWAL 2 B TWO YEARS PRIOR TO WITHDRAWAL 3 C T H R E E YEARS PRIOR TO WITHDRAWAL E S T I M A T E D S U R V I V A L FUNCTION . + . 1 .0 +* * * * * *BB A C C * * B B A A CCB AAA *BB . 8 0 + A CC BBBBB AA C C C B A CCCBBB A C BBB A C C C C BBBBB . 6 0 + A CC BB A A A A C C C C C BB A CC B A C BBB A A A CC B . 4 0 + A A A C BB A A C C C B A AAA C AA CC A . 2 0 + A A A A A A A A 0 .0 + . + + + + + + . , 7 0 . 210 350 0 . 0 140 280 DAYS -101-APPENDIX I I . Figure 12 NORMAL PLOT OF CURRENT ASSETS / SALES (ONE .YEAR PRIOR) SYMBOL COUNT MEAN ST.DEV. * 109 0.411 0.192 , + + + + + + ..., / // * / // * * * * * * * * * * / ** / */ * ** *** / * * * * /* //* / * - // * + / * -/ * . + + + + + + . , .20 .60 1.0 0.0 .40 .80 CASLS1 VALUES FROM NORMAL DISTRIBUTION WOULD LIE ON THE LINE INDICATED BY THE SYMBOL / . -102-Figure 13 NORMAL PLOT OF WORKING CAPITAL / TOTAL ASSETS (FOUR YEARS PRIOR) SYMBOL COUNT MEAN ST.DEV. * 109 0.323 0.138 ....+....+....+....+....+....+....+. +....+... _ * _ / " * / / " + */ + */* _ - * _ - */* _ **** _ + ** + - ** _ _ * ** _ _ * * _ - * ** _ + ** + - /** _ _ /*** _ _ * ** _ _ **** _ + ** + _ *** * _ - * */ _ *// /* + * / + */ - // - * _ ....+....+....+....+....+....+....+....+....+... .08 .24 .40 .56 0.0 .16 .32 .48 .64 WCTA4 VALUES FROM NORMAL DISTRIBUTION WOULD LIE ON THE LINE INDICATED BY THE SYMBOL / . -103-Figure 14 NORMAL PLOT OF WORKING CAPITAL / TOTAL ASSETS (ONE YEAR PRIOR) SYMBOL COUNT MEAN ST.DEV. * 109 0.272 0.226 . . . . + + + + + + . / E - * / X 2 + *// P */ E - **/ C - **/ T - ** / E 1 + ** D - ** _ * * N - * 0 - /* R 0 + /** M - /** A - /** L _ * ** //* V -1 + /*** A - **/* L - **/ U - **// E - ** / * * / / / . + + + + + + . , -.3 .3 .9 -.6 0. .6 WCTA1 VALUES FROM NORMAL DISTRIBUTION WOULD LIE ON THE LINE INDICATED BY THE SYMBOL / . -104-Figure 15 NORMAL PLOT OF NET INCOME / SALES (FOUR YEARS PRIOR) SYMBOL COUNT MEAN ST.DEV. * 109 0.019 0.037 , + + + + + . . / E - */ X 2 + * / P - */ E ** C - ** •p — * * * E 1 + * / D - **/ _ * */ N - **/ O - */ R 0 + ** M - * A - ** L - /* _ /* * V -1 + / * A - /** L - * ** U - /* E - ** -2 + * / / / -.06 .06 -.12 0.0 .12 * _ VALUES ON THE NETYSL4 FROM NORMAL DISTRIBUTION WOULD LIE LINE INDICATED BY THE SYMBOL / . -105-Figure 16 NORMAL PLOT OF NET INCOME / SALES (ONE YEAR PRIOR) SYMBOL COUNT MEAN ST.DEV. * 109 -0.019 0.096 ....+....+....+....+....+....+....+....+....+... _ * _ E - * X 2 + * /+ P * / -E - // -C - * / T - * / E 1 + * // + D - */ - * * _ N - /* O - /** R 0 + // * + M - / ** A - / ** L - /** ** _ - /* * _ V -1 + /** + A - *** * -L ** U * * // E - ** / -2 + * / • + / / / _* _ ....+....+....+....+....+....+....+....+....+... -.35 -.21 -.07 .07 -.42 -.28 -.14 0.0 .14 NETYSL1 VALUES FROM NORMAL DISTRIBUTION WOULD LIE ON THE LINE INDICATED BY THE SYMBOL / . -106-APPENDIX III Figure 17 LOG MINUS LOG SURVIVAL FUNCTION S t r a t i f i e d on: Cash flow / t o t a l debt two years prior . + + + + + + -2 + + AA -AAA AAA -3 + AAAA + AAAAAA B B AAAAA B B B A B B B B AAAAA B B -4 + A B B + - A B - A B B - A B - AA B -5 + AA B + - AA B B - A B - A B - A B -6 + A B + - A B - A B - A B - A B -7 + A B + - A B B A . + + + + + + 70. 210 350 0.0 140 280 DAYS -107-Figure 18 LOG MINUS LOG SURVIVAL FUNCTION S t r a t i f i e d on: Net income / sales (two years prior) . + + + + + + . . . . 0 + AA -AA -AAAAAA AAAAAAAAAA BBBBBBBB -3 + AAAA BBBBBBB + AAAA BBBBBBB A BBBBB AAAAA BB AA BB - A BB - A BB - ABB -6 + ABB + - AB - AB - AB - AB - AB - AB -9 + + . + + + + + + . , 70. 210 350 0.0 140 280 DAYS -108-Figure 19 LOG MINUS LOG SURVIVAL FUNCTION S t r a t i f i e d on: Total claims / Assets (two years prior) . + + + + + + ., -2 + B A A* *AA BBBBBBBB**B BBBB AA -3 + BB A B A BBBBB A - B A BB AAAAAAAA -4 + • A*AAAAAAAAA AAAAA B - A B - A BB - A B -5 + AA BB A B ABB AB AB -6 + AB AB AB AB AB -7 + * _ * B . + + + + + + . , 70. 210 350 0.0 140 280 DAYS 

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