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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., M c M a s t e r 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 in THE FACULTY OF GRADUATE (Commerce and B u s i n e s s  We a c c e p t to  this  Administration)  t h e s i s as  the required  STUDIES  conforming  standard  THE UNIVERSITY OF B R I T I S H COLUMBIA September 1987 ©Sandra  Ann B e t t o n , 1987  In  presenting  degree freely  at  this  the  available  copying  of  department publication  of  in  partial  fulfilment  University  of  British  Columbia,  for  this or  thesis  reference  thesis by  this  for  his thesis  and  study.  scholarly  or for  her  of I  gain  be  It  shall  that  agree  may  representatives.  financial  requirements  agree  I further  purposes  the  not  that  the  be  Library  permission  granted  is  by  understood allowed  of  Commerce end B u s i n e s s  The University of British C o l u m b i a 1956 Main Mall Vancouver, Canada V6T 1Y3 Date  September 29, 198?  the  an  Administration  advanced  shall for  make  that  it  extensive  head  without  permission.  Department  for  of  copying my  my or  written  ABSTRACT  The rate,  recent  dramatic  coupled with  failure  r a t e , has  interest  i n the  future  actively  re-awakened  area  possibility The  proportional  has  not  explanatory by  an  many e x p e r t s  the  already  do  not  firm's  i n an  in this  risk  of  any  censoring  information  of  i n the  Cox  [1972],  failure,  analysis. Unlike logit  and  model e s t i m a t e s t h e  given  various  t i m e . The  i n medical  to the  bank  failure  model p e r f o r m e d  regulated, this  Cox  banking  approach  i s that  s u r v i v a l times observed  data thereby using  p r e d i c t i o n m o d e l s , s u c h as models, the  highly  p r i n c i p a l advantage of both the  the  coefficients multiplied  r e c e n t l y been a p p l i e d  modi i n c o r p o r a t e s  to  models  Cox  i s a function of  unknown f u n c t i o n  the  an  paper.  occurred,  [Lane, L o o n e y & W a n s l e y , 1 9 8 6 ] . The  The  The  of  question  industry.  b e n e f i t of  the  narrowly defined,  current  endeavour t o p r e d i c t  but,  i n the  Bankruptcy  have the  studies;  well  government  s e c u r i t i e s from which  outlined  estimated  bank  to a firm's  H a z a r d model i s u s u a l l y a p p l i e d has  and  function,  v a r i a b l e s and  Proportional  lender  h a z a r d m o d e l , p i o n e e r e d by  hazard  a r b i t r a r y and  investor,  bankruptcy  i n the  debtor's v i a b i l i t y .  of d i s a s t e r are  assumes t h a t failure  often  about the  commonly u s e d by  increase  of p a r t i c u l a r value  market i n the  make i n f e r e n c e s  corporate  of bankruptcy p r e d i c t i o n .  c r e d i t o r s who  traded  i n the  a s i m i l a r rate of  p r e d i c t i o n models are and  increase  more o f  the  and  available  many b a n k r u p t c y p r o b i t based  regression  probability distribution  -ii i -  of s u r v i v a l times.  The  p r o p o r t i o n a l h a z a r d model w o u l d ,  t h e r e f o r e , appear t o o f f e r traditional  a u s e f u l a d d i t i o n to the  b a n k r u p t c y p r e d i c t i o n models mentioned  T h i s paper  evaluates  the  applicability  p r o p o r t i o n a l h a z a r d model i n t h e e n v i r o n m e n t . In o r d e r f i r m s was  s e l e c t e d from the  Industrial  data  tapes.  p e t i t i o n s under the between 1972 not  filed  view o f  to t e s t  and  various  1985  and  legal  framework o f The  evaluated  the  by  based model.  comparing  of  The  classification  bankruptcy acts  capability  information  and  o f t h e Cox  1978,  also  the  examined. then  descriptive analysis  indicate that model was  a n a l y s i s , t h e model p r o v i d e s  beyond t h a t a v a i l a b l e from the  In  regulatory  discriminant  study  had  same p e r i o d .  model was  its classification estimated  which  act of  was  Cox  Research  filed  firms  bankruptcy  estimated  109  applicable  the  bankruptcy process  r e s u l t s of t h i s  that of discriminant  analysis.  these firms  Bankruptcy reform  t o t h o s e o f an  industrial  I n d u s t r i a l and  were matched t o 67  performance o f the  capabilities  the  one  the d r a m a t i c changes i n the the  Cox  t h i s m o d e l , a sample o f  p e t i t i o n s f o r bankruptcy during  e n v i r o n m e n t c a u s e d by  above.  o f the  more d i v e r s e  Compustat  Forty  more  while  less  than  additional  discriminant  - iv-  T A B L E  OF  C O N T E N T S  ABSTRACT  ii  L I S T OF TABLES  vi  L I S T OF FIGURES  I. II.  v i i  INTRODUCTION  1  BANKRUPTCY A. DEFINITION  5  B. LEGAL ENVIRONMENT  7  C. THE BANKRUPTCY RECORD III.  IV.  V.  MODELS COMMONLY USED A. STOCK-PRICE BASED MODELS  19  B. UNIVARIATE RATIO ANALYSIS  20  C. STATIC MULTIVARIATE ANALYSIS  21  D. REGRESSION AND TIME BASED MODELS  25  PLAN OF ANALYSIS A. RATIO SELECTION  29  B. THE DATA SET  31  SAMPLE  CHARACTERISTICS  A. SAMPLE  VI.  17  STATISTICS  38  B. RATIO DISTRIBUTION  41  C. CHANDLER AND  42  DISCRIMINANT  REFORM ACTS  ANALYSIS  A. THEORY  48  B. ONE YEAR RESULTS  52  -v-  VII.  THE COX MODEL A. SURVIVAL THEORY B. THE COX PROPORTIONAL  VIII. IX.  55 HAZARD MODEL  57  C. ONE YEAR PRIOR ESTIMATION  62  D. FOUR YEARS PRIOR ESTIMATION  70  E . "TIED" OBSERVATIONS  75  MODEL COMPARISON  79  SUMMARY AND  86  CONCLUSION  FOOTNOTES  89  BIBLIOGRAPHY  94  APPENDIX  97  I . SURVIVAL PLOTS  APPENDIX I I . APPENDIX I I I .  NORMAL PROBABILITY PLOTS STRATIFIED COX ESTIMATES  101 106  -vi-  ii  I S T  O F  T A B L E S  1  MAJOR CORPORATIONS  2  LIST  3  W.  4  C H A R A C T E R I S T I C S OF  5  SUMMARY  6  TESTS  7  CLASSIFICATION  FUNCTION  8  CLASSIFICATION  FUNCTION  9  COX  OF R A T I O S  FILING  CHAPTER  XI  USED  14 29  T . GRANT S A L E S  33 I N C O M P L E T E DATA  STATISTICS  34 38  OF GROUP S I M I L A R I T Y  46 53  (4 Y E A R S  PRIOR)  MODEL E S T I M A T I O N  54 63  10  CORRELATION MATRIX  64  11  COX  12  C O R R E L A T I O N MATRIX  13  COX  14  "TIED"  15(a)  MODEL PERFORMANCE  ( D I S C R I M I N A N T MODEL)  80  15(b)  MODEL PERFORMANCE  (COX MODEL)  81  16  LINEAR DISCRIMINANT  MODEL E S T I M A T I O N  (4 Y E A R S  (4 Y E A R S  PRIOR)  PRIOR)  MODEL, R E - E S T I M A T I O N  70 72 73  OBSERVATIONS  76  FUNCTION  SCORES  84  -VI1-  L I S T  OF  F I G U R E S  1  ANNUAL FAILURE RATE  17  2  RATIO PROFILE OF BANKRUPT SURVIVING FIRMS  AND 39  3  DISCRIMINANT ANALYSIS (GRAPHICALLY)  48  4  LOG MINUS LOG SURVIVAL FUNCTION  68  5  GOODNESS OF F I T  69  6  GOODNESS OF F I T (4 YEARS PRIOR)  74  7  GOODNESS OF F I T ("TIED" OBSERVATIONS)  78  APPENDIX I : SURIVIAL PLOTS 8  SURVIVAL FUNCTION #0 42078  97  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)  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  105  (1 YEAR PRIOR)  101  -viii-  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.  On  average  minutes  during  a U.S. 1970.  INTRODUCTION  business Thirteen  firm  failed  every  forty-nine  years  later,  i n 1983,  a  firm  *1 failed,  on a v e r a g e ,  increase similar  rate  management  often the  debtor's  viability.  "Prediction the  signal  measures this  way,  become  Model"  a  from  One  disaster  doom  the f i l i n g  'good'  experts will  allow  be  i n an endeavour outlined  taking  creditor are of  traded  who  market i n about  the  successful t o a c t on  corrective  f o r bankruptcy. would,  The models  to predict  in this  i n the  creditors  management  of bankruptcy  prophesy.  a  has r e -  inferences a  a firm's  of petitions  predictor  models  and f u t u r e  that  and by  with  to investor,  t o make  hope  coupled  identification of a  prediction  which  startling  interest  of a actively  would  would  a self-defeating  many  invaluable  current  This  f a i l u r e rate,  The e a r l y  Bankruptcy  o f impending  avoid  be  the benefit  securities  rate,  and government  to a firm's  do n o t have  firm's  would  alike.  value  i n t h e bank  prediction.  bankrupt  minutes.  bankruptcy  lender  of bankruptcy  particular  by  of increase  investor,  potential and  sixteen  i n the corporate  awakened area  every  In  in effect,  commonly  used  the p o s s i b i l i t y  of  paper.  _ On a v e r a g e i n 1970, a f i r m w a s 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 o n a v e r a g e i n 1983, o n e was i n c o r p o r a t e d every f i f t y - t w o seconds.  -2-  A l t m a n ' s Z S c o r e m o d e l , b a s e d on d i s c r i m i n a n t is  one o f t h e most  models.  This  different  commonly a p p l i e d  bankruptcy  t y p e o f model h a s b e e n a p p l i e d  Z Score performed s i g n i f i c a n t l y c h a n c e m o d e l . Any new model  [1975] f o u n d  better  i m p r o v e on t h e d i s c r i m i n a n t these l a t t e r  t h a t Altman's  than a p r o p o r t i o n a l offer similar  and r e l i a b i l i t y .  Many o t h e r m o d e l s have been d e v e l o p e d  as  i n many  should, therefore,  "general purpose" a p p l i c a b i l i t y  the  prediction  i n d u s t r i e s and s i t u a t i o n s and h a s , on a v e r a g e ,  p e r f o r m e d w e l l . J o y and T o l l e f s o n  While  analysis,  i n an e f f o r t t o  a n a l y s i s based Z Score  model.  m o d e l s have added t o o u r u n d e r s t a n d i n g o f  bankruptcy c o n d i t i o n ,  t h e y have n o t b e e n a s w i d e l y u s e d  t h e Z S c o r e . A l t m a n ' s model a p p e a r s t o be one o f t h e most  generally  a p p l i c a b l e b a n k r u p t c y p r e d i c t i o n model a n d ,  therefore,  acts  as the standard  j u d g e d . Among t h e l a t t e r analysis factor  of financial  a n a l y t i c models  [Santomero and V i n s o ,  by w h i c h a l l o t h e r s must be  a r e B e a v e r ' s [1966]  ratios,  logit  models  Univariate  [Martin,  [West, 1 9 8 5 ] , and F i r s t  1977],  P a s s a g e Time  1977].  The Cox P r o p o r t i o n a l  H a z a r d model  i s usually applied i n  medical studies;  b u t , h a s r e c e n t l y been a p p l i e d  failure  [Lane, Looney & W a n s l e y , 1 9 8 6 ] . The model  question  performed w e l l banking is  i n the narrowly defined,  industry.  highly  The model  regulated,  The p r i n c i p a l a d v a n t a g e o f t h e Cox model  t h a t more o f t h e a v a i l a b l e i n f o r m a t i o n  analysis.  t o t h e bank  incorporates  i s used i n the  both the s u r v i v a l times  -3observed  and  any  when t h e s t u d y  censoring of data. Censoring  terminates before every  U n l i k e many b a n k r u p t c y probit  based  probability  f i r m has  distribution  of s u r v i v a l  would, t h e r e f o r e , appear  to offer  bankruptcy  occurs  failed.  p r e d i c t i o n models, such  r e g r e s s i o n m o d e l s , t h e Cox  more t r a d i t i o n a l  of data  as  logit  and  model e s t i m a t e s  the  t i m e s . The  a useful  Cox  model  addition  to  the  p r e d i c t i o n models mentioned  above. T h i s paper Cox  seeks  to e v a l u a t e the a p p l i c a b i l i t y  P r o p o r t i o n a l h a z a r d model i n a more d i v e r s e  environment. f i r m s was  In o r d e r  selected  Industrial petitions  to test  from  F o r t y one  under t h e v a r i o u s b a n k r u p t c y  between 1972  and  the bankruptcy  1985.  r e g u l a t o r y environment  r e f o r m a c t o f 1978,  bankruptcy  p r o c e s s was  a sample o f 41  between 1972  and  f i r m s w h i c h had  not  same p e r i o d . The t h e n e v a l u a t e d by descriptive  that  Cox  f i r m s which f i l e d  petitions  the  model for  f o r bankruptcy  performance  of the estimated  comparing  its classification  capabilities  discriminant  by  changes i n  to those  a n a l y s i s based  model.  o f an The  while the c l a s s i f i c a t i o n  Cox  the was  bankruptcy  T h e s e f a i l u r e s were matched t o  filed  Research  filed  framework o f  The  109  applicable  caused  a l s o examined.  e s t i m a t e d on  1985.  acts  the l e g a l  and  firms  In view o f the d r a m a t i c  Bankruptcy  indicate  Industrial  of these  the  industrial  t h i s m o d e l , a sample o f  t h e Compustat  data tapes.  of  67  during model  the  was  and  estimated results  of t h i s  capability  of the  study Cox  -4model  was l e s s  than  model  provides  information  discriminant  that  analysis.  of discriminant beyond  that  analysis,  provided  by  t h e Cox the  -5II.  A.  BANKRUPTCY  DEFINITION The  terms  "bankruptcy" situations each  are often  described  a r e very Business  which  often  failure  used  by t h e s e  terms  describes  In such  1  and  However, t h e  and t h e consequences o f  financially  Insolvency  the economic  a case  but s u f f i c i e n t  i s not necessarily  Technical  "insolvency"  interchangeably.  r e a l i z e d on a s s e t s  costs.  minimal  become  failure",  different.  the return  opportunity  firm  "business  i s less  occurs  when  Such  i t may  a  even  future.  to liquidity  a firm  costs.  bankrupt,  p r o f i t a b l e i n the near  insolvency  earnings are  variable  t o become  essentially refers  than the  the firm's  t o cover  going  condition i n  cannot  problems. meet i t ' s  2 current  obligations  condition  f o r bankruptcy  obligations firm.  and i s n o t i n i t s e l f  Such  as the i n a b i l i t y  c a n be a temporary  crisis  situations are likely  a  sufficient  t o meet  current  t o an otherwise  t o occur  i n highly  healthy seasonal  industries. Bankruptcy firm  i s by f a r t h e most  has t o face.  and  the previously  the  Bankruptcy  firm  which  unlikely  The major  becomes  t o emerge  difference  discussed  Courts,  serious  crises  h a s now  embroiled unchanged:  financial  between  i s that  entered  a third  party, Any  proceedings i s  either  be  a  condition  the proceedings.  i n bankruptcy i tw i l l  this  crisis  reorganized  -6and  emerge  as  disappear. original control acting the  firm  being the  best  three  i s the of  and  practically  a in  hardest  the  market  rates  The  the  is  the  state  and  petition  has  i s very  Courts  a  as  outlined,  who  will, whether  be  determining  a l t e r n a t i v e use  of  a  the  of  return  actual  of  a  rate  to an  on  to  active  compare  of  the  arrive  s e c u r i t i e s are  used  firm's  determination  return  firm without  can  business  i t involves  difficult  data  "distress" conditions  usually  easier of  firm's  filed.  a  both  firm's  at market  actively  these  relative  insolvency  which  cannot  of  the  can  statements.  condition hide  and  Insolvency  values  of  financial  firm  of  identify.  relative  identifiable  entered,  been  the  to  obligations,  the  easily  once  destiny,  return.  current  most  the  creditors, decide  rate  firm's  comparison  from  market  of  nor  firm's  the  requires  the  requires  determined  to  If  are  and  i n an  rate  and  case  bankruptcy  flows  identify  comparison  valuation  financial  a  to  this  value  market of  to  and  is liquidated.  possible  i t ' s securities.  traded,  the  the  "distress" conditions  comparing  Such  holders)  relinquished  or  liquidated  control  i n t e r e s t s of  return  market  be  (stock  retain full  r e a l i z e d . This  true  i t will  owners  l a r g e l y been  the  assets.  for  the  or  i s re-organized  rate  assets  firm  management  i n the  failure  new  Neither  has  Of  the  a  as  often  be  Bankruptcy  i t is a  the  cash  fact  legal that  the  -7This  paper  prediction  LEGAL  therefore, concentrate  of the f i l i n g  objectively  B.  will,  verifiable  o f a bankruptcy  was f i r s t  of the late  primarily  aimed  involuntary solvency  the  law's  As need  generally  the area,  that  t o remove  retaliatory  i n nature.  i f ever  debts  l a w was  i t was a n  questioned,  were p a i d  before  insolvency  laws  the  "bankruptcy"  insolvency  rather  than  flight  and c r e d i t o r  co-operative laws were  of giving  Unlike  he c o u l d  mutual  i n nature  and  honest  h i s assets  and encouraged  for their  the courts,  a basically  the bankruptcy  and  nature.  voluntary  of distributing  allowed  of insolvency  unlike  insolvency  among h i s c r e d i t o r s .  complex, the  cases,  o f a more  a means  became more  f o r t h e management  These  involved  on t h e n o t i o n  "unfortunate"  satisfied  bankruptcy  was r a r e l y  environment  mechanism  were  British  based  debtor  from  of  mercantile  who w a s p l a n n i n g  and e s s e n t i a l l y  i n Britain.  consequently,  were  As e a r l y  was t o e n s u r e  the economic  The  i n a case  jurisdiction."^  arose  cases,  recourse  by t h e E u r o p e a n  ages.  o f the "bankrupt"  fora legal  cases  middle  or himself  purpose  a  recognized  procedure  The  for legal  a t the merchant  h i sassets  leaving  as i t i s an  ENVIRONMENT  bankruptcy  either  petition  condition.  BACKGROUND; T h e n e e d  states  on t h e  laws,  equitably the  n e g o t i a t i o n between  b e n e f i t . I f an i n s o l v e n t  be d i s c h a r g e d  from  h i s debts  -8-  and  begin again with a clean  s l a t e which  was n o t p o s s i b l e  4 under  the bankruptcy All  laws.  modern b a n k r u p t c y  legislation  has developed  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 THE CHANDLER ACT: The C o n s t i t u t i o n vests the sole  jurisdiction  from  and c o - o p e r a t i o n .  of the United States  over bankruptcy  laws w i t h t h e  5 F e d e r a l Government.  The a i m i s t o e s t a b l i s h  treatment of a l l bankrupts  and t h e i r  I n 1898, t h e U.S. C o n g r e s s and  essentially  u n i f o r m and  creditors.  passed  the Bankruptcy A c t ,  i t served the United States u n t i l  when t h e G r e a t D e p r e s s i o n f o c u s s e d p u b l i c on t h e f u n c t i o n i n g  o f the Bankruptcy  t h e U.S.  Congress  t o the massive  economic upheaval  caused  amendment  sponsored  by C h a n d l e r , a l t h o u g h t e c h n i c a l l y  t o the Bankruptcy  amendment, made s u c h wide s w e e p i n g that  the Bankruptcy  A c t . I n 1938  s o c i a l and  by t h e d e p r e s s i o n by p a s s i n g an  extensive  act,  t h e 1930's  and g o v e r n m e n t  attention  responded  fair  A c t . The amendment o n l y an  changes t o t h e o r i g i n a l  A c t became known a s t h e C h a n d l e r  Act. Several Firstly,  f e a t u r e s of the a c t deserve  special  mention.  w h i l e a n y f i r m may become i n s o l v e n t , n o t a l l f i r m s  may d e c l a r e b a n k r u p t c y . The A c t d o e s n o t a l l o w b u i l d i n g and loan associations either  voluntarily  Act, rather  their  and i n s u r a n c e and b a n k i n g or i n v o l u n t a r i l y liquidation  file  corporations to  under  or r e h a b i l i t a t i o n  the Chandler i s l e f t to  6 state authority.  The h i s t o r i c a l  basis of this  exemption  isa  -9basic is  deference  also  denied  governments  1933,  receive  the only  Section  77, d e a l i n g with  special  course  was t o e n t e r  1933  Involuntary  open  either with  treatment  process  federal  railroad  while  under  to a financially or state  state  the Act.  taking  receivership. was  and s t r e a m l i n i n g into  Prior  distressed  reorganization,  the aim o f f a c i l i t a t i n g  reorganization  and  bankruptcy  farmers.  railway  in  authority.  to the creditors of federal  and  Railroads to  to state  account  enacted the  "the public  7 interest". Act no  made  I t i s i n t e r e s t i n g t o note  extensive  changes The  to Section  Chandler  voluntarily voluntary has  only  exists.  A c t c a n be a p p l i e d  pay the f i l i n g  fee,  The s o l v e n c y  relevant  the Chandler  Act,  i t made  77.  p e t i t i o n f o r bankruptcy  debts,  while  t o the Bankruptcy  t o a debtor  or i n v o l u n t a r i l y . The only  institutions. the  revisions  that  matter  either  requirements  are that  fora  the petitioner  and n o t be one o f t h e exempt  of the petitioner  i s that  i sirrelevant,  a t l e a s t one c r e d i t o r  A petition for reorganization  can only  be  entered  voluntarily.^ Except can  i n certain circumstances  be f i l e d  against  any debtor  an i n v o l u n t a r y  whose  total  debts  petition  exceed  g  $1000.  The p e t i t i o n must  creditors twelve  with  exist,  required."^  be s i g n e d  $500 i n d e b t s otherwise  However,  only  by a t l e a s t  three  ( i naggregate)  i f more  one c r e d i t o r ' s  signature  a bankruptcy  p e t i t i o n cannot  than i s  be f i l e d  on  -10a whim;  rather,  bankruptcy". assets,  These  giving  allowing  a  the  debtor "acts"  must can  preferential  lien  or  have  be  committed  summarized  treatment  assignment  of  to  assets  an  as:  "act  hiding  certain to  of  creditors,  occur  while  12 insolvent  or  voluntary  petition  adjudication  admitting  of  i n the  unable  to  prove  of  "Acts  In  a  with  no  assets  satisfy impose  reduce  as  continue  under  cost  of  have  i n an  the  I f the  petition  under  on  been  debtor  Chapter  XI  bankruptcy  immediate  of and  Act,  allow  least  one  dismissed.  the  bankrupt  generally, to  proceedings  alike.  An  attempts  to  the  be  are  i n order  these  creditor  the  can  at  be  V,  but,  liquidated  and  of  will  Chapter  financially;  a  creditors  commission  claims. Unfortunately  serious costs  the  slate"  they  results  Unlike  involuntary petition  the  bankruptcy,  "clean  t o pay.  Courts.  Bankruptcy",  creditors'  Arrangement,  an  i n s o l v e n c y and  of  a  usually  Bankruptcy  straight  emerges w i t h  which  inability  bankruptcy,  contested  the  an  business  both to  activity.  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 a n e m b a r r a s s e d d e b t o r , by a g r e e m e n t w i t h h i s c r e d i t o r s and subject to c o u r t approval, remains i n business but s e c u r e s e i t h e r an e x t e n s i o n on t i m e fojj^payment or 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 . Chapter and  X  of  reorganize,  interruption Arrangement creditors  change  of  Act  allows  corporate  business  both  with  the  corporations to structure,  activity.  While  courts  acting  as  without  Reorganization  i n v o l v e n e g o t i a t i o n between  the  refinance  debtor  intermediary,  and  and  there  exist  -11-  considerable  d i f f e r e n c e s b e t w e e n C h a p t e r s X and  areas of c o n t r o l , r e p r e s e n t a t i o n , Control debtor. debtor  can  debtor  i s that  the A c t  can  proceeding file  The  makes no  the  in  the  fairness. i s vested  the p e t i t i o n  in  and  the  only  the  major weakness i n a C h a p t e r  independent v e r i f i c a t i o n  d i s c l o s e d by  information other  XI  propose a p l a n .  information  two  a Chapter  Only the  proceeding  as  of  and  XI  debtor  of  XI  financial  i s o f t e n not  undertaken  provision for investigation. This  problem  f o r u n s e c u r e d c r e d i t o r s i s compounded  features of  the  Chapter: the  "friendly"  by  creditors 13  c o m m i t t e e and The  the  expense reimbursement  c r e d i t o r s ' committee, t h e o r e t i c a l l y ,  unsecured c r e d i t o r s r e p r e s e n t a t i v e . is  made up  o f major c r e d i t o r s who  a s s o c i a t i o n with  the  debtor.  The  o f t e n have a problems of  are  compounded by  provision  the  e x p e n s e s i n c u r r e d by  that  reimbursed  i f the  is  the  However, i n p r a c t i c e , i t  representation  be  provision.  the  inadequate  Chapter's the  close  reimbursement  c o m m i t t e e may  d e b t o r ' s arrangement p l a n  is  not  not  14 confirmed. cursory  i n v e s t i g a t i o n as  often better plan  C o n s e q u e n t l y , most d e b t o r s a r e  financially  under C h a p t e r  c r e d i t o r s with Chapter trustee court  X,  rather  appointed  XI  acceptance of the  subject  proposed p l a n  than f o r c i n g l i q u i d a t i o n  i s required  more t h a n w o u l d be in contrast,  vests  to provide provided  in  as  a  a  is  fair  general liquidation."^  c o n t r o l i n an  t h a n e i t h e r c r e d i t o r or e q u i t y t r u s t e e has  to only  independent  owners.  The  wide i n v e s t i g a t i v e powers and  has  -12th e f i r s t  opportunity  All  interested parties,  file  other  proposals.  time t o f i l e  t o propose a p l a n o f r e o r g a n i z a t i o n .  The d e b t o r  except  may o n l y  the debtor, file  after  may  the trustee's  has e x p i r e d . * ' 1  Representation  requirements  are s i g n i f i c a n t l y  between C h a p t e r s X and X I . C h a p t e r XI o f f i c i a l l y with  different  deals  only  u n s e c u r e d c r e d i t o r s and h a s no r e g u l a t i o n s r e g a r d i n g t h e  appointment or s e l e c t i o n Chapter that  also  of creditors representatives.  X, i n c o n t r a s t , d e a l s w i t h  t h e t r u s t e e and h i s a t t o r n e y  a l l c r e d i t o r s and r e q u i r e s 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 a r e f r e e o f any c o n f l i c t s Chapter  also requires f u l l  standards  o f i n t e r e s t . The  d i s c l o s u r e and imposes  fiduciary  on any r e p r e s e n t a t i v e s . T h e r e a r e no f e e 17  reimbursement r e s t r i c t i o n s Fairness of the plan and  similar  t o those  i s another  area  i n Chapter XI.  i n which Chapters X  XI d i f f e r m a r k e d l y . As o r i g i n a l l y e n a c t e d i n 1938, C h a p t e r XI p l a n s h a d t o be i n t h e b e s t i n t e r e s t s o f 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 . C h a p t e r X p l a n s , on t h e 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 fair  p l a n under C h a p t e r  r e c e i v e more t h a n contrast  they  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  would  in a liquidation.  follows the p r i n c i p l e s of absolute  junior  c r e d i t o r s have no i n t e r e s t s  senior  c r e d i t o r s are paid  was i n t e n d e d  priority.  The  under t h e p l a n u n t i l 19  more  in full.  A major p r o b l e m i n u s i n g C h a p t e r A c t makes no d i s t i n c t i o n  Chapter X i n  X and XI i s t h a t t h e  between who may a p p l y .  f o r u s e by s m a l l e r  C h a p t e r XI  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  individuals.  T h e r e have b e e n s e v e r a l  the S e c u r i t i e s and Exchange Commission t o f o r b i d Chapter  XI t o any p u b l i c  a t t e m p t s by t h e use o f  c o r p o r a t i o n w i t h more t h a n one  20 hundred s t o c k h o l d e r s .  T h e s e moves have n o t b e e n  successful. G i v e n a c h o i c e between f i l i n g debtor,  i n g e n e r a l , would p r e f e r  under C h a p t e r  Chapter  X or X I , a  XI a s he m a i n t a i n s  c o n t r o l o f t h e b u s i n e s s and t h e p r o c e e d i n g s . W h i l e t h e c o n t r o l a n d r e p r e s e n t a t i o n p r o b l e m s may n o t be major small firm  t h e s e weaknesses c a n o f f e r  t h e c r e d i t o r s who a r e n ' t Chapter although there  rather  protection to  "friendly".  XI c a s e law h a s e v o l v e d t o t h e p o i n t  the chapter only d e a l s with unsecured  i s sufficient  secured  little  p r e c e d e n t and p r o c e d u r e  creditors within disturbing  informal  trend  a Chapter of large  proceedings o f Chapter  a p p r o p r i a t e Chapter  ina  that  creditors,  to deal  XI b a n k r u p t c y  with  action. A  c o r p o r a t i o n s u s i n g t h e more XI r a t h e r  X has developed  t h a n t h e more  and i s i l l u s t r a t e d by  T a b l e 1. THE BANKRUPTCY REFORM ACT OF 1978; By t h e l a t e and  early  1970's i t h a d become o b v i o u s t h a t  was no l o n g e r f u n c t i o n i n g bankruptcy  1960's  the Chandler A c t  i n i t s i n t e n d e d manner. The  c o u r t s were f a c e d w i t h a n e v e r  increasing  number  o f b a n k r u p t c i e s a s more a n d more c o n s u m e r s a n d b u s i n e s s e s made u s e o f t h e p r o c e s s . The a n n u a l c a s e  load of a t y p i c a l  -14-  +  + Table  1  MAJOR CORPORATIONS F I L I N G 1971 - 1973 Name 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 S c h o o l s Federal's Inc. King Modular Housing Topper Toys Botany I n d u s t r i e s DCA D e v e l o p m e n t  CHAPTER XI  Date  Debt  5/73 1/72 2/7 2 2/72 8/7 2 na 2/73 2/73 4/7 2 2/73  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 f r o m : R e p o r t o f t h e C o m m i s s i o n on t h e B a n k r u p t c y I Page 261  I I  Laws  +  r e f e r e e was  132  c a s e s i n 1947;  by  1967,  i t had  risen  +  to  1074  21 cases. . . . i t i s c l e a r t h a t i n recent years 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 c a s e l o a d t h a n was c o n t e m p l a t e d e i t h e r a t t h e t i m e o f e n a c t m e n t o f t h e B a n k r u p t c y A c t i n 1898 o r a t t h e t i m e ^ f i t s c o m p l e t e r e v i s i o n by t h e C h a n d l e r A c t i n 1938. 2  In  an e f f o r t  procedure, it Act  t o s t r e a m l i n e and m o d e r n i z e  the Bankruptcy  i s commonly r e f e r r e d was  officially  The  two  (liquidation)  generally  within  120  t o , was  e n a c t e d i n 1978.  chapters of i n t e r e s t and  11  bankruptcy  A c t , or Bankruptcy  r e p e a l e d on O c t o b e r  involuntary petition, is  Reform  the  1,  Code  The  i n t h e Code a r e C h a p t e r s 7  (reorganization).  In order t o f i l e  t h e c r e d i t o r s must show t h a t  to f i l i n g ,  Chandler  1979.  an  the debtor  n o t p a y i n g h i s d e b t s as t h e y become due  days p r i o r  as  or  that  a c u s t o d i a n took p o s s e s s i o n  -15-  o r was a p p o i n t e d .  This  cumbersome  "Acts  reasonable  solvency  filing  s e c t i o n e l i m i n a t e s t h e more  o f B a n k r u p t c y " and r e p l a c e s type  of test.  may  file  number  his petition.  may  file  h i s plan of  After this  period,  by t h e c o u r t s , any i n t e r e s t e d r e q u i r e s t h a t the  by two t h i r d s i n amount and one h a l f i n  o f e a c h c l a s s o f 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 confirm court  (X and XI) o f t h e o l d  a p l a n as w e l l . C o n f i r m a t i o n  p l a n be a c c e p t e d  o f number, o f s h a r e h o l d e r s .  The c o u r t  a p l a n even i f a c l a s s o f c r e d i t o r s o b j e c t  may  i f the  f i n d s that the i n t e r e s t s of that c l a s s are not  impaired  the plan. Chapter  business  11 p e r m i t s  unless  creditors is  filing  a t r u s t e e h a s been a p p o i n t e d  party  by  chapters  Under t h e r e v i s e d C h a p t e r , a d e b t o r  reorganization after if  t o $5000.  11 o f t h e Code c o n s o l i d a t e s and r e f i n e s t h e  A r r a n g e m e n t and R e o r g a n i z a t i o n Act.  a more  The amount o f d e b t h e l d by  c r e d i t o r s has been i n c r e a s e d  Chapter  them w i t h  the debtor  the court  t o continue  f i n d s i t i n the best  running h i s i n t e r e s t s of  a n d / o r t h e owners o r i f " c a u s e " c a n be shown.  g e n e r a l l y c l a s s e d as f r a u d ,  incompetence or  Cause  gross  mismanagement."^ One o f t h e m a j o r g o a l s  o f t h e Bankruptcy Reform A c t o f  1978 was t o s p e e d up t h e p r o c e s s in  the bankruptcy  system, the higher  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 . Commission  as t h e l o n g e r the costs  According  [1973], t h e average time spent  a f i r m spends to debtors,  t o the Bankruptcy  i n 1971 by  court  -16-  officials  on C h a p t e r  X c a s e s was  243.2 h o u r s . The  t i m e s p e n t on C h a p t e r  XI c a s e s r a n g e d  depending  of the firm  from  average  29 t o 57 h o u r s , 26  on t h e s i z e  costs attributable  i n question.  t o the c o u r t s i n a Chapter  The  X case  average was 27  $7660 w h i l e i n a C h a p t e r  XI c a s e t h e c o s t s were $1207.  T h e s e c o s t s a r e among t h e d i r e c t  costs o f bankruptcy,  however, a m a j o r component i n t h e t o t a l the  indirect  costs of bankruptcy 28  foregone o p p o r t u n i t i e s . spent time  bankruptcy  that bankruptcy  escape  rather  s a l e s and  than as a l a s t  before Congress  with the problems caused  t o reduce  t h e A c t l a y s down i t easier  i s t o o easy;  b a n k r u p t c y more h a z a r d o u s  that  such as l o s t  However, r e c e n t l y  voiced  proposals  system,  and g e n e r a l l y makes process.  is likely  In an e f f o r t  i n the bankruptcy limits  costs  resort.  t o be  the time several  t o enter the  c o n c e r n has been  f i r m s were u s i n g i t t o T h e r e were  several  i n 1983 t o n o t o n l y make g o i n g and l e s s e a s y ;  but, also t o deal  by t h e r e c e n t Supreme C o u r t  t h e powers o f t h e B a n k r u p t c y 29  into  ruling  Courts are  unconstitutional. It  i s u n c l e a r e x a c t l y what t h e r e p e r c u s s i o n s o f t h e  C o n g r e s s i o n a l p r o p o s a l s and t h e Supreme C o u r t r u l i n g w i l l for  the bankruptcy  process.  be  -17-  C. THE BANKRUPTCY Figure occurred  RECORD  1 illustrates  t h e d r a m a t i c c h a n g e s w h i c h have  i n the bankruptcy  Bankruptcy  record  since  Figure  1  the passage  of the  Reform a c t .  ANNUAL FAILURE RATE (Number o f f a i l u r e s  p e r 10,000  concerns)  +  +  100  +  +  +-75 +  +  +-50  + +  +  + +  + +  +-25  +- 0 +  + 74  Source:  The whether  + 75  + I + I I I  + 76  +• I + + I I I  + 77  + | I I I  + 78  •-+  + 79  + 80  + 81  + 82  " General Business Indicators", Business 1984.  primary area of concern t h e new B a n k r u p t c y  i n this  A c t has caused  situation,  + 83  Statistics,  is  t h e d e c i s i o n making  process words, the act.  of a firm a r e some  same  into  firms  circumstances  A major  significant, the  a p p r o a c h i n g b a n k r u p t c y t o change.  issue  now  filing  would  i s whether  and what  account this  f o r bankruptcy which  n o t have this  filed  change  change.  models  under  i s  are the implications  A c t f o r Bankruptcy Prediction  In  other under  t h eo l d  statistically  o f t h e change i n  which  do n o t take  - 1 9 -  III.  The  purpose  to  classify  to  predict  past  differing  or i d e n t i f y  views  identified  of  o f bankruptcy  o f stock  implicitly does  assume  not fully  financial group,  static  nature.  based  models  often  analyze. seeks  data  available  models,  i s either  information,  drawback  but, cannot  solvency  which  unavailable or utilize to a  series  an event,  largely  peer based  atheoretic  or describe the  e x p l a i n t h e phenomenon  a r e n o t based  modern  o f t h e common  i s their  may p r e d i c t  be  The more  ways: c o m p a r i s o n  o f bankruptcy  as they  reflect the  the underlying  traditional  market  A major  models  and  t o use the  m u l t i v a r i a t e a n a l y s i s and time  well;  examination  used  fold:  o f c u r r e n t and  can typically  to evaluate  i n one o f t h r e e  models  These  very  that  analysis.  statistical  or f a i l u r e  t h e more  reflect  data  regression  data  while  i s two  efficiency.  they  o f t h e market  the firm,  on t h e b a s i s  of data  price  models  troubled businesses  and t h e techniques  by t h e type  efficiency  failure  o f market  USED  prediction  financially  future  The data  Models  approach  o f bankruptcy  their  data.  MODELS COMMONLY  on any u n d e r l y i n g  under financial  theory.  A.  STOCK-PRICE  BASED  Stock-price most  theoretically  MODELS  based  models  appealing  of business  as, according  failure  a r ethe  t o the e f f i c i e n t  -20-  capital  markets h y p o t h e s i s ,  are c o n t i n u a l l y information. be  and f a i r l y  The d a t a  acquired with  the s e c u r i t i e s priced  b a s e d on a l l a v a i l a b l e  r e q u i r e d f o r t h e s e models c a n u s u a l l y  minimal e f f o r t  and t i m e  In g e n e r a l , t h e s e models b e g i n "expected  o f an i n s t i t u t i o n  delay.  by e s t i m a t i n g an  r e t u r n " f u n c t i o n , u s u a l l y b a s e d on an a s s e t  model s u c h  as t h e C a p i t a l  Asset p r i c i n g  model.  pricing  The r e s i d u a l s  from such  a regression analysis,  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 w h i c h may be due t o t h e m a r k e t ' s p e r c e p t i o n  o f t h e company's l o n g t e r m s o l v e n c y . g e n e r a l l y y i e l d e d very promising [1980] f o u n d  t h a t from  downward t r e n d b e f o r e  T h e s e m o d e l s have  results.  1967-1974 s t o c k  Shick  and Sherman  p r i c e s began a  bank e x a m i n e r s r e c o g n i z e d  an  adverse  change i n t h e b a n k ' 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 a d v a n t a g e s on b o t h more t r a d i t i o n a l  theoretic  financial  and p r a c t i c a l  ratio  grounds, over t h e  based models, they do,  however, d e p e n d on t h e e x i s t e n c e o f a r e a s o n a b l y market f o r t h e s t o c k of bankruptcy institutions their  B.  i n question.  and weakness o c c u r  many  active  U n f o r t u n a t e l y , many i n small, closely  which haven't t h e n e c e s s a r y  cases  held  a c t i v e market f o r  stocks.  UNIVARIATE RATIO ANALYSIS One  financial  of the o l d e s t technique distress  forpredicting  f a i l u r e or  i s b a s e d on P e e r Group c o m p a r i s o n .  In  -21this  technique  compared  financial  t o Peer  Group  of this  Peer  and t h e r a t i o  Peer  Group  are calculated  results.  weaknesses Group  ratios  procedure  The major  arise  from  comparison  selection  statistical  the selection  part  of this  analysis  as the observed  not  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 ,  only  then  o f the  techniques.  i s a vital value  and  of a financial  type o f  ratio  depends  but also  on  2 other the of  factors  ratios  financial peer  to that  type  o f a t o y manufacturer  a jewelry Peer  unique  models  ratios norms  essentially  a r e not comparable  typically  t o those  make u s e o f s e v e r a l  and t h e comparison causes  attempting  multivariate unimportant  For example,  retailer.  group  group  of business.  data. ratios  many  of these  statistical  t o do u n i v a r i a t e  In fact,  seemingly  on a u n i v a r i a t e  ratios  problems analysis  to the  as one i s on  insignificant  basis  key  or  c a n become  very  3 important failure  i n combination  model  especially  with  other  can consequently  i fthe firm  ratios.  yield  very  This type of  confusing  i n q u e s t i o n i s above  results,  standard i n  4 certain C.  areas  STATIC This  and substandard  MULTIVARIATE type  ANALYSIS  of failure  model  information  found  i n t h e many  a  score  or value.  composite  i n others.  seeks  to d i s t i l l  financial  ratios  T h i s approach  the  available  was p i o n e e r e d  into by  -22-  Altman in  an  who  applied  effort Altman  firms  to  between this  examined  bankrupt  was  evaluated was  to  in  potential  to  prior  s t i l l  to  good  discriminatory failure  Altman  years  first  a  ratios  66  well  data  found  the  set The  A  to  declined  classify  drawn  from  test  was was  classified  from  two  years  prior  model performed  failure.  of  function  i t ' s classification  prior  to  second  model  evaluating  validity  ability  sample.  the  that  The  data  well.  manufacturing  discriminated  the  second  extremely how  best  firms.  initial  and  ability  financial  accuracy  However,  significantly  well was  the  as  the  time  to  increased.**  This  type  criticized been  by  failure,  two  ways:  the  firms  bankrupts  which  using  determine  bankruptcy.  just  two  as  to  r a t i o s from  non-bankrupt  evaluated  classify  undertaken  function  and  analysis  bankruptcy.^  financial  a  same p o p u l a t i o n  found  to  predict  determine  correctly the  to  discriminant  on  raised  normality  several  i n the the  can  evaluation  financial  regarding  assumptions concerning  of  fronts. the  validity The  d i s t r i b u t i o n s of  the  significant  costs  analysis  of  has  Statistically,  analyses.  cause  of  ratio  of  the  primary  the  been concerns  underlying concerns  variables,  problems  erroneous  have  as  issued non-  regarding  classification  inference, and  the  7 estimation  of  Multivariate in  the  hope  error  rates  analysis of  of  developing  of  these  financial more  models  among  r a t i o s has  useful  tools  others.  been  for  the  extended early  -23-  identification the  approach  o fa troubled firm.  by a p p l y i n g  a Logit  [1977]  Martin  Regression  extended  analysis  t o the  g problem,  while  conjunction  [1985]  West  with  Logit  has  used  factor  analysis i n  estimation t oanalyze  the  bank  9 condition on  problem.  financial  analysis  data  ratios  are  Any  and  and  duet o the  accounting  reported  honestly  the  time  i t has  been  accurate  i n the  sense  the  and  statements  period  are are  current  decision  systems  i s that  data the  are  The the  Deposit  a l l the  the  Financial  data,  values  are  period  o f the  data  values  must  most p u b l i c l y  financial  cost  data  even i f  o f date by  Thedata  may b e  independently  in question  a c o n s i d e r a b l e time  on an h i s t o r i c a l  but  after  i s limited  i f  the  for  o fa l l accounting be i n d e p e n d e n t l y  disclosed basis.  financial  Not  only  highly suspect;  is  but  the  highly susceptible t o manipulation. o f record manipulation records.  Corp.  between  on f i n a n c i a l  of financial  Theb a s i c tenant  consequently,  failure  relies  presented.  f o r the  value  a l l reported  Insurance  difficulties  that  published  prevalence  bank  nature  and  rely  criticisms.  a c c u r a t e l y , i s g e n e r a l l y out  correct  i s also  which  theoretical  which  techniques.  making.  reported  itself  very  models  discriminant or factor  entity  collected  t i m e l i n e s s o f the  data  in  and  in question,  verifiable,  either  o f a business  i s suspect,  verifiable,  use  or failure  s u b j e c t t o s e v e r a l major  model  reporting  Bankruptcy  I n a study  i n s u r e d banks  1960 a n d 1 9 7 2 ,  i s very  o f the  57  evident Federal  c l o s e d duet o f i n a n c i a l  i t was f o u n d  that  nearly  -2430%  of the f a i l u r e s  were  due  to fraud,  embezzlement  and  manipulation. The subject  ratio  based  models  to criticism  outlined  for their  thus  far are  also  essentially static  nature.  Rather than obtaining evidence concerning the banks l i k e l y exposure to f a i l u r e i n i t s operations, these 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 with i t ' s present asset c h a r a c t e r i s t i c s .  A major largely  atheoretic  bankruptcy should  concern  be  or  with  nature.  failure  deduced  a l ls t a t i s t i c a l In order  t o have  from  a  models  i s  f o r a model  of  economic meaning,  theory  their  the  of the underlying  variables  economic  12 and  decision  The  p r i n c i p a l reason  the  failure  between  processes  studies  failure  faced  reason.  statistical  model  an  i s to predict  interested  The  i s of  occur  major or  particular  firm  probability  failure  nature  fail  within  useful  however, insight  based  yield  i n either  models  well  purely  purpose  one  into  their  i s  of  often  why  occurrence.  models  of  a p r o b a b i l i t y that  one p e r i o d .  making.  of a  i f the sole  of the t r a d i t i o n a l  decision  analysis  concern  they  of  f o r any p a r t i c u l a r  as p r e d i c t i n g  i s that  i s not very  i n management  discriminant  will  not  bankruptcy;  as w e l l  r a t i o s i n many  appear t o d i s c r i m i n a t e  the atheoretic  little  management.  specific  which can o f f e r  drawback  bankruptcy  or  While  i n models  bankruptcies  they  non-failure,  theoretical  analysis  t h e company  for including i s that  and  by  Such  a  investment  Another i s that  drawback data  a  analysis of the  from  one  year  -25prior  t o f a i l u r e cannot  prior  t o f a i l u r e . Consequently,  specific  from  two y e a r s  these models a r e v e r y  i n that a l l the available  only s p e c i f i c subsets  D.  be m i x e d w i t h d a t a  data  i s n o t used,  data rather  are analyzed.  REGRESSION AND TIME BASED MODELS In  a n e f f o r t t o model t h e d y n a m i c s o f f a i l u r e , Santomero  & Vinso  [1977] a p p l y  q u i t e commonly u s e d Essentially  their  firm's capital  series  i n modelling  techniques insurance  model i s d e r i v e d from  which had been risk  exposure.  the premise  that the  a c t s a s 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  that v a r i a t i o n s techniques,  time  i n this  b u f f e r occur  known a s F i r s t  stochastically.  The two  P a s s a g e Time o r G a m b l e r ' s R u i n and  Maximum R i s k e x p o s u r e a r e u s e d  t o m o d e l t h e bank  capital  buffer . Santomero & V i n s o risk  exposure technique  relies drift  c o n c e n t r a t e on a p p l y i n g t h e maximum as t h e Gambler's Ruin  on t h e u n p a l a t a b l e a s s u m p t i o n i n the c a p i t a l  account.  technique  o f a zero or negative  T h i s assumption  would appear t o  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 o r c h a r i t a b l e 14 organizations  than  f o r p r o f i t maximizing  institutions.  maximum r i s k e x p o s u r e model o f t h e b a n k i n g analyzed  i n cross  The  s y s t e m was  section.  Santomero & V i n s o ' s  results  asset ratio  indicate  t h a t the  traditional  capital  i s a useful  tool i n  identifying  t r o u b l e d banks; b u t , t h a t a bank's c a p i t a l  stock  -26variability a  bank's  survival  conclude capital screen  that  offers  The  model. capital  model,  the  exact  previously available  order  to  over  from  a  continuous the  Federal  essentially  the  best  of  one  three  Reserve.  The  most  the  market  values  as  the  model  "Altman" a  type  valued  model  reports  institutions  values "Fed."  set  capital  weekly  banking  of  company's  d e s i r a b l e data  i s the  capital  Vinso  Exposure  The  hundred  proposed  identification  and  of  Risk  do  a  this  1  traditional  can  therefore,  methods. *'  Santomero  Maximum  determining  account  and  behaviour  data.  record  accounting  the  more  the  of  approximately  the  the  time,  series  however,  of  estimate  would  with  into  classification  time  by  takes  in  Vinso,  a more  a  filed  and  i n conjunction with  requires  levels;  component  Santomero  which  requirements  stock  be  important  potential.  different  In  very  variability,  than data  very  a  their  stock  technique  are  i s also  reported does  not  are require  17  market  value  extensive on  the  time  firm  contrast,  restatement  of  series  i n these  data  interest.  responsible  for monitoring  concern subset  an to of  "Altman"  require cross-sectional is unlikely  to  portfolio  an  industry.  data.  concern the  manager  a  based While  While  to  who  models, such  only  in  a  r e g u l a t o r y agency  population of  industry, i t i s likely a  reports.  i s required, i t i s required The  requirement  within  weekly  be  of  who  businesses  considerable  is interested  in a  small  is  -27THE [1986]  COX MODEL;  have extended  analysis  t o t h e bank f a i l u r e  s e v e r a l advantages that  fewer of  the basic  the  type o f c r o s s - s e c t i o n a l  p r o b l e m . T h i s model o f f e r s  o v e r t h e more t r a d i t i o n a l  i t g e n e r a t e s an e x p e c t e d time u n t i l  restrictive  Model,  t h e "Altman"  and Wansley  t h r o u g h t h e a p p l i c a t i o n o f t h e Cox P r o p o r t i o n a l  Hazard Model  in  R e c e n t l y , L a n e , Looney  underlying  assumptions  which w i l l  distributional  underlying  be d i s c u s s e d  failure failure  a s s u m p t i o n s . One  the Proportional  i n more d e t a i l  below,  Hazards i s that  as e i t h e r f a i l u r e  or non-failure  as y e t . P r o p o r t i o n a l  companies  a n d do n o t t a k e i n t o a c c o u n t  a l l one c a n s a y a b o u t a n o n - f a i l e d failed  faced  firm.  The more t r a d i t i o n a l m o d e l s t e n d t o c l a s s i f y  not  and h a s  observed values of the v a r i a b l e s e f f e c t the hazard  by an a v e r a g e  that  models  firm i s that  Hazard models,  i t has  i n contrast,  19 can a n a l y z e such c e n s o r e d d a t a Lane, part  Looney,  and Wansley  o f an e a r l y warning  by a s s e s s i n g failure  evaluated  t h e Cox model a s  f o r bank f a i l u r e  i n two ways:  t h e model's a c c u r a c y i n p r e d i c t i n g time  a n d by c o m p a r i n g  individuals  system  samples.  t h e model's a b i l i t y  until  to classify  i n t h e f a i l u r e / n o n - f a i l u r e c o n t e x t w i t h t h e more  common m u l t i p l e  discriminant  analysis  approach.  Twenty-one r a t i o s were u s e d a s p o t e n t i a l p r e d i c t o r s o f failure.  These  r a t i o s were s e l e c t e d  t o represent  CAMEL d i m e n s i o n s o f bank o p e r a t i o n s w h i c h bank s o l v e n c y , a n d a r e u s e d e x t e n s i v e l y  appear  the five t o measure  by t h e bank  -28examiners.  20  (leverage),  CAMEL Asset  composition, The Hazard  r e s u l t s of  model  to  appears  analysis  that  information  Cox  regarding  pricing),,  Lane  study  Capital  and  the  bank  offers  probable  the  time  that  Hazard  rates. examiner  to  and  Liquidity.  the  financial  Proportional  classification  model  (loan  Earnings,  indicate  in analyzing  similar  the  representing  q u a l i t y , Management or  the  is useful  yield  acronym  (loan)  efficiency  Discriminant appear  i s an  failure  Cox  condition. models  Therefore,  i t  additional without  losing  21 significant The offers by and  classification  hazard  several  providing by  function advantages  an  lessening  nature  of  the  appear  that  estimate the  approach, over of  burden  traditional  this  accuracy.  approach  the  the  more  analysis.  by  on  survival-theory,  traditional  probable  imposed  merits  based  time  the  highly  I t would,  further  until  approach failure,  parametric  therefore,  examination.  -29IV.  PLAN OF  I n t h i s p a p e r , t h e Cox applied  t o the problem  industrial compared  setting  p r o p o r t i o n a l h a z a r d model w i l l  of bankruptcy p r e d i c t i o n  and  in a  the model's performance w i l l  t o the performance  discriminant  ANALYSIS  diverse be  o f an e s t i m a t e d l i n e a r  f u n c t i o n b a s e d on A l t m a n  [1963].  A. RATIO SELECTION " R a t i o s " were s e l e c t e d p o p u l a r i t y , performance performance it's  refer  performance  significance Altman  and  Availability  ratios  reported  L I S T OF  2.  refers  Popularity  studies of  Cash Cash Cash  Net  Income  1. 2. 3.  Net Net Net  [1966]  the necessary data.  2.  RATIOS USED.  flow Ratios:  1. 2. 3.  and  flow to sales. flow to T o t a l Assets. f l o w t o T o t a l Debt. Ratios.  income / S a l e s . income / T o t a l A s s e t s . income / T o t a l D e b t .  2.  1  and  major and  to data l i m i t a t i o n s  used are found i n t a b l e  Table  Cash  criteria:  t o the f r e q u e n c y o f use o f t h e r a t i o i n o t h e r s t u d i e s . Two  not a l l the f i r m s  1.  availability.  f o r t h i s p u r p o s e were B e a v e r  [1966].  The  on t h e b a s i s o f t h r e e  be  as  -30-  4. 5.  Retained Earnings  earnings / T o t a l Assets. b e f o r e I n t e r e s t and Tax / t o t a l  Assets.  Debt t o T o t a l A s s e t s . 1 Long t e r m d e b t / T o t a l A s s e t s . 2. C u r r e n t + l o n g t e r m d e b t + p r e f . s h a r e s Assets. 3.  Interest / long  Liquid  Assets  term  - Current  / Total  debt. Liabilities  Ratios.  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. Current assets / current 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. 2. 3. 4. 5. 6. 7. 8.  Inventory / Sales. Current Assets / Sales. Quick Assets / S a l e s . Total Assets / Sales. No c r e d i t i n t e r v a l , ( q u i c k a s s e t s m i n u s c u r r e n t l i a b i l i t i e s / funds for operations) Defensive I n t e r v a l , (quick a s s e t s / funds f o r operations). M a r g i n . S a l e s / c o s t o f goods s o l d . Change i n m a r g i n .  Market R e l a t e d 1. 2. 3.  Ratios.  C l o s i n g market v a l u e o f e q u i t y / t o t a l Change i n M a r k e t v a l u e o f e q u i t y . Invested C a p i t a l / T o t a l Assets.  assets.  c a s h f l o w = income f r o m 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 a c c o u n t s p a y a b l e m i n u s 2 c h a n g e i n a c c o u n t s r e c e i v a b l e m i n u s change i n i n v e n t o r y . working c a p i t a l quick  = c u r r e n t a s s e t s minus liabilities.  assets equals  cash  plus accounts  current received.  funds expenditures f o r o p e r a t i o n s equals 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 . invested c a p i t a l preferred stock,  s a l e s minus  e q u a l s t h e sum o f l o n g t e r m debt, m i n o r i t y i n t e r e s t s and common s t o c k .  -31-  *  change i n market e q u a l s c l o s i n g by c l o s i n g v a l u e t i m e ( t - 1 ) .  B.  market time  (t) d i v i d e d  THE DATA SET Data  S o u r c e s : The p r i n c i p a l  data sources f o r t h i s  were t h e Compustat r e s e a r c h and i n d u s t r i a l These tapes c o n t a i n f i n a n c i a l  statement  number o f f i r m s f o r t h e p e r i o d Research  industrial  the Compustat from  for a variety  reporting,  bankruptcy  including  or r e t u r n i n g t o  Most f i r m s l i s t e d publicly  the published  and t h e 10K r e p o r t s f i l e d  S e c u r i t i e s a n d Exchange C o m m i s s i o n  financial  by f i r m s w i t h t h e  i n the United States.  on t h e Compustat t a p e s a r e t h e l a r g e r  t r a d e d ones r a t h e r  t h a n t h e more common s m a l l e r  firms.  Any  u s e o f an a n a l y s i s o f b a n k r u p t c y  must t a k e  i n t o account  this  potential  based  on t h e s e  data  d a t a b i a s when a p p l y i n g  t o the general population of firms.  Sample S e l e c t i o n ; i n s u r a n c e and banking  T h i s study excluded institutions,  a s s o c i a t i o n s due t o t h e i r Bankruptcy estate,  o f reasons,  ownership.  statements  results  from  t a p e . F i r m s c a n be e l i m i n a t e d  Compustat d a t a i s d e r i v e d from  private  d a t a on a l a r g e  1966-1986. The Compustat  annual  tape  mergers, i n c o n s i s t e n t private  f o r 1986.  t a p e c o n t a i n s d a t a on f i r m s removed  industrial  the i n d u s t r i a l  tapes  study  A c t s , both  special  the Chandler  other f i n a n c i a l  railroads,  and s a v i n g s and l o a n  treatment  under t h e  and R e f o r m A c t s .  Real  companies, o t h e r t r a n s p o r t a t i o n  firms  -32-  and  service  industries  such as t r a v e l  a g e n c i e s were  e x c l u d e d a s most o f t h e d a t a a v a i l a b l e failure  r a t e s appears  industries. commercial  to either  manufacturing  industrial and  mining,  failures and  on b a n k r u p t c y  e x c l u d e or s e p a r a t e  T h e r e f o r e , t h e sample was and  also  restricted  including  the r e t a i l  and these  to  construction,  and  wholesale  trades. B a n k r u p t c i e s were i d e n t i f i e d structure  by  changes o f the r e m a i n i n g  industrial  file,  Of  f i r m s e x a m i n e d , 84 were  t h e 618  petitions  In  order to develop  bankrupt  Compustat t a p e  the  as  filing  XI o f t h e C h a n d l e r  t o the bankruptcy  for at least  the p r e f e r r e d  following  Beaver's  Changes R e p o r t e r .  identified  a non-failure  f i r m s were r e q u i r e d  y e a r s was  capital  Act  or  11 o f t h e R e f o r m A c t .  characteristics  for  X and  the  f i r m s on t h e r e s e a r c h  as r e p o r t e d i n t h e C a p i t a l  under C h a p t e r s  under C h a p t e r  examining  similar  sample, bankrupt  t o have had  and  non-  d a t a r e p o r t e d on  f i v e years prior  to f a i l u r e ,  v a l u e . T h i s t i m e p e r i o d was  the six  selected  reason:  study of f i n a n c i a l that  sample w i t h  ratios  failure  found  at approximately f i v e  failure  i t becomes more d i f f i c u l t  as p r e d i c t o r s years prior  to distinguish  the  of to future  3 failure  from  the f u t u r e  survivor.  f i r m s were matched t o s i m i l a r years p r i o r  to failure.  The  non-bankrupt  aim  b e g i n w i t h a sample o f s i m i l a r  In t h i s  study  bankrupt  firms five  of t h i s procedure f i r m s b e f o r e the  was  and s i x to  failures  -33-  began t h e i r of  financial  the f i n a n c i a l The  five  slide  ratios  i n order t o ensure  t o be a n a l y z e d .  t o s i x year p r i o r  28 f a i l u r e s  from c o n s i d e r a t i o n  which  petitions  filed  comparability  data requirement leaving  f o r bankruptcy  eliminated  a sample o f 56  firms  between 1971 and 1985.  D a t a V a l i d a t i o n . A c c o r d i n g t o t h e C o m p u s t a t Codebook, the  d a t a does n o t exceed  the  largest  t h e F10.6 f o r m a t ,  value possible  i s 999.999999 m i l l i o n .  when t h e d a t a o b t a i n e d was requirement, This  one f i r m , W.  result  bankruptcy  questionable.  against  T. G r a n t , was  However,  the format  rejected.  At the time o f  T. G r a n t h a d 82,000 e m p l o y e e s , 4  s t o r e s and s a l e s o f o v e r Compustat s a l e s  checked  was n o t u n e x p e c t e d .  i n 1975, W.  i n o t h e r words,  $1.6 b i l l i o n .  However, when t h e  f i g u r e s were e x a m i n e d , t h e d a t a  (See t a b l e  1200  appeared  3.)  +  +  I I I  I I I  Table 3 T. GRANT SALES ( Tn m i l l i o n s )  Piatt  (p35)  Compustat  1969  1970  1971  1972  1973  1974 |  1096  1210  1254  1374  1644  1849 |  1214  1254  1374  1644  1849  1761 |  +  + U n f o r t u n a t e l y , W.  verifiable earliest  T. G r a n t ' s  financial  d a t a were n o t  t h r o u g h o t h e r s o u r c e s s u c h a s Moody's, a s t h e  Moody's  corporate directory  available  i n the  University due  of B r i t i s h  C o l u m b i a M a i n L i b r a r y was  f o r 1977, and  t o t h e a b o v e p r o b l e m t h e company was e l i m i n a t e d  from  consideration. D a t a was a l s o e x a m i n e d t o e n s u r e n o t m i s s i n g . S e v e n t e e n f i r m s were immediately  prior  to failure.  examination  are presented  that v i t a l  identified  The r e s u l t s  i n table  v a l u e s were  as m i s s i n g  data  of further  4.  +  + Table CHARACTERISTICS  OF INCOMPLETE FINANCIAL DATA  # of firms  Characteristics st Filed l quarter. F i l e d 2^ quarter. Filed 3 quarter. Missing 3 years of data.  7 7 2 1 +  The  4  n  d  r  above r e s u l t s a r e a d i r e c t  problem o f t i m e l i n e s s o f f i n a n c i a l  +  consequence o f the data.  In the m a j o r i t y of st  cases, c l o s i n g of  the year In  prior  to failure.  an e f f o r t  to maintain  bankrupts, data, year  s t o c k p r i c e s were r e p o r t e d f o r December  and h a d m i s s i n g  sample.  In these  a s t h e one y e a r actually  an a d e q u a t e sample s i z e o f  and i n v i e w o f t h e s l o w d e l i v e r y  f i r m s which f i l e d  petitions  financial  cases, prior  i n the f i r s t h a l f  the l a s t  filed  statement  d a t a . T h e r e f o r e , one y e a r  b e t w e e n 1 a n d 18 months p r i o r  "matching" bankrupt  of financial of the  d a t a were i n c l u d e d i n t h e  C o m p a r a b i l i t y . The d a t a u s e d by  31  was t r e a t e d prior  data i s  to failure.  i n this  study  were  obtained  f i r m s w i t h n o n - b a n k r u p t f i r m s f o r two  -35-  reasons. F i r s t , industries finance,  a random sample o f f i r m s drawn f r o m t h e  (industrial  insurance,  r a i l r o a d s and  provide a s u f f i c i e n t inferences  any  services)  number o f b a n k r u p t  and  1985,  80  firms within  f o r b a n k r u p t c y , however, over  listed  firms  on t h e C o m p u s t a t  industrial  be p r e d o m i n a n t l y u n - f a i l e d f i r m s  The  a failure  will  file  financial  f o r bankruptcy  the t e s t  in principle  "absolute"  bankrupt to  firms  isolate  " m a t c h i n g " was nonbankrupt  t o ensure samples.  i s to isolate  i n the b e l i e f to predict the  The  and  c h a r a c t e r i s t i c s of firms  i n the f u t u r e  Comparing  of the " r e l a t i v e " a f u t u r e bankrupt  f a c i n g s i m i l a r economic  t h e d i f f e r e n c e s due  f r o m t h o s e due  would  which  that failure.  firm's  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 f i r m .  were  Therefore,  s u c h as t h i s  accounting data r e f l e c t s  financial  industries  t a p e i n 1986.  t h e s e u n i q u e a t t r i b u t e s c a n t h e n be u s e d While  study.  1%.  o f t h e b a n k r u p t and  the unique  any  8000 u n - f a i l e d f i r m s  o f most s t u d i e s o f b a n k r u p t c y  identify  to enable  as the p r o b a b i l i t y o f  i s l e s s than  second reason f o r t h i s  comparability purpose  i s u n l i k e l y to  firms  random sample drawn f r o m a p o p u l a t i o n  selecting  excluding  t o be drawn f r o m t h e r e s u l t s o f t h i s  Between 1972 filed  and c o m m e r c i a l  test  financial to  condition  "similar"  conditions  enables  t o the pre-bankruptcy  t o i n d u s t r y or s i z e  differentials.  non-  state  one  -36-  Th e s a m p l e o f u n - f a i l e d f i r m s was Compustat bankrupt  industrial  tape.  represented  from the  A n o n - f a i l e d f i r m "matched" a  i f t h e f o l l o w i n g c o n d i t i o n s were  1. The f i r m s must  met:  be i n t h e same o r s i m i l a r i n d u s t r y as  by t h e SIC c o d e s . An u n - f a i l e d f i r m ' s  was  considered  the  units digit  "matched" i f i t was w i t h i n p l u s of the f a i l u r e ' s  2. N e t income b e f o r e a s s e t s were compared prior  obtained  to failure.  o r minus  items,  s a l e s , and n e t  i n t h e same y e a r w h i c h was i f a firm failed  5 to 6  accepted  comparisons, three  i f on a t l e a s t  four  of these s i x  the u n - f a i l e d firm's  data  was  (less than  3 times but g r e a t e r  failed  firm's  within  a factor of three  factor  of three  the  failures Net  selected firms  data.  was  The r e q u i r e m e n t t h a t  t o be matched t o a t l e a s t extraordinary  of s i m i l a r e f f i c i e n c y ,  i n an e f f o r t t h i s paper (sales),  a factor of  times) o f the  firms' values  factor that permitted  as a b a s i s o f comparison  m a r k e t power,  t o match f i r m ' s  'efficiency'  be A  most o f  one n o n - f a i l u r e .  i t e m s and s a l e s  i n an a t t e m p t t o  were  identify  a s m e a s u r e d by n e t i n c o m e , and  a s i n d i c a t e d by s a l e s . N e t a s s e t s were  attempted  A  a r r i v e d a t somewhat a r b i t r a r i l y .  the lowest  income b e f o r e  within  t h a n 1/3  years  i n 1981, t h e  c o m p a r i s o n w o u l d be c a r r i e d o u t on 1975 and 1976 d a t a . match was  5 of  SIC c o d e .  extraordinary  F o r example  SIC code  of s i m i l a r size.  t o match f i r m s o f s i m i l a r ( n e t income) and  'size'  included  Essentially, 'market (assets)  power' five  -37-  to for  s i x years prior  order  failure  to ensure  the  and  exchange  information exclusion  such  two  as  firms'  different  survivors firms.  as  "matching"  total  and  the  filing  a  petition  by  such  industrial  Compustat on  as  and  the  codes  of multiple  each  exchange member  sample  of  or  used  as;a  matches each  S  to  Poor's final ensure  & P  index  firms. been  matched  size  include  S t a n d a r d and  and  p r o c e s s had were  in  composition  inclusion  were  case  on  2 matches  samples.  listed  These  criteria  remained  for a  indices  i n the  imposes  failures  between  exchange  comparability  the  t o a t most  reported  Codebook).  criteria  After  restricted  codes  further  one  the  non-bankrupt  i n various  (Compustat  matching  was  similarity  bankrupt  The  500  of  bankruptcy. Each  of  t o one  to  one  undertaken,  forty-  sixty-seven hundred  and  eight  -38-  V.  SAMPLE CHARACTERISTICS  A. SAMPLE S T A T I S T I C S 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  Table  i n table  5.  5.  SUMMARY S T A T I S T I C S 'millions 5 years prior  CHANDLER ACT Failure Match  Total Assets: mean 36.02 s.t.dev. 31.96  REFORM ACT Failure Match  OVERALL Failure Match  37.22 43.00  82.42 108.72  75.94 88.02  54.80 75.78  52.93 67.31  57.11 71.80  69.01 80.15  132.64 157.77  115.60 125.69  87.68 118.91  87.92 102.87  Net Income: mean .65 s.t.dev 1.14  1.73 2.17  2.51 3.87  3.02 3.75  ' 1.40 2.73  2.25 2.96  41  16  26  Sci16 S *  mean s.t.dev  N  25  In failure eight  order  to describe  and s u r v i v a l  the c h a r a c t e r i s t i c s  samples,  a graphical  occurred presented  The  exist  statistical  i s descriptive,  to  t i m e . The p r o f i l e s a r e  2.  T h e s e p r o f i l e s show t h a t , differences  of the o v e r a l l  r e p r e s e n t a t i o n o f t h e changes which  i n t h e two g r o u p s o v e r i n figure  67  a p r o f i l e was c o n s t r u c t e d o f  r a t i o s . The a i m o f t h i s a n a l y s i s  present  41  on a u n i v a r i a t e  basis,  b e t w e e n b a n k r u p t and n o n - b a n k r u p t  significance  of the apparent  firms.  differences  -39-  b e t w e e n t h e 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 in section VI(b).  However, any f u r t h e r  c o n d u c t e d on a u n i v a r i a t e is  capable of completely  interrelationships  basis  will  analysis  be  evaluated  c a n n o t be  a s no s i n g l e f i n a n c i a l  representing  which c o n s t i t u t e  Figure  ratio  t h e complex  a firm.  2.  RATIO PROFILE of BANKRUPT AND SURVIVOR FIRMS . «5Uruioof  Cash flow / T o t a l Debt  •h+  +  Net income / Total Assets +  VDCVCVVH  uupt  Long t e r m d e b t / Total Assets + +  L  .1  I I 4  •+ 1  •iS+ 4  3  2  + 1  years pr i o r  Work, Total  •H+  capital assets  +  /  Current Ratio +  i-H+  Margin  +  13  I--. 1.2 I.I  •i  o  + 4  + 3  2  1  U+ 4  • +  3  2  1  prior years  -41B.  RATIO The  ratios any  DISTRIBUTIONS normality  was  evaluated  inferences  Model,  of the distributions i n order  drawn  i n contrast,  from does  of the  to establish  the v a l i d i t y  the discriminant not rely  financial  analysis.  on any such  of  The  Cox  distributional  assumptions. Multivariate  normality  description  and e s t i m a t i o n  it's  i s felt  impact  practical exist the  tests  The  kurtosis and  and  probability  the normal  that  the d i s t r i b u t i o n  less  normal few  probability  the closer exceptions  income/sales,  became  bankruptcy.  This  into  matched  5  two g r o u p s  less  was  as bankruptcy  become  showed  average  involving  showed  as t h e sample  any  net  that  the  moved  as one would  to failure  becomes  on  apparent  bankruptcy.  ratios  I I . ) which  prior  the histograms  d i d n o t become  toward  not surprising  to 6 years  was  ratios.  which  were  normal  from  t h e skewness and  of the ratios  plots  to this  do n o t  normality  by e x a m i n i n g  of the  one moved  Unfortunately,  of the ratios  of the variables  (see appendix  distribution  firms  secondly, plots  theory,  variables.  by e x a m i n i n g  characteristics  from  A  first  1  data  essentially  multivariate  of the d i s t r i b u t i o n  statistics  Several  of multivariate  normality  of the underlying  i n two w a y s ,  normal  infers  f o r the  of inference.  of multivariate  normality  evaluated  aspects  i n the area  and one g e n e r a l l y  normality  i s not required  to  expect  to begin  imminent  closer  to  i f there  split does  -42exist  a difference  between  the non-bankrupt  and bankrupt  groups. It that  i s apparent  imminently  ratios  In  prior  Due from  possible  plot  merely  time  capital  / sales,  would  variable Such  from  firm's each  other  plots  be v e r y  assets  ratios,  between t h e  plot  any  undertaken  and the  inferences  on t h e un-  suspect. I t i s often distributed  variable  a l o g o r power  t r a n s f o r m a t i o n s were  not undertaken i n  area of interest  The d i s c r i m i n a n t  t o provide a comparison  fall  (see appendix I I ) .  analysis  by u s i n g  as the primary  performance.  path  to total  t o transform a non-normally  study  model's  non-bankrupt  probability  o f cash  variables  transformation.  previously  failure.  the discriminant  a normal  this  constructed  t o the nonnormality o f these  transformed  into  to  different  o f the working  abnormal  drawn  a very  and s i m i l a r  g e n e r a l t h e normal  extremes very  the profiles  bankrupt  exhibited  immediately  from  model  was t h e C o x  analysis f o r more  was  undertaken  descriptive  purposes.  C.  C H A N D L E R V S . REFORM A  second  issue  ACTS  t o be a d d r e s s e d  difference  exist  the  a c t and t o those  Reform  date?  between  firms  was:  declaring  declaring  Does a  significant  bankruptcy  bankruptcy  prior  at a  to  later  -43As  the  underlying  the  Kruskal-Wallis  The  formal n u l l  the  d i s t r i b u t i o n s of  r a t i o s were n o t  normally d i s t r i b u t e d ,  t e s t of group s i m i l a r i t y  hypothesis of the  two  the  was  undertaken.  Kruskal-Wallis  groups are  test  is  i d e n t i c a l , but,  that not  2 necessarily  normal.  Analysis  Variance, t e s t of d i s t r i b u t i o n s i m i l a r i t y ,  of  Kruskal-Wallis that  Unlike  p o p u l a t i o n s are  The  Kruskal-Wallis  hypotheses, f i r s t l y ,  that  no  t e s t was  that  no  existed those  B a n k r u p t c y Reform A c t  of  at  indication Table  a t i m e and that  6 gives  b a n k r u p t and  surviving  firms,  between f i r m s filing  1978.  Similar  can  a summary o f  the  only  for  passage of  give  one  a  does not,  the  Kruskalone  general exist.  comparing  year p r i o r to  for data  the  secondly,  they t e s t e d  test results  bankrupt firms  r e s u l t s were o b t a i n e d  and  U n f o r t u n a t e l y the  does, or  two  between  filing  a f t e r the  therefore  a difference  non  assumption  test  existed  t e s t s u n d e r t a k e n were u n i v a r i a t e ,  variable  basic  undertaken to  differences  o f b a n k r u p t and  differences  to the  ANOVA,  normally d i s t r i b u t e d .  b a n k r u p t c y b e f o r e and  Wallis  more commonly a p p l i e d  test i s less sensitive  the  distributions  the  four  failure.  years prior  to  failure. From t h e  ratio profile  certain variables failures basis.  and  are  capable of  non-failures  and  i t i s apparent  discriminating  when e x a m i n e d on  I t would a l s o appear  inventory/sales  (figure 2),  current  that  a  between  univariate  c e r t a i n r a t i o s such  assets/sales  are  not  good  as  that  -44discriminators form any  on  a univariate  conclusions  variables  regarding  when examined  has  evaluate on  the  t h i s concern, the  differences for  existed  at  results  of  At  these  the  0.01  individually t o be  tests  year  firms  to  evaluate  Bankruptcy  bankruptcy,  to  order  filing  that  conducted no  firms  Reform A c t s . in table  the  filing  The  6. variables,  t h e r e does not  between t h e under  of  and,  to  failure  l e v e l , a l l the  indicate  of  the  distributions  summarized  a significant difference  distributions  prior  C h a n d l e r and  significance  evaluated,  these  K r u s k a l - W a l l i s t e s t was one  are  that  b e e n a b u s e d . In  between t h e  b a n k r u p t c y under t h e  cannot  setting.  easy to d e c l a r e  p r o c e s s has  hypothesis that  performance of  been e x p r e s s e d  made i t t o o  c o n s e q u e n t l y , the  the  However, one  in a multivariate  R e c e n t l y c o n c e r n has reform act  basis.  appear  ratio  Chandler  and  Reform  Acts. In  order  the  overall  Kruskal-Wallis  tests  u n d e r t a k e n , the  used t o  at  overall  are  arrive  t o be  overall  1  i s the  l e v e l of  l e v e l was  (probability  value occurring  of  under t h e  the  approach  l e v e l . If K  significance  was  tests  0.01,  the  1  level,  l e v e l f o r each t e s t . At  an  individual  0.0003. I t i s a p p a r e n t the  of  B o n f e r r o n i approach uses a  minimum o v e r a l l  significance  significance  significance values  i s the  Bonferroni  significance  undertaken, then the  a / K where a where a  an  significance  o b s e r v e d v a l u e or n u l l hypothesis)  from the  p-  a more extreme  that  many o f  the  =  -45variables between  indicate  the  contrast,  samples  a t an  Kruskal-Wallis  test  exists  bankruptcy  under  the basis  of  a significant  o f b a n k r u p t and  overall  difference  On  that  nonbankrupt  significance  results  between  level  indicate  the  that  ratios  t h e C h a n d l e r and  difference  of  the Kruskal-Wallis  tests  In  the  significant  firms  Reform  firms.  0.01,  of no  exists  filing  for  acts. we  can  conclude the  following: A) level,  That  firms  individual Beaver's  C) increase  one  one  ratio  finding  That  identifying  be  exists year  that  not  a statistically year  Chandler  of  prior  and  were  a  useful  well  in  firms. been  a  startling  of bankruptcies  Act, there  firms  to  viability.  has  size  those that  an  perform equally  significant of  on  non-  i s similar  ratios  between  Reform  ratios  A c t and  result  firm  although there  of the  to failure  0.01  at the  b a n k r u p t and  financial  a l lratios  i n t h e number  passage  between  This  differences  That  significant,  prior  basis.  i n the evaluation B)  the  statistically  difference  bankrupt  tool  a  does  difference which  filed  not  appear  between  filed  under  since  the  under  to  the the  Reform  Act.  -46+  +  I  Table  6  I  I  TESTS OF GROUP SIMILARITY  I  I  ( u s i n g t h e K r u s k a l - W a l l i s methods)  I  I  of  I  I ' I |  H  H_ U  2  o^  :  n  o  d i f f e r e n c e between S u r v i v o r  and B a n k r u p t .  : no d i f f e r e n c e between B a n k r u p t b e f o r e 1978. Ratio  I  and a f t e r  p-value H  p-value H  Cash f l o w / s a l e s Cash flow / t o t a l a s s e t s Cash f l o w / t o t a l debt Net income / s a l e s Net income / t o t a l a s s e t s  . 0399 .0236 . 0001 0 .0 0 .0  . 4705 .7893 .7484 .9361 . 3360  Net income / t o t a l d e b t Long t e r m d e b t / t o t a l a s s e t s Total claims / t o t a l assets Working c a p i t a l / t o t a l a s s e t s Cash / c u r r e n t l i a b i l i t i e s  0 .0 .0103 0 .0 0 .0 0 .0  .2851 .6496 .1211 .1416 .2091  Current assets / current Inventory / s a l e s Current assets / sales Total assets / sales Quick a s s e t s / s a l e s  0 .0 .5883 . 8123 .3875 .1128  .1814 .9361 . 6689 .4705 . 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 Quick a s s e t s / t o t a l a s s e t s Quick a s s e t s / funds f o r o p e r a t i o n s No c r e d i t p e r i o d Retained earnings / t o t a l assets  0 .0 .0193 . 6970 0 .0 0 .0  .1211 .1995 .9361 .1566 .0215  Earnings before i n t e r e s t and t a x / t o t a l a s s e t s M a r k e t v a l u e e q u i t y / book v a l . d e b t Margin I n t e r e s t / long term debt  0 .0 0 .0 .0003 . 0001  .7283 . 3924 .6689 .1277  Invested c a p i t a l / t o t a l Change i n m a r g i n Change i n m a r k e t  0 .0 .0555 0 .0  liabilities  assets  .9149 1.0 .6689  ' I  I  -47-  D) using  A t an o v e r a l l s i g n i f i c a n c e  the B o n f e r r o n i  significant  significant 0.01,  C h a n d l e r and  between  firms.  difference,  between  the firms Reform a c t s  t h e sample  bankrupts.  o f bankrupt  a t an o v e r a l l s i g n i f i c a n c e filing  of  f o r b a n k r u p t c y under  ( b e f o r e and a f t e r  be c a r r i e d o u t on t h e e n t i r e  the  1978).  will  u n d e r t a k e n on t h e two g r o u p s o f b a n k r u p t f i r m s , will  0.01,  T h e r e d o e s n o t a p p e a r t o be a  In v i e w o f t h e s e r e s u l t s , t h e a n a l y s i s  analysis  of  a p p r o a c h , t h e r e a p p e a r s t o be a  difference  and n o n - b a n k r u p t  level  n o t be rather  sample  of  the  -48VI.  A.  technique single  which  value,  which  and w i l l  this  has a sample  population individuals  analysis  seeks  t o judge  Essentially, one  ANALYSIS  THEORY Discriminant  by  DISCRIMINANT  B,  to transform a series be used  i n this  the performance type from  population  from  of this  statistical of scores  paper  o f t h e Cox  of analysis  and on t h e b a s i s  drawn  representation  i s a multivariate  deals  with  the case  a n unknown p o p u l a t i o n . i s found  to A  a  "benchmark"  model.  A and a sample  o f these wish  situation  as a  into  when  from classify graphical  i n figure  3.  -49Linear "a  priori'  discriminant groups  analysis  results  f o rc l a s s i f i c a t i o n  i n one d i s c r i m i n a n t  i n t o two  function  o ft h e  form:^  Z = b  where:  + b.X. + b X „  0  1 1  r t  X.. = j b^  2 2  0  fch  +  . . . b X mm  attribute or i n d i v i d u a l variable  = discriminant function coefficient f o r j attribute  Z = discriminant The  discriminant  space in  function 3)  (x,yi n f i g u r e  figure  3)  score  maps t h e m u l t i d i m e n s i o n a l  onto  and maximizes  attribute  a one-dimensional space  the separation  between  (line  I  t h e two  3 groups. The  output  somewhat form. for  o f t h e BMDP S t a t i s t i c a l  d i f f e r e n t form  I n t h e two g r o u p  each  than case  n  Oi  where  firm  Z^.  The reduction  classified  advantage  i n dimensions. ratios,  Non-normality severe  +  into  problems  which  two f u n c t i o n s , one  which  ever  group the  group  has the  Software) type o f a n a l y s i s  than having t o  o n e now o n l y  evaluates  o f the underlying  i ndiscriminant  single equation  mim  of this Rather  i s i na  . . . + b .X  ( S e e BMDP S t a t i s t i c a l  major  twenty-seven  n  111  the s u b s c r i p t i denotes function i s evaluating.  i s then  largest  common  BMDP p r o d u c e s  group. Z. = b . + b , . X I  A  t h e more  package  evaluate  a single  variables  analysis  i s the  score.  c a n cause  particularly i n  -50quadratic function  discriminant  analysis.  i s an appropriate  The l i n e a r  assignment  discriminant  r u l e when  the following  4 assumptions  are  A)  satisfied:  The u n d e r l y i n g  normally  populations  are multivariate  distributed.  B)  The c o v a r i a n c e  matrix  i s t h e same  f o r t h e two  populations. C)  The  belonging  "a p r i o r i '  to either  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  population  D)  T h e mean  E)  The i n i t i a l  i s known.  and c o v a r i a n c e  matrices  classifications  a r e known.  were  done  correctly. A  major  estimation partition  concern  o f an e r r o r the original  discriminating sample  i n discriminant  function  and p e r f o r m a n c e  rate. sample  analysis  The most into  i s then  i s the  common a p p r o a c h  two g r o u p s .  estimated  i s evaluated  using  i s to  The  using  one s u b -  the other  sub-  sample. This several  " p a r t i t i o n i n g " approach  fronts.  The b a s i c  not  a l l the available data  can  be  it  does  a severe  problem  not evaluate  has been  criticized  c r i t i c i s m s are that i s used  i n a small  t o develop sample;  the discriminant  on  i t wastes  data;  t h e model  which  and second,  function  which  that  will  be  5 used  i n practice.  used  to classify  data  available,  The d i s c r i m i n a n t firms  i n practice  to partition  function should  the data  which  will  be  u s e a l l t h e sample  and.then  use a  function  -51-  derived use  on j u s t  a l l the information The  in  one p a r t i t i o n  available  "leaving-one-out"  a slightly  i snot efficient  discriminating  function  remaining  i s then  firm  i n the total  approach  d i f f e r e n t manner.  estimates  In this  i s estimated classified  as i t does n o t sample. theerror  rate  method, t h e  using  N - l f i r m s . The  on t h e b a s i s  of this  g function. can  This  be very In  using  time  this  identifying  function.  that  Observations higher  score.  was c a r r i e d o u t  uses  stepwise  a r e only  i n mind  included of the linear  that  the optimal  subset  the step-  procedure f o r  of thevariables  presents  error  a  i s  i s the  "jackknife" technique  classification  functions,  are classified  I t  performance.  The J a c k k n i f e  two c l a s s i f i c a t i o n  size.  the performance keep  data, but,  inclusion i n theanalysis.  o f model  matrix.  "leaving-one-out"  yields  for  BMDP:7M p a c k a g e  classification the  One m u s t  another  s e t i n terms  The  package  variables  improve  sample  analysis  i snot necessarily  variables  unlikely  optimal  whereby  significantly  procedure  This  o f t h e sample  a large  discriminant  analysis  discriminant  most  with  t h e BMDP:7M p a c k a g e .  when t h e y  not  uses  consuming  study,  discriminant  wise  technique  i s essentially  method.  one f o r each  i n t o which  ever  BMDP:7M group.  group y i e l d s the  -52-  B. ONE-YEAR  RESULTS  Results one  year  of the discriminant  prior  All  to failure  the variables  data  on a u n i v a r i a t e  interesting  t o note  significant  variables  that  were  analysis.  used  variables  not significantly  included appear  considered when  affect  with  o f one v a r i a b l e  may  were  6.)  becomes  I ti s individually  multivariate  whereby any  performance  becomes  therefore  when  less  In other  subsumed  were n o t  I t would  be s i g n i f i c a n t  variable.  7.  due t o t h e s t e p w i s e  function.  i t ' s effect  another  study  analysis  improving  a variable  i n isolation,  combined  i n this  i n the discriminant  while  i n table  (See T a b l e  i s partly  i n the c l a s s i f i c a t i o n  that  o u t on t h e  a f e w o f t h e many  used  This  procedure  by t h i s  basis.  only  carried  a r e summarized  identified  significant  discriminant  analysis  significant  words t h e  i n the effect  o f the  other. Most very  of the variables  different  t o those  identified  identified  by t h i s  by Altman's  analysis are Z  Score  7 model.  Altman's  following retained and  taxes  value  discriminant  variables: earnings to total  of total  working  to total assets,  liabilities  analysis  capital  assets, market  identified  to total  earnings value  and s a l e s  assets,  before  of equity  to total  the  interest t o book  assets.  -53-  +  +  I  table  I  CLASSIFICATION FUNCTION  I I Total claims / assets I No c r e d i t p e r i o d I Earnings before i n t e r e s t I and t a x e s / a s s e t s I Constant  (Jackknife  Bankrupt 23.89600 -2.10626 6.92492  -5.75120  -10.44621  I + When d i s c r i m i n a n t year p r i o r ' data, e x p e c t e d , the the  61 8  6 33  69  39  Accuracy 91.0% 80.5%  c a r r i e d out  accuracy declined.  a n a l y s i s b a s e d on  The  d i s c r i m i n a t i n g v a r i a b l e s c h a n g e d . None o f  appeared This  i n the  best  long  year  As  results  However, o f more i n t e r e s t  prior discriminant  was  the function  year p r i o r model.  r e s u l t i s not  p r e d i c t o r s of the  four  one  'four  year p r i o r  that  i n the  the  emerged.  summarized  v a r i a b l e s used  8.  four  on  data are the  in table  the  I +  87.0%  interesting features  classification  discriminant  (1 YEAR PRIOR)  Bankrupt  a n a l y s i s was  several  I I | | I I  technique)  Survive Survive Bankrupt  |  Survive 17.11449 1.21465 17.86440  CLASSIFICATION ACCURACY  of  I  7  u n e x p e c t e d . One  term v i a b i l i t y  p r e d i c t o r s of  short-term  would e x p e c t  would not survival.  that  necessarily  the be  -54-  Table  8  CLASSIFICATION Four Years P r i o r  FUNCTION to Failure  Survive N e t income / t o t a l a s s e t s Total assets / sales Invested c a p i t a l / t o t a l assets Constant  Bankrupt  -4.61612 2.60267 41.57300  -26.18338 4.95144 36.40367  -15.58192  -13.48379  CLASSIFICATION ACCURACY  (4 YEAR PRIOR)  (Jackknife technique) Survive Survive Bankrupt  I t would,  on t h e s e r e s u l t s  13 26  80.0% 74.0%  61  39  78.0%  useful results.  t h a t Altman's  Z score  However, any i n f e r e n c e  i s s u b j e c t t o doubt  of the d i s t r i b u t i o n s  Accuracy  52 9  t h e r e f o r e , appear  approach y i e l d s  Bankrupt  based  due t o t h e n o n n o r m a l i t y  of the underlying v a r i a b l e s .  -55-  VII.  A.  SURVIVAL There  survival which  MODEL  THEORY are three  basic  experience.  defines  instantaneous  f (t)  T H E COX  The f a i l u r e  the pattern risk  functions  density  of failure  of financial  which  describe the  function, f ( t ) ,  by d e s c r i b i n g t h e  collapse.  ( t < T < t + At )  = l i m Pr Afc-5>0 +  At where The of  The  T i s the time  survival function, surviving at least S(t)  = Pr  F(t)  = 1 - S(t)  third  already  risk  occurred.  H(t)  as long  failure.  describes  the probability  as t .  ( T _> t )  function,  instantaneous  S ( t ) , which  of  S(t)=  1  at t =  d i s t r i b u t i o n o f time failure.  the Hazard of failure  function, providing  0 until  H ( t ) ,describes the failure  has not  1  = lim P r ( t < T < t + A . t | T > _ t )  Afc-»o  +  At As  these  survival  three  process,  f(t)  = -dS(t)  S (t)  = exp [  H(t)  basic  they  functions  are closely related.  / dt  J* H (u) o = f(t) /S(t) -  describe  du ]  2  t h e same  - 5 6 -  Consequently, two.  As  the  estimate hazard  failure  or  hazard  function the  analysis  the has  data  may  ensure  function,  restricted failure.  to  The  distribution dependent.  In  that are  the  has  to  very  concentrate  other  hard  on  to  the  survival  such  an  the or  order a  t o make very  seem more  change  proportional  the  Time  the  of  can  the  time  The  basis of  and,  inference  determine  In  one  year  the  was prior  first  time,  time  estimate  and  to  probability  covariates are  must  an  the  analysis  estimate  dependent  hazard  analysis.  the  just  the  one  the  then  c o v a r i a t e s were  not  paper.  constant  reasonable  hazards  varying  time,  when  covariates  p e r i o d was to  assume  validity  c o v a r i a t e assumption on  time  of  c o v a r i a t e and  significantly.  independent sample  times  in this  short  time  for s t a t i s t i c a l  over  analysis,  model.  analyzed  The  over  c o v a r i a t e s , which  however,  the  complications:  constant  short period  of  Cox  would  major  results  constant  model,  estimate  palatable,  be  the  the  Cox  between  In  two  censored.  of  very  relationship  estimated  not be  interpretation  hazard  the  functions are  serious implications  to  not  faces  f u n c t i o n may  effort  it  survival  f u n c t i o n i m p l i e s the  function.  secondly,  and  and  c h a r a c t e r i z e , one  Survival the  d e s c r i b i n g one  time,  assumptions  assumption  analyzed  over  that  ratios  of  the  the  was  evaluated  and  then  remained  which did  time by  stratifying  observing valid.  i f the  There  was  -57-  little  evidence  covariates Data survival  t o suggest  had a s i g n i f i c a n t are censored  data,  terminates  that  when  usually  before  i n the study.  samples  one must  impact  because  response  that  dependent  yields  or  or event  to analyze  model.  incomplete  the experiment  In order  assume  time  on t h e o v e r a l l  t h e sample  a desired  subject  omitted  study  occurs  i n every  the censored  c e n s o r i n g and f a i l u r e a r e  3 generated  B.  by independent  T H E COX  PROPORTIONAL  The m a j o r the  form  of the hazard  Proportional the of  problem  hazard  Hazard  function  mechanisms.  HAZARDS  MODEL  remaining function  Model  i n survival  analysis  i s unknown. The Cox  presents  a technique  forestimating  by a l l o w i n g a s e m i - p a r a m e t r i c  the relationships  among  i s that  the hazard  functions.  assessment The  proposed  model i s : ^  H(t)  = HQ (t) exp H  where :  This B  model  (t)  ( X' B ) is  an a r b i t r a r y  X  is  a vector  o f concomitant  B  is  a vector  of  Q  i s semi-parametric  of regression  parameters.  no  distributional  or  „ 5 B.  information  parameters  as i t depends  However,  assumptions  function,  on the vector  Hg(t) i s a r b i t r a r y  are necessary  and  t o estimate Hg(t)  -58-  Cox  defines H(t)  The  the "Relative  / H ( t ) = exp  hazard  function  hazards,  hazard  model  assumes  i s constant through  the survival  Function" as:  ( X' B )  Q  proportional  Hazard  distribution  that  the  time.In  relative  proportional  for the different  X's a r e  g related  as powers  o f one  another.  t S(t)  = exp =  [  -  J  H  (  u  )  e  0  [ S ( t ) ]*exp Q  x  P  (  !  ) du ]  ( 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 the average f i r m . Sg(t) corresponds t o H g ( t ) . The  major  approach  to survival  restricted without In the  the  A the  words,  observed  approach  o f the form  the problem  The  tied  model  c a n be  distribution. t o the impact  of  i n f o r m a t i o n , on t h e  not having  to estimate  distribution.  i n t h e u s e o f t h e Cox m o d e l  of continuous  and  while  hazard  information  our a n a l y s i s  the concomitant  functions  versus  on c o n t i n u o u s can occur  i n practice,  inference  of the survival  can r e s t r i c t  arising  i s based  i s that  of the concomitant  of the survival  or f a i l u r e s  However,  analysis  v e c t o r X,  problem  issue  deaths  we  or survival  form  o f t h e Cox p r o p o r t i o n a l  to the effect  knowledge  other  hazard  advantage  discrete time  time.  a t t h e same  failure  o b s e r v a t i o n s cause  makes u s e o f t h e t e m p o r a l  time  difficulty  ordering  The  hazard  and, t h e r e f o r e , point  one h a s t o use d i s c r e t e  of "tied"  i s due t o  no  i n time. time  periods  observations  arises.  as the hazard  model  o f t h e o b s e r v a t i o n s and,  therefore, survival  c a n n o t be d i r e c t l y  applied  t o the case o f t i e d  times.^  The  obvious s o l u t i o n  time p e r i o d  t o the problem  i n question i n a effort  death o c c u r r e d per p e r i o d . feasible  i s t o decrease the  t o e n s u r e t h a t o n l y one  However, i n many c a s e s t h i s  i s not  o r i s e x c e s s i v e l y e x p e n s i v e . Many d i f f e r e n t  t e c h n i q u e s have b e e n p r o p o s e d  t o deal with the issue of t i e d  o b s e r v a t i o n s r a n g i n g from e v a l u a t i n g of o b s e r v a t i o n s t o randomly  every p o s s i b l e  and a r b i t r a r i l y  ordering  breaking the  8 ties. This measuring results failure,  study s o l v e s the problem survival  i n no t i e d i n this  of the year firms  time  failed  i n days  survival  which,  time  i n which  failure  on J a n u a r y  and  results  t h e goodness  assumption  stratifying  be  a one month  i n many t i e d o b s e r v a t i o n s . e v a l u a t e d i n two ways: by t e s t i n g  of f i t . 9 tested.  The p r e d i c t i v e  a b i l i t y of  o f p r o p o r t i o n a l h a z a r d s i s e v a l u a t e d by  the o v e r a l l  estimating  observations w i l l  time  o 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 and  t h e model i s r a r e l y The  until  o c c u r r e d . I n o t h e r words, i f a  t h e Cox m o d e l u s i n g  models a r e u s u a l l y  by e x a m i n i n g  sample,  5, 19xx, t h e r e c o r d e d s u r v i v a l  by e s t i m a t i n g  the r e a s o n a b i l i t y  i n this  s t u d y , was m e a s u r e d , i n d a y s , f r o m J a n u a r y 1  i n t e r v a l which Cox  o b s e r v a t i o n s by  t i m e o b s e r v a t i o n s . The t i m e  was 4 d a y s . The i m p a c t o f t h e t i e d illustrated  of tied  sample on t h e b a s i s o f a v a r i a b l e ,  a h a z a r d f u n c t i o n based  on e a c h  strata. If  -60-  p r o p o r t i o n a l hazards own  base l i n e  hazard if  is valid,  hazard,  but  f u n c t i o n w o u l d be  would e x p e c t  cumulative function lines.  hazard  versus  the  Therefore,  i s supported  the graph o f the  the  by  l o g of the  l o g o f - l o g o f the  the  underlying survival  or near  parallel  10  'residuals'  which  transformation: e.  = exp  The  i s evaluated  for the  examining  the  model are determined  by  the  ( B'  X.  )  D r e s i d u a l s u s e d i n t h e more common r e g r e s s i o n  predicted  or  'fitted'  the  model a s  probability distribution distribution.  and  cumulative  while  Consequently,  cumulative comparing  observed  v a l u e minus  v a l u e . T h i s approach  the p r o p o r t i o n a l h a z a r d  'fitted'  Cox  by  1 1  a n a l y s i s a r e d e f i n e d as  date.  assumption  t o produce p a r a l l e l  Goodness-of-fit  death  p o r t i o n of  same a c r o s s s t r a t a .  f u n c t i o n s or  time  c o u l d have i t ' s  the m u l t i p l i c a t i v e  the p r o p o r t i o n a l hazards  d a t a , one  each s t r a t a  one  the  'fitted'  there  i s no  must,  probability  of f a i l i n g  These r e s i d u a l s s h o u l d  o f 1,  by  one  would e x p e c t  in  is a  observed evaluate  the  before actual the a c t u a l  the observed  failure  behave a s a random sample  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 . the data w e l l ,  valid  value  in effect,  p r o b a b i l i t y of f a i l i n g i t t o the v a l u e  i s not  the  I f the  Cox  model  drawn "fits"  the graph o f the r e s i d u a l s  -61-  versus the cumulative  hazard  o f the residuals  to yield a  12 straight  l i n e with an expected  The  cumulative hazard  s l o p e o f 1.  f u n c t i o n was c a l c u l a t e d  using the 13  f o r m u l a g i v e n i n t h e BMDP S t a t i s t i c a l  H(e)  =  il ^  m. / t R j  Software  + ( e - e ^ m  /  1 + 1  appendix,  #R  1 + 1  let  where:  m.  = number o f d e a t h s  l  #R. 3  I  a t time  = number o f s u r v i v o r s a t t h e b e g i n n i n g o f p e r i o d ..  e and The using  e  1  < e <  Cox p r o p o r t i o n a l h a z a r d model was e s t i m a t e d  t h e BMDP:2L computer  stepwise  procedure  software.  T h i s package a l l o w s a  u s i n g t h e maximum p a r t i a l  values t o determine in  = residuals  e n t r y and e x i t .  Once a g a i n , one must  mind, t h e s u b - o p t i m a l i t y o f t h e s t e p - w i s e  identifying  variables  likelihood  procedure i n  for inclusion.  BMDP:2L e s t i m a t e s t h e r e g r e s s i o n c o e f f i c i e n t s model by m a x i m i z i n g  the l o g of the likelihood  a Newton-Raphson a l g o r i t h m . The a s y m p t o t i c is  t h e n o b t a i n e d by i n v e r t i n g  o f second  (See BMDP S t a t i s t i c a l  partials  function  covariance  using matrix  i s the negative of  of the l o g l i k e l i h o o d  Software,  Appendix  of t h e e s t i m a t i o n t e c h n i q u e s used of the information matrix  o f t h e Cox  1 ( b ) where 1 ( b ) i s t h e  i n f o r m a t i o n m a t r i x . The i n f o r m a t i o n m a t r i x the m a t r i x  bear  function.  31 f o r a d i s c u s s i o n  by BMDP:2L) The e i g e n v a l u e s  r a t h e r than  t h e more commonly  used  -62-  correlation if  matrix  s h o u l d be e v a l u a t e d  multicollinearity  i s a potential  evaluate m u l t i c o l l i n e a r i t y , correlation presented  matrix  i n order  both  i n order  determine  problem. In order t o  the estimated  and t h e common c o r r e l a t i o n to illustrate  to  asymptotic matrix  the differences  will  be  between t h e  two.  C. ONE YEAR ESTIMATION The  P r o p o r t i o n a l Hazard  step-wise  procedure  Software. found  in table for  prior  relationship  sign  the degrees  are zero with  o f the  o f freedom o f t h i s  are presented  the hypothesis  that  some c o n f i d e n c e . are of great  were t e s t e d t o d e t e r m i n e  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-distribution  be p r e s e n t e d  f r e e d o m due t o i n a d e q u a c i e s tests  by  o c c u r r i n g i f t h e r e i s no t r u e  approximate p-values w i l l  these  evaluated are  measures t h e p r o b a b i l i t y  the c o e f f i c i e n t s  observed  ratios  i s v e r y good a s i l l u s t r a t e d  the signs o f the c o e f f i c i e n t s  importance,  Statistical  o f t h e Cox e s t i m a t i o n  T h e r e f o r e , we c a n r e j e c t  the c o e f f i c i e n t s As  data  using the  o f t h e Cox e s t i m a t i o n a r e found  significance  The p - v a l u e  relationship. all  set of financial  9. The o v e r a l l  the p - v a l u e .  i n t h e BMDP  2. The r e s u l t s  the one-year  observed  available  The o v e r a l l  i n table  m o d e l was e s t i m a t e d  i n table  test.  As  a r e 102,  f o r 60 d e g r e e s  i n the t-tables.  i f the  of  The r e s u l t s o f  9. I t w o u l d a p p e a r t h a t a t  -63-  a s i g n i f i c a n c e l e v e l o f 0.05, each c o e f f i c i e n t ' s s i g n i s s i g n i f i c a n t when evaluated  individually.  +  +  I  Table  I  I  9  I  COX MODEL ESTIMATION  I  ONE YEAR PRIOR TO BANKRUPTCY SAMPLE LOG LIKELIHOOD = 114.4753 GLOBAL CHI-SQUARE — 99.14 D.F. = 7 P-VALUE VARIABLE  *  CLAIM1 DELMKT1 INTLTD1 NETYSL1 CFTD1 QKCL1 CASLS1  COEFFICIENT 1.7504 -1.5624 0.1738 -2.1242 -1.7469 -1.3441 1.5477  TEST OF SIGN SIGNIFICANCE CLAIM1 DELMKT1 INTLTD1 NETYSL1 CFTD1 QKCL1 CASLS1 *  STANDARD ERROR  COEFF./S.E.  0.8452 0.8917 0.0770 1.3748 0.7184 0.5804 0.7804  EXP(COEF)  2.0710 -1.7522 2.2579 -1.5451 -2.4315 -2.3159 1.9833  APPROX. P-VALUE. 6 0 DEGREES . 025 .05 . 01 .075 . 01 .01 .05  = Current + longterm debt + p r e f . s h a r e s / Total Assets. DELMKT1 = Change i n Market Value o f e q u i t y . INTLTD1 = I n t e r e s t / long term debt • NETYSL1 = Net income / S a l e s . CFTD1 Cash flow / T o t a l debt. QKSL1 Quick a s s e t s / Current l i a b i l i t i e s . CASLS1 = Current A s s e t s / S a l e s . CLAIM1  =0 .0  5. 7572 0. 2096 1. 1899 0. 1195 0. 1743 0. 2608 4. 7008  -64Intuitively, hazard from  level  that  t h e Cox model p r o p o s e s  exists  average  instantaneous  Consequently,  results  risk  H.(t)  f o r an average  i n a change  of failure,  faced  = H ( t ) exp( X ' Q  the estimated  has  not already  and any  line  deviation  i n the hazard, by t h e non-average  coefficient  instantaneous  a base  firm.  B )  A  any n e g a t i v e  in  firm  that  risk  results  of failure  i n a  decrease  given  failure  occurred.  +  + 10  Table CORRELATION  CLAIM DELMKT INTLTD NETYSLS CFTD QKCL CASL  CLAIM DELMKT INTLTD 1 -.416 1 .05 6 -.068 1 -.570 . 342 - . 0 9 8 -.488 .709 .018 - . 5 62 .614 -.148 -.010 .111 .195  ESTIMATED  CLAIM CLAIM DELMKT INTLTD NETYSLS CFTD QKCL CASL  MATRIX  1 .276 .205 .124 . 347 .237 -.101  (ONE Y E A R  PRIOR  DATA)  NETYSLS  CFTD  QKCL  1 .325 .475 .029  1 . 477 .095  ASYMPTOTIC CORRELATION (ONE Y E A R P R I O R D A T A )  DELMKT  1 .039 -.191 .049 -.178 -.079  INTLTD  1 -.103 .079 .269 -.231  NETYSLS  1 -.110 -.199 .063  1 .213  MATRIX  CFTD  1 .326 -.024  QKCL  1 -.233  +  + The  examining  problem  of multicollinearity  the estimated  asymptotic  was  evaluated  correlation  by  matrix  o f the  -65-  variables.  (See t a b l e  problem o f excessive of and  10) T h e r e d o e s n o t a p p e a r t o be a  collinearity  among t h e v a r i a b l e s a s most  t h e 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 T a b l e 10 a r e l e s s t h a n .3 only  two a r e between  .3 and .4. T h e r e  i s quite a  r e m a r k a b l e d i f f e r e n c e between t h e c o r r e l a t i o n m a t r i x and t h e estimated  asymptotic  c o r r e l a t i o n m a t r i x . One m i g h t have  e x p e c t e d m u l t i c o l l i n e a r i t y on t h e b a s i s  of the c o r r e l a t i o n  m a t r i x a s s e v e r a l o f t h e c o r r e l a t i o n c o e f f i c i e n t s a r e above .6, is  however, when t h e e s t i m a t e d  examined, t h e apparent c o l l i n e a r i t y The  signs  have e x p e c t e d  the sign of the current  are it  i n the r a t i o .  the r e l a t i v e l y  receivable  less liquid  takes time t o convert  current assets sales  = cash sales  +  being  assets  and  rate also  inventory  f o r the simple into  fact  that  cash.  accounts r e c e i v a b l e sales  inventory sales  a s t h e a c c o u n t s r e c e i v a b l e and  difficulty  t h e s e two r a t i o s o f t e n credit  than cash  ratio  o f accounts  Accounts r e c e i v a b l e  to sales r a t i o s increase  i n financial  to sales  i n the hazard  assets  these assets  We w o u l d e x p e c t t h a t inventory  assets  However, c u r r e n t  less liquid  and i n v e n t o r y .  generally  i s reduced.  i n d i c a t i n g a n improvement  an i n c r e a s e  include  c o r r e l a t i o n matrix  o f t h e c o e f f i c i e n t s a r e a s e x p e c t e d . One might  t o be n e g a t i v e for  asymptotic  that  the firm's  would a l s o r i s e .  reflects  s a l e s and o r a n i n a b i l i t y  an i n a b i l i t y to sell  r i s k s of  An i n c r e a s e i n  t o c o l l e c t on  inventory.  -66According firm's  stock  publicly the  two  change  to the e f f i c i e n t  price,  available market  i n market  value  The dominant of  and  that  data.  As  the  is  the one-year  we  would  would long  expect that  already  have  time period The  graphical  occurred  technique  of  changes  or would  the  part  stock Shick  value financial in this  prior  to  i n the stock  be  the  (see  analyzed year  on the  i n the  masked  h a z a r d s a s s u m p t i o n was  discussed  versus  f o r the group  C h a n d l e r A c t and  of  under  the  Reform  can  found  i n Appendix  previously.  l o g o f minus of  their  filing  proportional  one  estimation.  by  study  failure, price  the  very  used.  the p l o t  be  i n market  changes  calculated  illustrates  the  failure  Studies  variable  the major  proportional  time  changes  i n market  change  of a  in  i s not  approaching bankruptcy  that  and  i n the  i n t h e Cox value  the  expect  to debt  variables  i n market  precede observable change  reflects  we'would  value  the  e x p e c t e d , the change  hypothesis.  firms  indicate  significantly  market  indicative  markets  behaviour of  fully  variable  t h e change i s not  traded,  important  significant  variable  Sherman)  t o be  hypothesis,  Therefore,  o f b a n k r u p t s . As  the e f f i c i e n t  price  ratios,  value,  i s a  fact  information.  related  identification market  i f actively  markets  firms  matches,  A c t . The  Figure  log survival  filing and  the  function  b a n k r u p t c y under group  for different  graphs  hazards assumption i s not  using  4  the similar  results  I I I . These  tested  indicate  strata  that  inappropriate.  the  -67Th e h i g h d e g r e e comparative support  plot  of s i m i l a r i t y  of the Chandler  t o the r e s u l t s of the  d i f f e r e n c e s which found  that  and  and  o v e r l a p i n the  Reform groups  univariate  test  two  stratification  analysis  t o have a d i f f e r e n t multiplicative i n each  strata.  p a r t of the hazard  rate;  base l i n e  a l l o w s each  but,  lines.  As we  hazard observe  does not e x i s t  a significant  and  groups.  lines  evaluated-graphically cumulative seen  hazard  in this  case  by p l o t t i n g  o f the the  "fit"  a slope of approximately of  1. O v e r a l l ,  unreasonable overall As  of  "fit"  line  there Chandler  is relatively  was  a g a i n s t the can  straight  r a t h e r than the expected  the g o o d n e s s - o f - f i t does not  as the  that  be with  value  appear t o  be  straight  and  the  regression i s significant. i t i s possible that  significance and  reasonably  and  would  (see F i g u r e 5 ) . As  l i n e was  0.30  holds  function  the r e s i d u a l s  residuals  t h e same  that  between t h e  G o o d n e s s - o f - f i t of the estimated hazard  group  the  r a t e s we  evidence  difference  a  The  f u n c t i o n s h o u l d be  overlap, there i s further  Reform A c t  groups.  Therefore, i f p r o p o r t i o n a l hazards  Kay's p a r a l l e l  essentially  in this  b a s e l i n e hazard  t h e g r o u p s have d i f f e r e n t expect  group  t h e r e d i d n o t a p p e a r t o be  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 o f the data  of  lends  c o u l d be  the very h i g h l e v e l  o v e r s t a t e d due  t h e r e f o r e , t h e model w i l l i t s performance  t o an e s t i m a t i o n  a l s o be  on non-sample  of  data.  e v a l u a t e d on  problem  the b a s i s  -684  Figure LOG  (1  MINUS LOG  SURVIVAL  Cox P r o p o r t i o n a l H a z a r d M o d e l year p r i o r t o bankruptcy data) STRATA  SYMBOL  CHANDLER REFORM  -1.8  .+  +  -2.7  +  -3.6  +  -  -4.5  -  +  -  -5.4  -6.3  -  +  -  -  +  — 0.0  FUNCTION  +  +  A B  +  +  +.  A*A AAAA*B AA B AAAA BB AAAA BBBB AAA*BBBBBBB A BB BBBB**B B AAA BBBB A BB AA AA BB A B AA B A B A B AA B A B A BB A B B AA B A B A B A BA  70.  210  140 DAYS  280  350  +  -  -  +  -  +  -  +  —  -69Figure 5 GOODNESS OF FIT OVERALL SAMPLE, 1 YEAR PRIOR TO FAILURE .+  +  +  +  +  XY.  .45 11 1 1 1 1 11  .36 C  1 2  u M H A Z R D  .27  1 1  .18  11  .09  0.0  Y 1 - 2 -11 +  11 1 2 2 1  .+. .  0.0  .+. , . 30  .+. , .60  R = .9807 P(R) 0.000 MEAN  X Y  .57752 .23239  XVAR =  .+. , .90  1.2  , .+. . 1.5  RESIDU ST.DEV. .46155 .13534 2 RESIDU  REGRESSION  LINE  X= 3.3445*Y-.19973 Y= .28756*X+ .06632 VERSUS  YVAR =  RES.MS. .00837 719E-6  1 CUMHAZRD  -70-  D. FOUR-YEARS PRIOR ESTIMATION The  Cox p r o p o r t i o n a l hazards model was a l s o estimated on  the b a s i s o f the four-year estimation  p r i o r data s e t . The r e s u l t s o f the  are summarized i n Table 11 w h i l e the goodness-of-  f i t graphs can be found i n f i g u r e 6. +  +  1  I  Table 11.  |  COX MODEL ESTIMATION  I  | I |  4 YEARS PRIOR TO FAILURE LOG LIKELIHOOD = -127.9253 GLOBAL CHI-SQUARE = 42.29 D.F.= 6 P-VALUE =0.0000  I I |  |  VARIABLE  *  NETYTD4 INVCTA4 NETYSL4 TASLS4 DELMKT4 QKTA4  *  NETYTD4 INVCTA4 NETYSLS4 TASLS4 DELMKT4 QKTA4  COEFFICIENT -12.1462 -6.3279 22.4321 1.6977 -0.4064 -3.0010 = = = = = =  STANDARD ERROR 3.0109 1.4204 6.7332 0.5012 0.2468 1.7569  I COEFF./S.E. -4.0341 -4.4548 3.3316 3.3875 -1.6464 -1.7082  EXP(COEF) 0.0000 0.0018 4 * 10 5.4615 0.6660 0.0497  Q  Net income / T o t a l debt. Invested c a p i t a l / T o t a l a s s e t s . Net income / S a l e s . Total assets / Sales. Change i n market value. Quick a s s e t s / T o t a l a s s e t s .  As one would expect, the s e t o f p r e d i c t o r s o f 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 s h o r t term model. However, d e s p i t e the h i g h s i g n i f i c a n c e o f the model, s e v e r a l o f the c o e f f i c i e n t s are somewhat unexpected.  -71-  I t w o u l d seem u n l i k e l y total  debt  failure  would have such  t h a t i n c r e a s i n g n e t income t o a dramatic  a s t h e model w o u l d s u g g e s t .  income t o s a l e s i s a l s o v e r y expect  impact  on t h e r i s k  The c o e f f i c i e n t  surprising.  efficiency  of f a i l u r e .  However,  One w o u l d  and t h e r e f o r e , s h o u l d  normally  according  t o the r e s u l t s  risk  of f a i l u r e dramatically.  results,  to identify  the source  the c o r r e l a t i o n matrix  c o r r e l a t i o n matrix 12).  of these  i n c r e a s e the  of these  "strange"  and t h e e s t i m a t e d  s i x v a r i a b l e s was  A s c a n be s e e n f r o m t h i s  asymptotic  examined  table there  income t o s a l e s ,  the  largest  those  and t o c h a n g e i n m a r k e t v a l u e .  correlation  i n t a b l e 10 where  coefficient t h e r e was  multicollinearity.  In order  multicollinearity,  the estimated  matrix  was  v a l u e s were  apparently  to evaluate  asymptotic  However,  similar  to  little of  correlation  c o r r e l a t i o n between n e t income  t o s a l e s and n e t income t o t o t a l  debt  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, using the f i v e  income t o s a l e s was selected  and  a l s o examined.  The e s t i m a t e d  calculated  debt  the p o s s i b i l i t y  asymptotic  (See  exists  c o n s i d e r a b l e c o r r e l a t i o n b e t w e e n n e t income t o t o t a l net  risk  o f the model,  i n c r e a s e n e t income t o s a l e s w o u l d a c t u a l l y  I n an e f f o r t  indicate  reduce the  this  table  of net  t h a t an i n c r e a s e i n n e t income t o s a l e s w o u l d  increasing  of  i s very high,  therefore, re-  v a r i a b l e s remaining  removed.  nearly.8  after  N e t income t o s a l e s  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  net  was assets to  sales i s included.  Therefore,  with the new s e t o f f i v e  v a r i a b l e s , no v a r i a b l e s use the same components. of t h i s r e - e s t i m a t i o n  The r e s u l t s  a r e found i n t a b l e 13.  +  +  I I  | I j | | I I  CORRELATION MATRIX  NETYTD INVCTA NETYSLS TASLS DELMKT QKTA  | I | I I | I | | +  I  Table 12.  NETYTD 1 .35 3 .734 -.026 .744 .155  INVCTA 1 .411 .134 .156 -.169  (FOUR YEARS PRIOR DATA) NETYSLS 1 .154 .412 .069  TASLS  DELMKT  1 .030 .036  1 -.160  | QKTA  1  ESTIMATED ASYMPTOTIC CORRELATION MATRIX (FOUR YEARS PRIOR DATA)  NETYTD INVCTA NETYSLS TASLS DELMKT QKTA  NETYTD 1 .237 -.783 -.170 .137 .050  INVCTA  NETYSLS  1 -.408 -.176 .016 .332  1 .076 -.243 -.043  TASLS  1 -.213 -.139  DELMKT  1 .074  | I I I I I |  | I QKTA  1  | I I I I I | +  -73-  Table 13. COX MODEL, RE-ESTIMATION 4 YEARS PRIOR TO FAILURE LOG LIKELIHOOD = -153.2074 P-VALUE = 0.0000 GLOBAL CHI-SQUARE = 36.90 D.F . = 5 VARIABLE  *  COEFFICIENT  NETYTD4 INVCTA4 TASLS4 DELMKT4 QKTA4 NETYTD4 INVCTA4 TASLS4 DELMKT4 QKTA4  -3.7497 -3.7199 1.3512 -0.2799 -2.8003 = = = = =  STANDARD ERROR 2.0162 1.2784 0.5041 0.2248 1.6581  COEFF./S.E.  EXP (COEF) 0 .0235 0 .0242 3 .8622 0 .7558 0 .0608  -1.8598 -2.9099 2.6804 -1.2453 -1.6889  Net income / T o t a l debt. Invested c a p i t a l / T o t a l a s s e t s . T o t a l assets / Sales • Change i n market v a l u e . Quick a s s e t s / T o t a l a s s e t s .  With the v a r i a b l e net income t o s a l e s omitted, the v a r i a b l e s now have the expected s i g n s and the impact o f a change i n each v a r i a b l e i s more reasonable. When the goodness-of-fit  was evaluated g r a p h i c a l l y , there was  d i f f e r e n c e from f i g u r e 6. T h e r e f o r e , i t would appear c o l l i n e a r i t y between the v a r i a b l e s has a s e r i o u s  little that  impact on  the c o e f f i c i e n t s o f those v a r i a b l e s but a r e l a t i v e l y minor impact on the " f i t " o f the model.  -74Figure 6 GOODNESS OF FIT 4 YEAR PRIOR .+ .45  +  +  +  +  11 .36 C U M H A Z R  + -  .27  D  .18  + +  . 0 9 + 1 Y 11 X 1 - 1 -11 0.0 +  .+  0.0  1 11 11 1 11 2  1 11  1 11 2  +  1  +  11  1 11 1 11  +  .30  11 1  XY  +  .90  .60  + 1.2  RESIDU R = .9720 P(R) 0.000 X Y  MEAN .46036 .23423  ST.DEV.  .37587 .13108  REGRESSION  X= Y=  LINE  2.7870*Y-.19243 .33898*X+ .07818  +. ,  1.5  RES.MS. .00802 976E-6  -75-  E.  TIED  OBSERVATIONS  The times  impact  until  examined  now  u s i n g time  the  time  by  to  period being  resulted  tied.  simulate  the  order  compare  ties  model.  result  estimation Once variable  Any  are  with  out  those i n the  was  also  proportionality The apparent can  be  one seen  the  were by  regression a l l have by  of  the  between  stepwise i n the  e v a l u a t e d , and  for  the the  to  "correct"  no-  therefore, these  two  observations  sign,  more  and  the  however,  procedure correct  are  very  model  proportionality  showed  that  was  not  by  the  many t i e d  examines  the  goodness-of-fit  graph,  using  significant  expected  o b s e r v a t i o n s . The  in this  until  14.  the  identified  caused  out  in  observations i n  would,  i s highly  the  times  i n order  tied  but  change  factors  used  model  sample  This  uncorrected tied  i n Table  hazards  same  carried  those  fall  identical  observed  the  corrections  this  the  correction  to  would  assumption  problem when  of  identified  ties  assumption  As  results  presented  from  no  caused  reasonable  the  on  i n months.  of  corrections  these  coefficients  variables  the model  with  with  proportional  e s t i m a t i o n was  case  results  Cox  i n most  package  again,  different  7.  The  extreme  The  the  measured  i n e s t i m a t e s which  extremes.  the  on  failure  o b s e r v a t i o n s . No  to  observations, firms  estimating  BMDP s t a t i s t i c a l tied  tied  bankruptcy,  was  failure  of  the  hazard  unreasonable.  the  o b s e r v a t i o n s becomes  "fit"  line  plot  in  i s far  figure from  -76being  linear  and i n f a c t  a p p e a r s t o be two l i n e s  rather  than  one.  +  +  I  Table  |  I  14.  I  "TIED" OBSERVATIONS RESULTS OF COX ESTIMATION (1 y e a r p r i o r ) LOG LIKELIHOOD = GLOBAL CHI -SQUARE VARIABLE CFTD1 CACL1 INVSLS1 EBIT1 DELMKT1 DELMRG1  I  I j j  +  *  = 7 6 . 09  COEFFICIENT -1.8776 -0.9892 4.7322 -4.6722 -1.8206 4.4704  -141.6433  D.F. = 6  P-VALUE =0.0000  STANDARD COEFF./S.E. ERROR 0.6206 0.3075 1.0407 1.5361 0.9886 2.2057  EXP(COEFF.)  -3.0255 -3.2172 4.5470 -3.0417 -1.8416 2.0268  0.1529 0.3719 113.5419 0.0094 0.1619 87.3882 I  CFTD1 = C a s h f l o w / t o t a l d e b t . CACL1 = C u r r e n t R a t i o I INVSLS1 = I n v e n t o r y / s a l e s EBIT1 = E a r n i n g s / a s s e t s ! DELMKT1 = Change i n m a r k e t v a l u e DELMRG1 = M a r g i n c h a n g e I  +  When compared t o t h e n o - t i e s m o d e l , t h e t i e d m o d e l h a s resulted  i n a v e r y 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  identified results  by t h e s t e p w i s e  indicate  distorted  that tied  procedure  and t h e g o o d n e s s - o f - f i t  o b s e r v a t i o n s can cause  e s t i m a t e s and p o o r l y f i t t i n g  estimated  very hazard  functions. I t w o u l d t h e r e f o r e , seem t h a t t h e Cox m o d e l , when corrected  for tied  o b s e r v a t i o n s , appears t o model t h e  i n t e r a c t i o n s between d i f f e r e n t financial  s t r u c t u r e as they  components o f t h e f i r m s  r e l a t e t o bankruptcy.  The model  -77identifies expect year  t o have  prior  survival The survival the  financial an  case,  related  variables  effect while ratios  on  also  one  s h o r t term  would  o f t h e Cox  function  estimates  identifying  more  proportional will  of the discriminant  be  intuitively  viability  analysis.  one  case.  hazards  examined  i n the  long-term  i n the four-year p r i o r  adequacy  results  which  and  model compared  to  -78-  F i g u r e 7. GOODNESS OF FIT, TIED OBSERVATIONS  5.6  4.9  +  4.2  +  3.5 C U M H A 2.8 Z R D 2.1  , + . .X. . . . +  +  + -  11 2 11  141 2111  2 1  12  + . . .Y. . . + .  1  1 1 1  11 2 1  +  + 4 - 1  1.4  +  .70  + Y  0.0  +Q77526 2121 1111 .+.X  0.0  +  .40  +  11 +  1.2 RESIDU  +.  .+  2.0  +.  VIII.  The p e r f o r m a n c e criteria:  first,  o f t h e Cox model was e v a l u a t e d u s i n g two  accuracy of c l a s s i f i c a t i o n  secondly, d e s c r i p t i v e performance The  power. The b a s e  classification  used  i n table  t o d e v e l o p t h e models,  classification  capability  of the  to failure.  the r e s u l t s  t h e improvement  a s we move c l o s e r  well  o f how t o c l a s s i f y  f a i l u r e was l e s s arbitrarily within  d a t a s e t was  from t h a t  time  period  the p r e d i c t i v e  r e s u l t s are presented i n model  to failure.  analysis,  t h e Cox model d o e s n o t f i r m s as  a s one i s p r e s e n t e d w i t h t h e p r o b l e m  a specific  e x p e c t e d time t o f a i l u r e as  o f bankruptcy or non-bankruptcy.  f i r m was c l a s s i f i e d  four,  The r e s u l t s a r e  t o t h e problem o f c l a s s i f y i n g  or non-bankrupt  indicative  model.  t o t h e d a t a from  The one y e a r p r i o r  Unlike discriminant  bankrupt  analysis  t o make any i n f e r e n c e s a b o u t  as t h e y h e l p i l l u s t r a t e  itself  level of  15. As t h e one y e a r p r i o r  power o f t h e m o d e l s .  filed  functions  two a n d one y e a r p r i o r  c a n n o t be u s e d  lend  and p r e d i c t i o n  o r p r e d i c t i o n and  and Cox m o d e l s was e v a l u a t e d by a p p l y i n g t h e  e s t i m a t e d one y e a r p r i o r  summarized  line  was t h a t o f t h e d i s c r i m i n a n t  discriminant  three,  MODEL COMPARISON  as bankrupt  In t h i s paper, a  i f i t s expected time  until  t h a n 350 d a y s . The v a l u e o f 350 d a y s a r e  chosen  a s a l l b u t one o f t h e b a n k r u p t  350 d a y s o f t h e end o f t h e p r i o r  f i r m s had  period.  -80-  +  + T a b l e 15 (a) MODEL PERFORMANCE  DISCRIMINANT ANALYSIS 4 Years  prior  Survivor Bankrupt Total 3 Years  prior  Survivor Bankrupt Total 2 Years  prior  Survivor Bankrupt Total 1 Year  prior  Survivor Bankrupt Total  +  Classification Survivor 66 31 97  Bankrupt 2 10 12  Classification Survivor 62 27 89  Bankrupt 6 14 20  Classification Survivor 63 15 78  Bankrupt 5 26 31  Classification Survivor 61 8 69  Bankrupt 7 33 40  +  -81-  +  + Table  15 (b)  MODEL PERFORMANCE  COX MODEL: 4 Years p r i o r  Survivor Bankrupt Total  Classification Survivor 57 21 78  3 Years p r i o r Survivor Bankrupt Total  Classification Survivor 60 19 79  2 Years p r i o r Survivor Bankrupt Total 1 Year  Bankrupt 8 22  30  Classification Survivor 58 14 72  prior  Survivor Bankrupt Total  Bankrupt 11 20 31  Bankrupt 10 27 37  Classification Survivor 57 3 60  Bankrupt 11 38 49  +  + As c a n be s e e n f r o m t a b l e  15 ( a , b ) ,  models t o f o r e t e l l b a n k r u p t c y d e c l i n e d failure  increased.  the a b i l i t y o f both  as t h e time  until  I t would appear t h a t both t h e d i s c r i m i n a n t  and Cox m o d e l s 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 . I n o t h e r w o r d s , t h e s e m o d e l s appear  underestimate  the time  discriminant analysis bankrupt, Cox  until  classified  4 years prior  model gave e x p e c t e d  d a y s t o 20 The  filing  before the p e t i t i o n  identify In  times u n t i l  that  both  bankrupts  was  see  f i r m was  four  evaluate  the v a l i d i t y  and  prior  to f a i l u r e  would  Cox  models t e n d  (two b a n k r u p t  f u n c t i o n over  Cox  and  against time.  In order  time  year p r i o r  and  and  to  hazard  to estimated  a t t h r e e , two  two  survival  of the e s t i m a t e d p r o p o r t i o n a l  one  to  bankrupts.  then p l o t t e d  u s i n g t h e Cox  last  i t i s not  sample. The  calculated  350  expect  power o f t h e  model on d a t a o u t s i d e t h e d a t a s e t u s e d m o d e l , a f u n c t i o n was  the  the o r i g i n a l  the changes i n the s u r v i v a l  the  o c c u r r e d a t some p o i n t  Consequently,  firms  than  i s usually  b e f o r e t h e y become l e g a l  drawn f r o m  f u n c t i o n o f each to  petition  the d i s c r i m i n a n t  model a random sample o f  while  of less  t h r o e s . T h e r e f o r e , we  filed.  as  filed.  order t o assess the d e s c r i p t i v e  survivors)  example,  being f i l e d  failure  o f t h e f i r m had  was  For  future bankrupts  t o the p e t i t i o n  of a bankruptcy  the t r u e f a i l u r e  surprising  14  f i r m s 4 years before they  stage i n a f i r m ' s death that  bankruptcy.  to  the  one  year  estimated  coefficients. These g r a p h i c a l 11  i n Appendix  obtained least  descriptions,  found  I, of the f i r m s ' s u r v i v a l  by p l o t t i n g  as l o n g a s  in figures  through  f u n c t i o n s were  the f i r m s p r o b a b i l i t y  ' t ' a g a i n s t ' t ' f o r each  8  of surviving year p r i o r  to  at  -83failure. which to  One w o u l d  were  expect  non-failures  the survival functions  a t t h e time  one f o r any ' t ' as these  probability contrast, firms  one would  to decline  faster  general,  give  one a  contrast,  merely  group  297882 would  most  time.  gives  failure. results.  analysis, i n  indicates  which  of a failure. which  i s very  probable  i s listed  mid  1970's, a n d i t i s p e r h a p s  reveal  any other  unexpected The  o n t h e AMEX  firm  number  here  Further  reasons  survival function  behaviour.  results of applying  t h e 1-year  discriminant  function  t o these  firms  Exchange.  the early to ETZ Lavud  examination  prior  this  one would  Stock  that  for this  one  297882, i s a n  represent  significant  i n 1972.  possible  exhibiting  on t h e American  presented  number  i s one o f t h e s u r v i v o r s ,  s i m i l a r t o what  ETZ L a v u d ,  survival functions  listed  of firm  t o see s u r v i v a l functions  o f behaviour  firm  firm  The  16.  to decline  probability of  The d i s c r i m i n a n t  r e s u l t was t h a t  11). As t h i s  not expect  Israeli  to  high  o f bankrupt  the expected  which  close  ' t ' . In  of actual  a firm's  one a s c o r e  unexpected  (figure  expect  only  exhibit  t o be  membership. The  type  graphs  over  as  firms  a very  and perhaps  * t ' was t o t h e t i m e  " p i c t u r e " o f how  changes  have  the survival plot  't' increases,  these  surviving  would  a t l e a s t as long  expect  as  the closer  In They  of surviving  firms  of analysis  of  was  failed  somewhat  linear  are presented  i n table  -84-  I t would firms,  that  t h e r e f o r e appear,  t h e Cox model and t h e d i s c r i m i n a n t model  very s i m i l a r  results.  f i r m s d i d n o t appear year in  prior  year p r i o r  Both  In both models, t h e f u t u r e t o be i n t h e b a n k r u p t c y  to f a i l u r e .  the p r o b a b i l i t y  second  of survival to f i l i n g  u n t i l one  i n the  petition.  t h e Cox and D i s c r i m i n a n t m o d e l s show t h a t  Discriminant  the time p e r i o d  analysis classifies  group  f u n c t i o n graphs  firm  i n question.  i t as a member o f t h e  i n a l l three prior show t h a t  yield  show a d e c l i n e  beginning usually  the bankruptcy  four  bankrupt  group  The Cox m o d e l ' s g r a p h s  #297882 was i n t r o u b l e o v e r  bankrupt  i n the case o f these  p e r i o d s , and, t h e s u r v i v a l  t h e f i r m was i n t r o u b l e  over  those  same y e a r s .  +  + T a b l e 16 LINEAR DISCRIMINANT FUNCTION SCORES Firm:  #564402  #868168  #297882  Three y e a r s p r i o r S u r v i v o r Score Bankrupt Score  7.26 4.84  3.09 0.93  2.43 -3.15  9.07 9.99  Two y e a r s p r i o r S u r v i v o r Score Bankrupt Score  8.29 6.70  1.46 1.04  2.91 -2.56  10.38 11.19  One y e a r p r i o r S u r v i v o r Score Bankrupt Score  4.01 9.50  2.64 6.01  4.89 1.33  11.17 12.24  Classify +  #042078  •  o b s e r v a t i o n i n t o whichever i s the highest.  group's  score +  -85-  Therefore, provide  i t would appear  information  that  cannot. E s s e n t i a l l y the benchmark w h i c h c a n  be  the  until be  provides  failure  Cox  model i s a b l e  discriminant  model  model p r o v i d e s  used t o c l a s s i f y  firms  indeterminate.  The  expected  a  single  as  either  Cox  model  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  f r o m w h i c h an  time u n t i l  to  the  in  time  failure  can  derived. For  e x a m p l e , ETZ  b o t h m o d e l s as analysis, Cox  linear  the  discriminant  bankrupt, non-bankrupt, or contrast,  that  the  a problem. According f i r m i s most p r o b a b l y  estimation  prior  period,  longer survive  L a v u d , a s u r v i v o r , was  finds that the  t h a n 353  a t the  company had  days o f over  f o r a t l e a s t t e n more  to the  identified discriminant  a b a n k r u p t . However,  beginning of  a p r o b a b i l i t y of 20%.  The  years.  by  the  one  year  surviving  company went on  the  to  -86IX. SUMMARY AND CONCLUSION  T h i s paper  h a s e v a l u a t e d t h e Cox p r o p o r t i o n a l  model's a p p l i c a b i l i t y t o t h e problem prediction.  The Cox model o f f e r s  more t r a d i t i o n a l p r e d i c t i o n  o f bankruptcy  several  advantages  probability expected  n o r m a l i t y and i t produces distribution  over t h e  m o d e l s . T h i s model d o e s n o t  depend o n t h e v e r y 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 multivariate  hazard  assumptions o f  an e s t i m a t e d  o f times u n t i l  f a i l u r e f r o m w h i c h an  t i m e o f f a i l u r e c a n be d e t e r m i n e d .  I n 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 e s t i m a t e a p r o b a b i l i t y o f f a i l u r e w i t h i n a g i v e n time Two  period.  major a r e a s o f c o n c e r n  model a r e 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  observations. Multicollinearity distorted  i n the application  appears  estimated c o e f f i c i e n t s ,  relatively  minor  affect  "Tied" observations i n contrast Cox  severely the  cannot  be h a n d l e d  distorted  model. Consequently,  applied  t h i s paper,  included  multicollinearity, in a  any a p p l i c a t i o n  account these p o t e n t i a l  of  problems.  t h e Cox p r o p o r t i o n a l h a z a r d model was  t o a sample o f 109 f i r m s ,  bankruptcy  by t h e  ordering of  treatment o f " t i e d " observations r e s u l t s  m o d e l must t a k e i n t o In  for  " f i t " o f t h e model.  i n i t s estimation procedure. Unlike  incorrect  i n severely  t o have a  m o d e l a s t h e model makes u s e o f t h e t e m p o r a l  events an  time  to result  but, appears  on t h e o v e r a l l  o f t h e Cox  41 o f whom f i l e d  between 1972 and 1985.  As t h i s  a major change t o t h e b a n k r u p t c y  time  petitions period  a c t , t h e two  -87g r o u p s o f b a n k r u p t f i r m s were examined t h a t no d i f f e r e n c e  existed  b a n k r u p t c y a c t s . The the s t r a t i f i e d appear  t o be  Cox  to test  between f i r m s  the h y p o t h e s i s  filing  under  r e s u l t s of the K r u s k a l - W a l l i s  model t e s t s ,  a significant  indicate  difference  that  the  two  tests  and  t h e r e does  not  between t h e 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  p e r f o r m e d on t h e b a n k r u p t  non-bankrupt  groups  performance.  I f t h e Cox model i s o f v a l u e ,  something The prior  beyond Cox  to establish  what i s a l r e a d y  model was  to failure.  one w o u l d prior)  intuitively  identified  the  in  e x p e c t . The  variables  industrial  insured  years  proportional In both the the  t e r m model  one  sign  (4 y e a r  from the s h o r t  term  i n the s u r v i v a l e x p e r i e n c e .  s e t t i n g d i d not p e r f o r m as  i n performance  study evaluated performance  definition,  the  four  v a r i a b l e s had  longer  a s t h e model e s t i m a t e d by L a n e ,  [1986]. T h i s d e c l i n e Lane  offer  e x p e c t , the p r o p o r t i o n a l h a z a r d s model e s t i m a t e d  t h i s more d i v e r s e  well  and  identified  different  of  i t must  t o be s a t i s f i e d .  model a s b e i n g i m p o r t a n t f a c t o r s As one would  level  available.  The d e g r e e o f f i t  four year models,  line  e s t i m a t e d f o r one y e a r and  hazards assumption appeared and  a base  and  only  the F e d e r a l  b a n k s were e v a l u a t e d  'representative'  Looney,  and  Wansley  i s not s u r p r i s i n g  i n a v e r y narrow  as  the  industrial  Deposit Insurance Corporation where t h e a s s u m p t i o n o f a  or average hazard r a t e  p r o p o r t i o n a l h a z a r d s model would  implicit  seem more  i n the  plausible.  -88Th e c o n c l u s i o n s sole  purpose  bankrupts,  of  drawn  the model  then  the  The  discriminant  analysis  periods  surprising in  certain  evaluating It  was  the  the  that  model.  use  This  does  not  the  of  that  Cox  exploit  of  i f the  potential  model  i s more  the  t o be  superior  result  the  model  in  i s not  assumptions  ability  of  as  based  shown  restrictive  the  purposes  was  are  firms  performance  model Cox  very  analysis  classification  shown  classification  based  of  analysis  i s to classify  classification  to that as  this  discriminant  appropriate.  all  from  were  Cox  made  model.  primarily  the model's  for  full  potential. Unlike single  score  bankrupt the  the discriminant  or  and  analysis  a classification  indeterminate,  the  d i s t r i b u t i o n of expected  survival picture  functions of  the  can  firm's  give  of  which  either  very  survival  until  model  failure.  interesting  potential  yields  a  survivor,  e s t i m a t e d Cox  times a  model  over  and  produces These a  useful  a period  of  time. The model  conclusion  i s applicable  bankruptcy.  The  information  to that  discriminant The and  research  this  analysis  of  commercial  case  provides  provided  analysis  intuitive  from  i n the  model  applicability  further  drawn  based  appeal of  additional  by  the  i s that  and  commonly  and  the  Cox  industrial  useful used  models. the  to bankruptcy i s warranted.  Cox  model,  prediction,  i t ' s performance indicates  that  -89F O O T N O T E S  I.  INTRODUCTION  ^ D e r i v e d f r o m t h e Economic R e p o r t o f t h e P r e s i d e n t ( T r a n s m i t t e d t o C o n g r e s s , F e b r u a r y 1 9 8 6 ) , p . 359.  II.  BANKRUPTCY  C Heath 2  H a r l a n P i a t t , Why Companies F a i l Company, 1 9 8 5 ) , p . 7. Piatt,  (Lexington,  Mass. :  p . 8.  3 U. S. C o n g r e s s , R e p o r t o f t h e C o m m i s s i o n on t h e B a n k r u p t c y Laws o f t h e U n i t e d S t a t e s , P a r t 1 ( W a s h i n g t o n , : GPO, 1973) , p . 63. 4 B a n k r u p t c y C o m m i s s i o n , p 63. ^ J o h n E . M u l d e r and L e o n S. Forman, B a n k r u p t c y and Arrangement P r o c e e d i n g s ( 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 E d u c a t i o n , 1 9 6 4 ) , p. 4. 6 7 8 9 10 11 12 13 14 15 16 17  Bankruptcy Commission,  P- 183.  Bankruptcy  P- 262.  Commission,  M u l d e r , p p . 16-19. Mulder,  p . 16.  Mulder,  p . 21.  M u l d e r , p p . 22-29. Mulder,  p . 143.  Bankruptcy  Commission,  PP.  243-244.  Bankruptcy  Commission,  P- 244.  Bankruptcy  Commission,  P- 245.  Bankruptcy  Commission,  P- 244.  Bankruptcy  Commission,  pp.  244-245.  -9018  Bankruptcy Commission,  p . 245.  Bankruptcy Commission,  p . 245.  Bankruptcy Commission,  p p . 245-247.  Bankruptcy Commission,  p . 2.  B a n k r u p t c y Commission,  p . 3.  19 20 21 22 23 International 1 9 8 5 ) , p . 154. 2  4  Insolvency  ( K l y n v e l d Main G o e r d e l e r ,  K. M. G., p . 157.  25 Edward I . A l t m a n , C o r p o r a t e F i n a n c i a l D i s t r e s s (New Y o r k : J o h n W i l e y & S o n s , 1 9 8 3 ) , p . 28. 26 B a n k r u p t c y C o m m i s s i o n , p . 136. 27 B a n k r u p t c y C o m m i s s i o n , p . 144. 28 A l t m a n , C o r p o r a t e 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, " M a r k e t I d e o l o g y a n d C o r p o r a t e Power; The U n i t e d S t a t e s " i n I n d u s t r i a l C r i s e s , E d s . K e n n e t h Dyson and S t e p h e n W i l k s (New Y o r k : S t . M a r t i n ' s P r e s s , 1 9 8 3 ) , p. 100.  I I I . MODELS COMMONLY USED R i c h a r d A. S h i c k a n d Lawrence F . Sherman, "Bank S t o c k P r i c e s a s an E a r l y W a r n i n g S y s t e m f o r Changes i n C o n d i t i o n " ( J o u r n a l o f Bank R e s e a r c h , Autumn 1 9 8 0 ) , p . 145. 1  2 L e o n Korobow and D a v i d P. S t u h r , "The R e l e v a n c e o f P e e r G r o u p s i n E a r l y W a r n i n g A n a l y s i s " (Economic Review, F e d e r a l R e s e r v e Bank o f 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 B u s i n e s s , F i n a n c e , and E c o n o m i c s " ( J o u r n a l o f F i n a n c e , 32, 1 9 7 7 ) , p . 883. 4 Edward A l t m a n , " 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 t h e P r e d i c t i o n o f C o r p o r a t e B a n k r u p t c y " ( J o u r n a l o f F i n a n c e , 33, 1 9 6 8 ) , p 591. ^ Altman,  "Financial  Ratios.  . .".  Altman,  "Financial  Ratios.  . .".  -91-  E i s e n b e i s , p.  7  876-893.  g D a n i e l M a r t i n , " E a r l y W a r n i n g o f Bank F a i l u r e " ( J o u r n a l o f B a n k i n g and F i n a n c e , 1, 1 9 7 7 ) , p 249,276. 9 R o b e r t West, "A F a c t o r - A n a l y t i c A p p r o a c h t o Bank C o n d i t i o n " ( J o u r n a l o f B a n k i n g and F i n a n c e , 9, 1 9 8 5 ) , p . 253256. Shick  and Sherman, p .  137.  A n t h o n y S a n t o m e r o and J o s e p h V i n s o , " E s t i m a t i n g t h e P r o b a b i l i t y o f F a i l u r e f o r C o m m e r c i a l Banks and t h e B a n k i n g S y s t e m " ( J o u r n a l o f B a n k i n g and F i n a n c e , 1, 1 9 7 7 ) , pp. 187 1  1  12 Firm  C r a i g J o h n s o n , " R a t i o A n a l y s i s and t h e P r e d i c t i o n o f F a i l u r e " ( J o u r n a l o f F i n a n c e , 25, 1 9 7 0 ) , p . 1166. 13 Santomero and V i n s o , pp. 185--189. 14 15 16 17  Santomero  and V i n s o ,  p.  188.  Santomero  and V i n s o ,  p.  196, 200- 203.  Santomero  and V i n s o ,  p.  203.  Santomero  and V i n s o ,  pp.  193--195.  18  W i l l i a m L a n e , S t e p h e n Looney and James W a n s l e y , "An A p p l i c a t i o n 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 M o d e l t o Bank F a i l u r e " ( J o u r n a l o f B a n k i n g and F i n a n c e , 10, 1 9 8 6 ) , pp. 512513. 19 Lane e t a l , p .  513.  Lane e t a l , p .  516.  20  2  IV.  1  Lane e t a l , pp.528-529.  PLAN OF 1  This  ANALYSIS classification  scheme i s b a s e d on B e a v e r , 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 , T o r o n t o , 1 9 7 9 ) , p. 162. 3 W i l l i a m H. B e a v e r , " 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 " (Empirical Research i n Accounting, Selected Studies, 1 9 6 6 ) , pp. 101-102.  Piatt,  p.34.  V. SAMPLE CHARACTERISTICS L e o n a r d 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 c i e n c e s (Brooks C o l e P u b l i s h i n g Comapany, M o n t e r e y , 1 9 8 3 ) , p. 203. 1  2 for  Lyman O t t and D a v i d K. H i l d e b r a n d , S t a t i s t i c a l Managers (Duxbury P r e s s , B o s t o n , 1 9 8 3 ) , p . 361.  VI.  DISCRIMINANT ANALYSIS  Thinking  W i l l i a m C o o l e y and P a u l L o h n e s , M u l t i v a r i a t e P r o c e d u r e s f o r t h e B e h a v i o u r a l S c i e n c e s (John W i l e y & Sons, New Y o r k , 1962) , p . 117. 1  2 0. M a u r i c e J o y and J o h n O . T o l l e f s o n , "On The Applications of Discriminant A n a l y s i s " (Journal of and Q u a n t i t a t i v e A n a l y s i s 10, 1 9 7 5 ) , 72~4~. Joy  and T o l l e f s o n ,  Financial Financial  1975.  4 New  Peter Lachenbruch, D i s c r i m i n a n t A n a l y s i s Y o r k , 1 9 7 5 ) , p. 40. 5 L a c h e n b r u c h , p. 33.  (Hafner P r e s s ,  g L a c h e n b r u c h , p.  33.  7 Altman,  VII.  THE  COX  Distress,  p.106.  MODEL  W a l t e r C a r t e r , G a l e n Wampler, and D o n a l d 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 o f S u r v i v a l D a t a i n C a n c e r Chemotheraphy (John W i l e y & S o n s , New Y o r k , 1 9 6 2 ) , p p . 39-40. 1  2 Carter  e t a l , p.  40.  3 R. Kay, " P r o p o r t i o n a l H a z a r d R e g r e s s i o n M o d e l s and t h e A n a l y s i s o f C e n s o r e d D a t a " ( A p p l i e d 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.  -935  Lane e t a l , p . 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J o u r n a l o f Bank R e s e a r c h , Autumn ( 1 9 8 0 ) , 136-146. U. S. C o n g r e s s . House. R e p o r t o f t h e C o m m i s s i o n on t h e B a n k r u p t c y Laws o f t h e U n i t e d S t a t e s . P a r t 1. U. S. 93d C o n g r e s s , 1 s t S e s s i o n . House Document No. 93-137. W a s h i n g t o n , D . C : GPO, 1973. West, R o b e r t C r a i g . "A F a c t o r - A n a l y t i c A p p r o a c h t o Bank Condition". J o u r n a l o f B a n k i n g and F i n a n c e , 9 ( 1 9 8 5 ) , 253-266.  -97APPENDIX I Figure 8 PLOT OF SURVIVAL FUNCTION FIRM: CUSIP = 042078 PATTERN  SYMBOL  1 2 3  A B C  (BANKRUPT)  ONE YEAR PRIOR TO BANKRUPTCY TWO YEARS PRIOR TO BANKRUPTCY THREE YEARS PRIOR TO BANKRUPTCY  ESTIMATED SURVIVAL FUNCTION  .+. 1.0  .80  .60  .40  .20  0.0  +**********CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC - A BBBBBBBBB A BBBBBBBBBBBB AA BBBBB A BBB + A BB A A A A + A AA A A A + A AA AA A A + AA A AA AAA AAAAAA + AAAAAAAAAAAAAAAAA  .+  0.0  +  70.  +  140  +  210 DAYS  +  280  +. ,  350  -98Figure 9 PLOT OF SURVIVAL FUNCTION FIRM: CUSIP = 564402 PATTERN  (BANKRUPT)  SYMBOL  1 2 3  A B C  ONE YEAR PRIOR TO BANKRUPTCY TWO YEARS PRIOR TO BANKRUPTCY THREE YEARS PRIOR TO BANKRUPTCY  ESTIMATED SURVIVAL FUNCTION  1.0  .80  .60  .40  .20  0.0  +**************CCCCCCCCCCCCCCC A BBBBBBBBBBBBBBB* ***CCCCCCCC A BBBBBBBB AA AAA + A AA A A A + A A AAA A A A AA + AAA AAA AAA AA AA + A AAA A AA  +  .+  0.0  +  70.  +  +  210  140 DAYS  + 280  +.,  350  -99Figure  10  P L O T OF S U R V I V A L FIRM:  PATTERN  FUNCTION  CUSIP = 868168  (SURVIVOR)  SYMBOL  1 2 3  A B C  ESTIMATED  ONE Y E A R P R I O R T O WITHDRAWAL TWO Y E A R S P R I O R T O WITHDRAWAL T H R E E Y E A R S P R I O R T O WITHDRAWAL  SURVIVAL  .+  FUNCTION  +  +  +  +  +. .  1.0  +***************************************** AAAAA  +  .80  +  +  .60  +  +  . 40  +  +  .20  +  +  0.0  +  .+  +  +  70. 0.0  +  +  210 140 DAYS  + 350  280  +  -100-  Figure  11  P L O T OF S U R V I V A L FIRM:  PATTERN  CUSIP  =  FUNCTION  297882  (SURVIVOR)  SYMBOL  1 2 3  A B C  ONE Y E A R P R I O R T O WITHDRAWAL TWO Y E A R S P R I O R T O WITHDRAWAL T H R E E Y E A R S P R I O R T O WITHDRAWAL  ESTIMATED SURVIVAL  FUNCTION  .+. 1.0  .80  .60  .40  .20  0.0  +* * * * * *BB ACC**BB AA CCB AAA *BB + A CC BBBBB AA CCC B A CCCBBB A C BBB A CCCC BBBBB + A CC BB AAAA CCCCC BB A CC B A C BBB AAA CC B + AAA C BB AA CCC B A AAA C AA CC A + AA AA AA AA +  .+  +  +  +  70. 0.0  +  210 140  280 DAYS  +. , 350  -101APPENDIX I I . F i g u r e 12 NORMAL PLOT OF CURRENT ASSETS / SALES (ONE .YEAR PRIOR)  ,+  SYMBOL * +  COUNT 109 +  +  MEAN 0.411  ST.DEV. 0.192 + ...,  +  /  //  /  *  // * *  *  *  *** * * */ ** /  * ** *** /  */ ** ** /* //* / * // * + / * -/ *  .+ 0.0  +  .20  + .40  +  .60  + .80  +. ,  1.0  CASLS1 VALUES FROM NORMAL DISTRIBUTION WOULD LIE ON THE LINE INDICATED BY THE SYMBOL / .  -102F i g u r e 13  NORMAL PLOT OF WORKING CAPITAL / TOTAL ASSETS (FOUR YEARS PRIOR) SYMBOL COUNT MEAN ST.DEV. * 109 0.323 0.138 ....+....+....+....+....+....+....+. +....+... _  * _ *//  +  */  */*  -  *  -  **** **  _ _  "  + _  _ +  **  _ _ _  * ** **  + _ _ _ + _ -  "  _  */*  _ +  +  /  * ** ** /** /*** * ** **** ** *** * * */ *// /*  _ + _ _ _ _ + _ _  */ */  +  - //  - * _ ....+....+....+....+....+....+....+....+....+... 0.0  .08  .16  .24  .32  WCTA4  .40  .48  .56  VALUES FROM NORMAL DISTRIBUTION WOULD LIE ON THE LINE INDICATED BY THE SYMBOL / .  .64  -103F i g u r e 14  NORMAL PLOT OF WORKING CAPITAL / TOTAL ASSETS (ONE YEAR PRIOR)  .. . .+  E X P E C T E D N 0 R M A L V A L U E  2  1  0  -1  SYMBOL * +  + + _ + _ + -  * *  .+ -.6  COUNT 109 +  MEAN 0.272 +  ST.DEV. 0.226 + +.  / * / *// */ **/ **/ ** / ** ** ** * /* /** /** /** * ** //* /*** **/* **/ **// ** / / / /  +  -.3  + 0.  +  .3  + .6  WCTA1  VALUES FROM NORMAL DISTRIBUTION WOULD LIE ON THE LINE INDICATED BY THE SYMBOL / .  +. ,  .9  -104F i g u r e 15 NORMAL PLOT OF NET INCOME / SALES (FOUR YEARS PRIOR) SYMBOL COUNT * 109 ,+ +  MEAN 0.019 +  +  ST.DEV. 0.037 +. .  * E X P E C •p E D N O R M A L V A L U E  2  1  0  -1  -2  / */ * / */ ** ** ** * * / **/ * */ **/ */ ** * ** /* /* * / * /** * ** /* ** * / /  + — + _ + _ + +  /  -.12  -.06  0.0 NETYSL4  .06  .12  VALUES FROM NORMAL DISTRIBUTION WOULD LIE ON THE LINE INDICATED BY THE SYMBOL / .  _  -105F i g u r e 16 NORMAL PLOT OF NET INCOME / SALES (ONE YEAR PRIOR) SYMBOL COUNT * 109  MEAN -0.019  ST.DEV. 0.096  ....+....+....+....+....+....+....+....+....+... _ E X  2  * _  +  * *  P  E C T E D N O R M A L V A L U E  *  1  0  -1  -2  + + -  -  /+ /  -  // * / * / * // */ ** /* /** // * / ** / ** /** **  -  /* *  + +  *  + _ + _  _  /** *** * ** * * // ** / / // /  + -  •  +  _* _ ....+....+....+....+....+....+....+....+....+... -.42  -.35  -.28  -.21  -.14  -.07  0.0  .07  NETYSL1 VALUES FROM NORMAL DISTRIBUTION WOULD LIE ON THE LINE INDICATED BY THE SYMBOL / .  .14  -106APPENDIX I I I F i g u r e 17 LOG MINUS LOG SURVIVAL FUNCTION Stratified  on: Cash flow / t o t a l debt two years  .+ -2  +  +  +  +  +  +  -5  -6  -7  + + + + -  .+ 0.0  AAA  AA  AAAA AAAAAA BB AAAAA BBB A  -4  +  +  AAA -3  prior  AA AA A A A A A A A A A A A  AA  A  AAAAA A A A  +  BBBB  BB BB B  +  BB  B B B BB  +  B B B B B B B B B BB  +  70.  +  +  +  +  210  140 DAYS  + 280  +  350  -107F i g u r e 18  LOG  MINUS LOG SURVIVAL FUNCTION  S t r a t i f i e d on: Net income / s a l e s  .+ 0  +  +  +  (two years p r i o r )  +. ...  +  +  AA  -3  -6  -9  +  + -  AA  AAAAAA AAAAAAAAAA BBBBBBBB AAAA BBBBBBB AAAA BBBBBBB A BBBBB AAAAA BB AA BB A BB A BB ABB ABB AB AB AB AB AB AB  +  .+ 0.0  +  +  +  +  70.  +  +  210  140 DAYS  + 280  +. ,  350  -108F i g u r e 19 LOG  MINUS LOG SURVIVAL FUNCTION  S t r a t i f i e d on: T o t a l c l a i m s / A s s e t s  .+ -2  -3  -4  -5  -6  -7  +  +  +  (two years  +  prior)  + .,  +  B A A* *AA BBBBBBBB**B BBBB AA + BB A B A BBBBB A B A BB AAAAAAAA + • A*AAAAAAAAA AAAAA B A B A BB A B + AA BB A B ABB AB AB + AB AB AB AB AB + * _ * B  .+  0.0  +  70.  +  +  210  140 DAYS  +  280  +. ,  350  

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