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The weak form of the efficient market hypothesis and its application to the Vancouver listed mining stocks Buis, Richard 1976

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THE AND  WEAK FORM OF T H E E F F I C I E N T  ITS APPLICATION  MARKET. H Y P O T H E S I S  TO T H E VANCOUVER  LISTED  MINING  by  RICHARD B.B.A.,  A  THESIS THE  University  BUIS o f Oregon,  SUBMITTED IN P A R T I A L REQUIREMENTS  MASTER  "~~  OF  FOR  1970  F U L F I L M E N T OF  THE DEGREE  OF  BUSINESS ADMINISTRATION  i n t h e Department of Commerce  We  accept  required  THE  and B u s i n e s s  this  thesis  Administration  as conforming  to the  standard  UNIVERSITY  OF  MAY,  BRITISH 1976  COLUMBIA  STOCKS  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y s h a l l I  f u r t h e r agree  in p a r t i a l  f u l f i l m e n t o f the requirements f o r  the U n i v e r s i t y of B r i t i s h Columbia,  make i t  freely available  that permission  for  I agree  r e f e r e n c e and  f o r e x t e n s i v e copying o f  this  that  study. thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s of  this  written  representatives. thesis  It  is understood that copying or p u b l i c a t i o n  f o r f i n a n c i a l gain s h a l l  permission.  Department o f The U n i v e r s i t y of B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date  AJ/9Y7, /?76  Columbia  not be allowed without my  i ABSTRACT  The purpose of t h i s study was  to t e s t the hypothesis t h a t  s e c u r i t y p r i c e changes f o r the L i s t e d Vancouver Mining Stocks conform to the weak form o f the E f f i c i e n t Market B r i e f l y stated  t h i s hypothesis asserts  f u l l y r e f l e c t the i n f o r m a t i o n i m p l i e d  Hypothesis.  that current  prices  by the h i s t o r i c a l  sequence  of p r i c e s .  I f such i s the case i t would not be p o s s i b l e f o r  an i n v e s t o r  t o enhance h i s investment performance  previous successive p r i c e  by  studying  changes.  In o r d e r to determine whether t h i s h y p o t h e s i s i s a p p l i c a b l e to the L i s t e d Vancouver Mining Stocks a s e r i e s o f t e s t s were performed on the monthly p r i c e d a t a f o r the p e r i o d , to February 1973.  March  The method of i n v e s t i g a t i o n c o n s i s t e d  1963 of  a number of seperate and d i s t i n c t experiments.  Initially  monthly p r i c e changes were s e r i a l l y c o r r e l a t e d  f o r various  the  d i f f e r e n c i n g i n t e r v a l s to determine the degree o f dependency i n the p r i c e changes. y s i s was  performed  F o l l o w i n g t h i s procedure, t r e n d  anal-  to measure the number of runs or p a t t e r n s  i n the p r i c e changes and t o compare these r e s u l t s w i t h what could  be expected i f the s e r i e s was  random.  stocks were a l s o s u b j e c t e d to a t r a d i n g filtering,  determine  individual  rule, refered  t o see i f a mechanical t r a d i n g  a buy and h o l d p o l i c y .  The  to as  r u l e c o u l d out perform  F i n a l l y an a n a l y s i s was  performed  to  i f s e c u r i t y p r i c e changes were i d e n t i c a l l y d i s t r i -  buted and whether they were s t a t i o n a r y  over time.  In price  a l l  cases  changes.  yielded rules to  the  is  i n i t i a t e d  buy  to  returns or  be  the  the  hold  there  is  The  stationary  over  conform  whether  the  time  require  Listed Market  from Mining  further this  a  to  to  indicate  Whether given  under The that  conform  to  of  vastly  general price  that  i t  a  does  changes  implies  move not tended security  d i s t r i b u t i o n  unrepresentative  conclusion  movements  weak  F i l t e r  inferior  once  this  i n  tests  that  price  was  runs  theory.  probability  study  the  dependence  and  walk  suggesting  time. some  l i t t l e  results  distribution  study. is  be  random  generated  period  study  Stocks  Hypothesis.  with  evidence  persist.  to  correlation  portfolios,  not  derived  s e r i a l  data  do  w i l l  appeared  consistent  to  and  necessarily not  Both  results  applied  there  form  of  of  to the  the  be Vancouver Efficient  iii TABLE OF CONTENTS  Page LIST OF TABLES  V  Chapter 1  INTRODUCTION  1  Statement o f Purpose  1  Need f o r the Research  2  Method o f Research  7  Method o f A n a l y s i s  9  O r g a n i z a t i o n o f Study 2  10  PREVIOUS CLOSELY RELATED RESEARCH  11  The Behaviour o f Stock Market P r i c e s by E. Fama  11  P r i c e Movements i n S p e c u l a t i v e Markets: Trends o f Random Walks by Alexander  3  . . . .  15  A d d i t i o n a l Research by Alexander  17  Fama and Blume Study on F i l t e r Rules . . . .  20  METHOD OF RESEARCH  22  Data Used  22  Serial Correlation  24  Runs Tests  25  T e s t i n g Independence  w i t h F i l t e r Rule  S t a t i o n a r i t y o f Returns  . . .  27 30  iv  Chapter 4  P  FINDINGS Correlation  e  32  Tests  Filter  39  Trading Rules  Stationarity Risk,and 5  g  32  Serial Runs  a  o f Returns  53  Return  I N T E R P R E T A T I O N OF General  44  58 NUMERICAL  Statement  Implications  RESULTS  59  of Findings  f o r Investment  Management.  59 . . .  69  Limitations  70  Avenues  71  o f Further Research  REFERENCES  74  APPENDIX  76  List  o f Firms  Computer  Used  Programs  i n Study Used  76 78  V  LIST  OF  TABLES  Table  !  5  I  North American  Trading  II  Monthly  Serial  Correlation  Through  S i x Months  III  IV  V  VI  Summarization Coefficients  of  f o r Lags  of  34  Results  of  Serial  Correlation  Correlation  Coefficients .  T o t a l A c t u a l and E x p e c t e d Numbers One - M o n t h P e r i o d  of  Total  of  Actual  - Month  One  36  Monthly S e r i a l Inactive Firms  One  and  Summarization  VIII  Filter  IX  and H o l d P o l i c y Returns Generated  Trading  of  for Inactive  Findings  Rules  as  from  Short  and  37  Runs f o r  Runs f o r 4 3  Firms  of F i l t e r  Compared  for  41  E x p e c t e d Numbers  Period  VII  X  Page  to  Rule a  Long  Tests  46  . . .  Buy Positions  .  .  4 8 51  C o m p a r i s o n o f S h i f t B e t w e e n Mean M o n t h l y R a t e o f R e t u r n a n d MAD f o r P e r i o d M a r c h 19 63 t o F e b r u a r y 1968 & M a r c h 1968 t o F e b r u a r y 1973 . . . .  54  XI  Fitting  56  XII  Monthly Rates of Return f o r the M a r c h 1963 t o F e b r u a r y 1973;  XIII  XIV  XV  a Normal  Comparisons o f VSEM a n d TSEM  Curve  Risk  and  to Observed  Data  Market: 64  Return f o r 65  Cumulative Monthly the Market: March  Rates o f Return f o r 1963 t o F e b r u a r y 1973  Seasonal Variation and D e c l i n e s  i n Market  68  Advances 71  vi  "I  h a d two  someone I  followed  dollars  s u g g e s t e d t h e VSE  h i s advice and  a n d made o n e  now  f o r even  and thought  I find  I have  more  no  more  i t would more."  suffice  CHAPTER  1  INTRODUCTION STATEMENT  The that  purpose  security  Exchange of  of this  price  Listed  paper  will  Stock  Exchange  relative  Market  Market  attempt  Listed  definition  Hypothesis  i s that  distributed.  (  j  R  t+ll  where  will to  equal  suggest  upward  process  t  where  +  j P  1  jP  such  t  , JV _ t  ir  = price  form  of the  and t h a t  the Vancouver risk  market  Efficient  changes a r e  the returns are  •-' i t - n > R  for security  that  only  periods.  overtime  this  Exchange.  .t-l'  (1-1) s t a t e s  the last  martingale  E ( j P  R  that  form  of  return  (1-1) i s n o t v i o l a t e d .  R  of return  drift  j  Furthermore,  Symbolically, rates  J ^- ~ return  Equation rates  i f Eq.  t o t h e weak  successive price  variables  V  j  Stock  Stock  Section i s a high  o f t h e weak  identically  E  the hypothesis  the hypothesis  Mining  random  a martingale  i s to test  Hypothesis.  to test  independent  are  study  S e c t i o n conform  t o the Toronto  The  PURPOSE  movements on t h e V a n c o u v e r  Mining  the E f f i c i e n t  OF  they  =  the next  Since  R  of  t.  historical  periods  security  i n effect  t  j at period  knowledge  that  j  prices  return tend  represent a sub-  that:  • . - ., J P _ ) > t  of security  n  JP  i n time t .  t  d-2)  2  Throughout Vancouver through  the  Stock  the  remaining  Exchange  use  of  the  Listed  i s widespread  investment  Market that  Hypothesis.  implies  obtained  Mining  THE  Section will  the  be  VSEM.  RESEARCH  interest  community  with  Simply  current prices  which  references to  I  There and  any  a b b r e v i a t e d form  N E E D FOR  Hypothesis  paper  that  fully  respect to  stated  this  reflect  superior  consistently  i n both  by  academic  the  Efficient  hypothesis explains  a l l available  investment  simply  the  results  information cannot  analyzing existing  be  infor-  mation . The  controversy started  developed numbers series and of  a  series  which of  had  of  numbers  the  stock prices.  weeks  raised fact  d i d move  provided  a body  of  security  is  particularly  in  greater detail  were  of  random  Moore(15),  in  Most  to  i n Chapter  with  the  one  that  a  the  random  time  actual  for a Thus  security  Further tests  and  this  as  prices  t o whether  the  cumulating  another.  fashion.  Some o f  early  noted  that  Roberts(17)  appearance  stock  Granger  relevent  the  as  evidence  prices.  concerned  with  questions  in a  also  i n weekly  corresponded  tenative  0sborne(16),  He  when  c r e a t e d by  same v i s u a l  s i m u l a t e d changes 52  i n 1959  period  his  work  prices by  M o r g e n s t e r n (.10.) ,  suggested more  random  recent  study  will  movements  research be  that  discussed  2.  studies  on  randomness  i n ..  stock of  price  price  behavior,  changes  and  were  accumulated  Theory.  This  Weak F o r m  of  walk  implies  does  not  under  theory the  efficiency,  Market  however,  identically  J  R t  Where  +  1  R t  -i'  f (jR^_)  =  are  the  prices does The  are  not  not  weak  form  i s not  the  hypothesis  price  and  volume  which  can  be  be  with  data  used  attained with  to a  market  efficient prices,  theory  t  _ )  =  n  (or  returns),  assumes and  that  that  the  that:  (J  f  random  R t  )  d-3)  security j  exactly  only  efficient  securities  earn  a  true  nearly  effectively  for  naive  for  at  t.  independent,  conflict  an  the  probability distribution returns  equation  R  as  A  stock  • • • •» J  Walk  become known  independent  period above  Random  d i s t r i b u t e d , such  of  The  the  Hypothesis.  random walk  p r i c e changes  are  ( J  The  of  subsequently  n e c e s s a r i l y mean t h a t  successive  f  has  heading  Efficient  move r a n d o m l y . ( 5 )  returns  the  so.  says  -  and  this  hypothesis.  that  contain  - hold  security  However,  market  trading profit  buy  in that  historical  no  information  above what  could  investment  strategy.(8) The that all  markets publicly  insiders earned on  semistrong  can  using  short  run  hypothesis  are  efficient  efficient  market  enough  that  available information earn a  a  naive  profit buy  which  -  and  p r i c e changes.  claims  that  no  one  so  can  prices that  exceeds  - hold  The  hypothesis  reflect  only  what  policy  strongly  states  a  could by  few be  trading  efficient  c o n s i s t e n t l y earn  market a  4 profit hold  over  what  could  s t r a t e g y by  because  inside  price  no  one  great  decade  deal with  however,  most  New  Stock  York  results.  of  respect  of  the  to  Exchange,  analysis with  of  the  value  equivalent  to  .3%  o f .the  and  the  i n terms  NYSE.  validity  the  the  the  by  VSE.  the  13.5% two  same  of  of  -  and  price  -  movements  random  to  valuable  the  number the  high,  of of  of  from  to  that  Table  of  traded  would  from  two  status  securities those  proportion  indicates the  VSE  on  the  the  VSE  studies  being  on  VSE.  traded NYSE  stocks'  the  vary  i n order  the  the  Further-  exchanges  needed  'penny  handled  question  the  t r a d i n g on of  1-1  weak  listed  reservation to f o r the  the  transactions  alone  drawn  consistent  listed,  shares  the  rigorous  shares  volume  financial  on  relatively  shares  the  hypothesis,  being  observations  type  different the  the  over  conducted  subjected  conclusions  and  form  with  value  requirements  size  Hence  significantly  on  access  accepted.  applied without  listing  listed.  evidenced  the  be  to  of  These  that  could  respect be  buy  security  been  result  is generally  approximately  more,  naive  accumulated  weak  have  the  i n terms  NYSE  a  independent  has  (NYSE),  that  by  the  studies  hypothesis  did  are  information  form  NYSE,  run  monopolistic  P r i c e movements were  scientific  is  short  changes  has  using  information.  A past  and  earned  t r a d i n g on  security  variables  be  with to  are as  listed  TABLE  1  NORTH AMERICAN Exchange  Value (000) 1973  New Y o r k S t o c k E x c h a n g e American Stock Exchange Midwest Stock Exchange The T o r o n t o S t o c k Exchange P a c i f i c Coast Stock Exchange PBW S t o c k E x c h a n g e Montreal & Canadian Stock Exchange Boston Stock Exchange Vancouver Stock Exchange D e t r o i t Stock Exchange C i n c i n n a t i Stock Exchange N a t i o n a l Stock Exchange C a l g a r y Stock Exchange Spokane Stock Exchange Honolulu Stock Exchange Intermountain Stock Exchange Winnipeg Stock Exchange Totals  Source:  1973  Review,  TRADING  The T o r o n t o  Shares (000) 1972  1973  1972  $ 1 4 6 , 7 9 3 , 295 11 , 0 0 7 , 2 4 1 8 , 1 3 1 , 369 6 , 7 3 7 , 076 6 , 3 5 9 , 460 4 , 3 9 4 , 916 2 ,173, 992 1 , 7 9 3 , 047 483, 271 3 8 0 , 588 1 1 8 , 849 2 3 , 952 7, 123 6, 685 1, 897 996 613  160,177,580 21,379,253 8,434,019 6,258,153 8,126,060 5,282,478 2,057,294 1,562,882 784,103 362,790 103,445 112,448 6,493 4,498 3,990 2,326 840  4,375,224 815,893 241,523 663,856 214,804 128,182 296,475 42,193 592,745 10,686 2,838 7,530 10,215 13,031 260 2,262 1,458  4 ,593,889 1 ,188,062 230,642 635,886 269,202 144 ,496 330,125 38,605 906,053 9,844 2,354 15,912 12,208 9,258 565 3,841 521  1 8 8 ,414, 372  214,658,650  7,419,176  8 ,391,474  Stock  Exchange  6 Hypothesis  The high  II  VSE  risk  has  historically  market,  securities.  This  in  by  the  rumor  Exchange,  state  most  that  expectation Douglas(4) of  616  are  adverse  high  of  where  a  risk  with  the  in high  the  and  of  the  Toronto  being  a  mining  deny  the  truth  Stock  risk  i t i s reasonable  undertaken  annual  1963.  of  that  risk  to  are  positive  amount  shown  Jensen(11)  with  risk), less  listed  securities  of  with  undertaken  returns of  The  results  correlation  variation  investors  stocks than  securities,  through  greater risk  (systematic  with  as the  risk.  mining  a  the  by sample  indicated  that  between  the  i t displayed.  On  earned  i f they  a higher had  return  invested  in.  i t has  been  the  study  measured market,  I f we  (portfolios),  then  i f he  were  placed  a l l his  to  funds  securities assume  buy at  i s that that  a l l the risk.  existing  mutual  funds  funds,  beta  investor this  to  that  coefficients  higher returns  than  invest  available  only  list  of  investment opportunity.  mining  "The  mutual  their  had  a l l o w an  securities  of  by  represents his universe of  Hence,  could  1946  combinations  funds  one  of  securities.  by  risky  the  S t u d i e s were  examined  degree  i t was  investing  the  to  investments  returns.  he  high  average  found  in  risk  high  r e t u r n s and  funds  confirm or  investors  s t o c k s between  For  either VSEM  stock  low  will  folklore  reference to  the  was  by  paper  with  comparing  there  the  particularly  a  (TSE).  Since to  developed  stocks l i s t e d  optimal  i n the were  he  combination  market"(18). efficient  has of  If  portfolios,  7  the  returns  would  a l s o be a l i n e a r  function of the  standard  deviation.(19) Therefore, is  a high  risk  generated by  to test market  b y t h e VSEM  the standard  TSE. if for  i s a high  by a v e r a g e  this  paper  and t h e i r  deviation, with  I n an e f f i c i e n t  t h e VSEM  the second  higher  market risk  basic  supplied  data  by Ronald  returns  10 y e a r  closing  used D.  data  period  price  from  was  as  measured  should be  on t h e  indicate  that  compensated  t o t h e TSE.  f o r the analysis i n this  S. P o u l i e r ,  was  not contained  summaries  were  a single  which  was  crepencies  a  former  price  as a c r o s s  between  from  was  the last  summary,  was  each  quoted  reference,  the V.S.E.  r e s o l v e d by c h e c k i n g  graduate  was  student  collected for  1963 t o F e b r u a r y  s u c c e s s i v e l y examined price  study  Columbia.  i n 'The P r o v i n c e '  i n this  monthly  used  March  obtained  month as r e c o r d e d  were  the returns  earned  i t should  relative  on t h e c l o s i n g  the  If  the returns  t h e VSEM  RESEARCH  the University of B r i t i s h Monthly  a  compare  variability,  market  that  Used  The  at  will  the results  METHOD OF  Data  hypothesis  Review  daily  1973.  weekend  This  summary o f  newspaper.  If a  price  of the preceding  for a closing  price.  i n t h e V.S.E.  Review,  i t was  Any d i s -  used.  and t h e weekly  sales.  summary  8  The some  data  clarifying  company  names  company. of  idation.  ticker  a r e needed.  subsequently  instances a  during  tape  changed  symbol  i t was  the computation  relative',  (IPR).-  it  d i d change  a  company  within  was  -100% a t t h e time  to  assume  than or  that  t o assume  delisting For  security  Additional  1.  to  a n d was  that  was  the l a s t  the price i n which  a  would  b e when  a s a new  changed  company  to  performance  checked  to insure  o f r e t u r n was I t appeared  more  h i s investment  recorded  before  security  d i d not trade  t o assume what i s no m a r k e t  that  If  reinstated  s e t equal  the investor  there  a s many  I f a company  a t which  as i t i s i m p o s s i b l e  periods  and had not been  lose  price  same  therefore, trading.  of delisting. would  the  o f name o c c u r e d  was  or delisted  investor  a  reasonable rather suspension  sold. no  IPR  the value  was  of  for i t .  Information  A l lsecurities market  2.  an  months  computed, a  stock  of  v i a a consol-  'investment  the period studied the rate  to  i n fact  names  period.  of the  names  suspended  their  treated  Hence each  were  However,  the l i s t  i n the e a r l i e r  change  the ten year  i n total.  Although  4 2 5 many o f t h e s e  facilitate  i n fact  companies  100 o f t h e c o m p a n i e s  I n some  s i x times  its  comments  equals  Over  the study  as  c o n s i s t e d o f 425  were  movements.  equal  relative  A l lsecurities dividends.  given  equal  That  i s equal  price  changes.  were  adjusted  weights  i n computing  weights  f o r stock  were  splits  assigned  and  stock  9 3.  Prices  were  not r e s t r i c t e d  stocks  traded  only  i n odd  t o round lots  l o tprices  f o r extended  as  some  periods  of  time. 4.  Neither this  5.  transaction  nor taxes  are accounted  for in  study.  Dividends  were  companies  do  for  costs  future  stock  excluded  not give  high  dividends  cost  from  the study.  dividends  as c a p i t a l  exploration.  but this  Most  Many  mining  i s retained  companies  has been accounted  give (2)  for in  above.  METHOD OF  The only  method  briefly  summarized  Computer to  compute  the  data  Rates  the rate  as w e l l  were  of return  written,  were  done on  i n Chapter  developed  i n each  return  The  then  rigorous  tests  to determine  whether there was  subjected  written  correlation  coefficients for price  lags  o f one  t o s i x months.  test  t h e number  of  occasional  of runs  non-random  t h e VSEM  in price  t o a number were  any  t o compute  of  price the  serial  changes o f one month  A programme  trends  on  equal  basis.  changes were  programme  in  security.  assuming  returns  price  A  f o r each  f o r t h e VSEM  security.  a cumulative  f o r all.companies  The  dependencies.  3 and i s  (detailed i n appendix),  p e r month  as t h e cumulative  investment  also  i s detailed  here.  programmes  of return  dollar were  of analysis  ANALYSIS  was  also  written  changes t o detect in a  series  with  the  of prices.  to  presence The  10 . number of runs observed were compared with the number of runs t h a t would be expected from a sequence of t r u l y random numbers. F i n a l l y , s i n c e i t has  been argued t h a t these t e s t s  are  not a c c u r a t e enough to p i c k up s e n s i t i v e p r i c e movements, f i l t e r t e s t s were conducted on the data f o r f i l t e r s from .5% to  50%.  ORGANIZATION OF The  ranging  THE  STUDY  r e s u l t s of t h i s study are r a t h e r e x t e n s i v e  i n that  425  stocks were observed, t h e r e f o r e , t h i s r e p o r t p r e s e n t s o n l y  the  summaries o f the  the  f i n d i n g s r a t h e r than the e n t i r e d e t a i l o f  findings. Chapter Two  p r e s e n t s a summary o f some of the c l o s e l y  r e l a t e d empirical research  performed i n t h i s  area.  Chapter Three p r e s e n t s the d e t a i l e d methodology used i n the r e s e a r c h  and  the r a t i o n a l e u n d e r l y i n g i t .  Chapter Four p r e s e n t s the research  and  c a t i o n s , and The research  summarized f i n d i n g s o f  Chapter F i v e comments on the  influences,  possible explanations  findings.  l i m i t a t i o n s of the are a l s o i n c l u d e d  o f the  the impli-  study as w e l l as avenues f o r f u r t h e r i n Chapter.Five.  CHAPTER 2 PREVIOUS CLOSELY RELATED RESEARCH THE  BEHAVIOR OF STOCK MARKET PRICES(6)  P r o f e s s o r Fama s t u d i e s i n t h i s paper t h e theory o f random walks i n s e c u r i t y p r i c e s which i s based on t h e h y p o t h e s i s t h a t 1.  S u c c e s s i v e p r i c e changes a r e independent,  2.  the p r i c e changes conform t o some p r o b a b i l i t y distribution.  and,  Independence The p r o b a b i l i t y d i s t r i b u t i o n f o r the p r i c e changes d u r i n g time p e r i o d t i s independent  o f t h e sequence o f p r i c e changes  d u r i n g p r e v i o u s time p e r i o d s . Fama goes t o g r e a t l e n g t h s to show i n t u i t i v e l y how the random walk theory i s c o n s i s t e n t w i t h r e a l i t y . the presence  That i s , how  o f s o p h i s t i c a t e d t r a d e r s who can a s c e r t a i n  i n t r i n s i c v a l u e s i n s e c u r i t i e s h e l p t o cause p r i c e s t o move independently  of t h e i r previous p r i c e .  the Random Walk Hypothesis  The i m p l i c a t i o n o f  i s t h a t the a c t i o n s o f t h e t e c h -  n i c i a n s are f r u i t l e s s and t h a t should t h e r e be d i s c e r n a b l e p r i c e p a t t e r n s t h a t may e x i s t , t h e i r a c t i o n s c o l l e c t i v e l y would e l i m i n a t e these p r i c e p a t t e r n s .  L i k e w i s e , f o r the  f u n d a m e n t a l i s t , u n l e s s he can c o n s i s t e n t l y , i n t e r p r e t new i n f o r m a t i o n i n such a manner as t o earn h i g h e r p r o f i t s , h i s efforts will  a l s o y i e l d him no more o r no l e s s than what the  market i n g e n e r a l  earns.  12  T e s t s f o r Independence A.  Serial  Correlation  Data - Dow Jones I n d u s t r i a l Averages (end of 1957 to Sept. 26, 1962) Serial correlation in log prices  coefficients  f o r d a i l y changes  were computed f o r each stock f o r l a g t of from  1 to 30 days. Results: 1.  A l l c o e f f i c i e n t s were s m a l l  2.  Eleven c o e f f i c i e n t s  ( l a r g e s t was  f o r a l a g of t = 1 were more  than twice t h e i r standard e r r o r . cases a c o e f f i c i e n t as s m a l l as twice i t s standard B.  Coefficients  f o r 4,  .123)  However, i n most .06 was  more than  error. 9, and  16 day changes were computed.  Results: 1.  A l l c o e f f i c i e n t s were s m a l l .  2.  23 out of 30 c o e f f i c i e n t s  f o r d a i l y changes were  positive. 3.  21 and  24 c o e f f i c i e n t s  f o r 4 day and  9 day  differences  were n e g a t i v e . Conclusions: There were no m a t e r i a l dependencies i n p r i c e The h i g h degree o f p o s i t i v e series  and negative  changes.  signs f o r various  i s accounted f o r by the market i n f l u e n c e s ( 1 2 )  and  i s not s u f f i c i e n t enough to imply the e x i s t e n c e o f p o r t f o l i o trading C.  rules. Runs T e s t s  Fama found the percentage d i f f e r e n c e  between the  actual  and  expected number of runs were q u i t e s m a l l ,  dependence.  indicating  S i m i l a r l y the d i f f e r e n c e between the  litt  actual  and  expected number of runs o f a c e r t a i n s i g n are a l l very  small.  In a d d i t i o n t h e r e seems to be no  the  s i g n s of the and  differences.  important p a t t e r n s  For a l l the  stocks,  the a c t u a l d i s t r i b u t i o n s o f runs by  length  the  in  expected  t u r n out  to  be  extremely s i m i l a r . The  D i s t r i b u t i o n of P r i c e Changes Much of the  relevant  current  l i t e r a t u r e has  suggested t h a t  d i s t r i b u t i o n of p r i c e changes i s Normal.  t h a t the d i s t r i b u t i o n i s r a t h e r  the  T h i s means  f l a t i n the middle and  has  relatively thin tales. Fama argues, on  the b a s i s o f emperical evidence and  t h e o r e t i c a l grounds, t h a t p r o b a b i l i t y d i s t r i b u t i o n s o f changes conform b e t t e r to a s t a b l e P a r e t i a n which there i s i n f i n i t e Unlike deviation),  price  Distribution in  variance.  Normal, where two  parameters,  (mean and  standard  f u l l y s p e c i f y the d i s t r i b u t i o n , f o u r parameters  f u l l y specify a stable Paretian c*. =  on  Distribution. (<*- < 2  measures h e i g h t o f extreme t a i l s , d i s t r i b u t i o n i s non-normal)  ft  =  index o f skewness  £  =  l o c a t i o n parameter  =  defines  *y  the  scale of a stable  Paratian  distribution. For purposes of p o r t f o l i o a n a l y s i s , a key stable Paretian  distributions is stability.  property of  T h i s means that: ,  14  the values o f the paremeters oc and  remain constant  under  addition.  Tests f o r Dispersion Frequency d i s t r i b u t i o n s were computed f o r a l l o f the stocks, of  ( p r i c e changes), i n the sample and t h e i r  occurrence  frequency  w i t h i n given standard d e v i a t i o n s o f the mean.  These r e s u l t s were compared with the u n i t normal. cases, some degree o f l e p t o k u r t o s i s was present ities. (^2S,  The a c t u a l number o f o b s e r v a t i o n s  In a l l  i n the securr. .  i n extreme  >3S, >4S, >5S), were a l s o c o n s i d e r a b l y h i g h e r  would be expected  tails, than  with a Normal Curve.  T e s t s were conducted where the d a i l y f i r s t d i f f e r e n c e s were r e g r e s s e d a g a i n s t a s t a n d a r d i z e d v a r i a b l e such t h a t :  Z  =  where:  U - R S Z = standardized v a r i a b l e st U = random v a r i a b l e ( d a i l y 1  * differences)  R = mean S = standard d e v i a t i o n I f data conformed t o a Normal D i s t r i b u t i o n the graph would d i s p l a y a s t r a i g h t l i n e . curve was generated  However, i n a l l cases an S  c o n f i r m i n g the r e s u l t s o f the p r e v i o u s  tests. The of  data was t e s t e d t o see i f perhaps t h e r e was a mixture  d i s t r i b u t i o n s with p o s s i b l y the same mean but d i f f e r e n t  variances,  and a l s o  to  f o rthe departures  account  i f there  the  evidence  i s against  One  Form o f Dependence  Mandebrot(14)  was n o n - s t a t i o n a r i t y from  could  partially  that  large  changes  one p l a u s i b l e  account  f o r the long  i n p r i c e may  However,  be  random  and o f f e r s no o p p o r t u n i t y  of  view  the  adjustment •  the sign  tend  changes.  t o enhance  In conclusion,  data,  i t was  independence  found  from that  there  of  changes  follow can  The Kendall,  serial  were  fully  Namely,  change  by  appears t o  an investment changes  large  point  a r e due t o  place. tests  performed  no s e r i o u s  an i n f i n i t e  departures  and that  describes  on t h e  a  from  Stable  the distribution  variance.  I N S P E C U L A T I V E M A R K E T S : TRENDS ,OR RANDOM WALKS (1)..  appears  discernable  be b r o u g h t  Prices,  implying  article  variability  large  the various  D i s t r i b u t i o n more  This  from  i n s e c u r i t y p r i c e movements  P R I C E MOVEMENTS  cases  o f dependence  t o be f o l l o w e d  i n t h e market  Paretian price  These  form tails.  o f the second  profits.  process  In both  normality.  suggested  that  normality.  evident  into  paths.  view  stock  i s based  The A n a l y s i s i n which  According  common  i n common  article  to indicate that  by  common  t o Alexander, 'filtering'  stock  prices  these  trends  o u t random  prices.  i n part  o f Economic  on a study Time  Series  he c a l c u l a t e d t h e f i r s t  correlations of the f i r s t  done  b y M.  - Part  twenty-nine  differences  G.  I . lagged  o f twenty-two  16  time s e r i e s r e p r e s e n t i n g s p e c u l a t i v e p r i c e s . K e n d a l l asks the q u e s t i o n : we  "How  good i s the best  can make of next week's p r i c e change i f we  p r i c e change and correspondingly  In t h i s  study  estimate  know t h i s week's  the changes o f the past twenty-nine weeks and f o r the monthly s e r i e s ? "  K e n d a l l found t h a t g e n e r a l l y the s e r i a l c o r r e l a t i o n s i n d i cated t h a t stock p r i c e s tended to f o l l o w a random manner, even when i n t e r v a l s were extended from one week to two, e i g h t , and  s i x t e e n weeks.  The  four,  a r t i c l e p o i n t s out f u r t h e r  s t u d i e s t h a t were done by Osborne(16) i n which he worked with the logarithms were normally  o f p r i c e changes.  He  found t h a t these  d i s t r i b u t e d with a standard  logarithms  deviation proportional  to the square r o o t o f the l e n g t h of the p e r i o d , which i s c h a r a c t e r i s t i c o f a random walk. In u s i n g logarithms  of p r i c e changes Osborne found t h a t  the p r o b a b i l i t y o f a change i n e i t h e r d i r e c t i o n of a g i v e n amount i n the l o g of a p r i c e was was  no longer a ' F a i r Game'.  e q u a l l y l i k e l y , hence i t  However, the d i f f e r e n c e s a t -  t r i b u t e d to the e x p e c t a t i o n of zero a r i t h m e t i c gain or l o g g a i n are minimal and only d e v i a t e s i g n i f i c a n t l y  zero  over  extremely long time p e r i o d s . Alexander d i d f u r t h e r t e s t s f o r randomness i n which he s t u d i e d the number o f runs t h a t occured cash wheat p r i c e s at Chicago.  i n the weekly  He d i s t r i b u t e d the runs i n  accordance with t h e i r d u r a t i o n and  found t h a t they  conformed  very c l o s e l y with what c o u l d be expected from a random group of data.  However, when the same t e s t was  attempted on  the  17  Standard and Poor's monthly composite r e s u l t s appeared  stock p r i c e index, the  to be i n c o n s i s t e n t w i t h the assumption  random walk o f equal p r o b a b i l i t y o f r i s e o r f a l l .  of a  By t a k i n g  these r e l a t i v e f r e q u e n c i e s i n t o account he found t h e r e s u l t s d i d f i t the observed data q u i t e w e l l .  The author  concluded  t h a t the month t o month movement o f stock p r i c e s , a t l e a s t i n d i r e c t i o n , i s c o n s i s t e n t w i t h the h y p o t h e s i s o f a random walk w i t h an approximate 6 to 4 p r o b a b i l i t y o f a r i s e . When Alexander  a p p l i e d f i l t e r r u l e s t o changes i n stock  p r i c e s he found p r o f i t s , e x c l u d i n g commissions, c o u l d be earned.  R e s u l t s i n d i c a t e d t h a t s m a l l f i l t e r s were s u p e r i o r  to a buy-and-hold p o r t f o l i o .  He concluded t h e r e are trends  i n stock p r i c e s p r o v i d e d we a r e not d e a l i n g with f i n i t e time p e r i o d s .  uniform  In s p e c u l a t i v e markets p r i c e changes appear  to f o l l o w a random walk over time, but a move once i n i t i a t e d , tends to p e r s i s t . PRICE MOVEMENTS IN SPECULATIVE MARKETS: TRENDS OR RANDOM WALKS, NO. 2(2) Alexander  i n t r o d u c e d t h i s study by p o i n t i n g out some  c r i t i c i s m s t h a t were r a i s e d a g a i n s t h i s p r e v i o u s r e s e a r c h concerning  filtering:  1.  You cannot buy the averages.  2.  By f o l l o w i n g the f i l t e r r u l e you negate your  3.  Estimated p r o f i t s from the use o f f i l t e r s were s u b j e c t to b i a s exaggerating t h e p r o f i t a b i l i t y .  efforts.  18  4.  Filter  profits  distribution day's  price  are  of  the  the  consequence  daily  change  price  of  the  changes  i s independent  of  frequency  even  i f each  the preceding  day's. 5.  Apparent the  profitability  upward  For  criticisms  are  not  one  valid.  1.  You  2.  This  trend  in  through  of  filters  simply  reflects  prices.  three  i t can  be  argued  that  they  Namely:  can  buy  might  the be  averages.  true  b u t we  practical  application  of  filtering  theory negates  are not filters  interested but  or modifies  i n the  whether  in  fact  random  walk  theory. 3.  Author with  Criticisms deals  4 and  commissions profit. a  21.7% the  5 are  that  profits  essentially  2% or  1928  had The  t o be most  f o r these  are  what  biases,  reduced.  the  present  study  greater  profits  1961 1%  paid,  to  show  however,  on  each  were  a  the  only  gains over  policy  would  smallest  a buy-and-hold  buy-and-hold  used.  filters  maintained i n h i s study  from  were  transaction  sizeable beat  45.6%  a l l the  profitable  commission  largest,  -  r a n g i n g from  Alexander nor  result  Findings  Filters  With  the  adjusted  with.  Empirical  a  i n present study  no  have  made  filters.  filters  of  commissions.  Only  policy.  that are  If  neither relevant  commissions f o r the  19  purpose stock  a t hand.  prices  move  dependencies. expected rules  with  the  be  profit  trend  expected  upward  -  1928  he  eliminating  filters  1940  showed  nor as  tested what  of  the  study -  filter there.  a  result  period the we  studied?  average would  movement.  were more p r o f i t a b l e  under 1940  compare  here  price  apparent  comparing  simply  against  i n h e r e n t i n the  and  with  during the  first  transaction  period  -  He  there are  To  earned  whether  than  expect  It  was  was  to  trend. was  1961.  split  into  two  In p a r t i c u l a r ,  profits  even  profits  on  i n the  sub-  the  absence  of  trend.  Thirdly, by  no.  not  i s neither  in prices  influence  1940  or  concerned  rules  filters  the  the  1928  sub-period  that  from  Secondly  an  trend  ascertaining  behavior.  policy  filter  per  factor  generally  periods,  observed  to Alexander  logarithmic  found  from  with  or whether  s h o u l d be  a buy-and-hold  g e n e r a l upward  the  concerned  randomly  H e n c e we  profits  According  from  was  behavior with  Are of  'He  were  computed  the  s t i l l  trend  the  factor  profitable  and  once  although  the  orginal  again  reduced  found  prices that  the  somewhat.  Conclusion Evidence the  hypothesis that  Standard walk  indicated  with  and  Poor's  drift.  from  by  filter  1928  -  Industrials  profits  1961  the  runs  strongly  movement  i s consistent  with  of a  against  the random  20  FILTER RULES AND  STOCK-MARKET TRADING  T h i s p a r t i c u l a r study was  (7)  undertaken  i n response t o the  r e s u l t s o b t a i n e d by Alexander i n h i s paper. to  There  appeared  be a number o f areas t h a t h e l d some a m b i g u i t i e s , (cost o f  d i v i d e n d s , s h o r t term p o s i t i v e p r i c e change dependencies  and  i n t e r m e d i a t e term n e g a t i v e p r i c e dependencies), t h a t prompted the authors t o do f u r t h e r study w i t h Alexander's f i l t e r technique was  filters. a p p l i e d to s e r i e s of  d a i l y c l o s i n g p r i c e s f o r each of the i n d i v i d u a l of  the Dow-Jones Average s t a r t i n g about the end of 1957  September 26, 1962. 50%.  F i l t e r s were used r a n g i n g from  a f t e r commissions,  were  r e t u r n s b e f o r e and  b e f o r e and a f t e r d i v i d e n d s , and  r e t u r n s f o r both long and s h o r t p o s i t i o n s . s i t u a t i o n s the f i l t e r method produced  r e s u l t s r e l a t i v e to a buy-and-hold  average  G e n e r a l l y under vastly  portfolio.  Alexander f a i l e d to take i n t o c o n s i d e r a t i o n was  inferior  One  variable  the e f f e c t  d i v i d e n d s would have on a f i l t e r generated p o r t f o l i o . idends d e c l a r e d when a stock was  to  .5% to  Given these f i l t e r ranges v a r i o u s computations  performed on the data, namely computing  all  securities  Div-  h e l d s h o r t should be c o n s i d e r e d  a c o s t , hence a r e d u c t i o n i n o v e r - a l l r e t u r n .  By  taking  d i v i d e n d s i n t o account, the r e s u l t s of Alexander's study might not have been as p o s i t i v e . for  Fama and Blume found that by  d i v i d e n d s they i n c r e a s e d the average advantage  o f buy-and-  h o l d over the f i l t e r technique by a t l e a s t two percentage The study a l s o i n d i c a t e d t h a t the s h o r t p o s i t i o n s by the f i l t e r technique produced  i n a l l but one  adjusting  points.  taken  security,  negative returns.  On long p o s i t i o n s 13 s e c u r i t i e s had a  g r e a t e r average r e t u r n per f i l t e r r e t u r n s from buy-and-hold. the  than the c o r r e s p o n d i n g  By averaging the r e t u r n s . o n a l l o  long p o s i t i o n s however, y i e l d e d a lower r e t u r n than a  buy-and-hold. The authors found t h e r e was  evidence o f p e r s i s t e n c e o r  p o s i t i v e dependence i n v e r y s m a l l movements o f stock p r i c e s , however, not enough to generate l a r g e r r e t u r n s than a buyand-hold p o l i c y once the i n c r e a s e d commission  charges were  considered. Evidence o f n e g a t i v e dependence i n i n t e r m e d i a t e s i z e p r i c e movements was  a l s o found.  For f i l t e r s  l a r g e r than  1.5%, average l o s s e s on s h o r t p o s i t i o n s exceeded value the average r e t u r n s from buy-and-hold. annual average r e t u r n on s h o r t p o s i t i o n s was with +9.8%  f o r the buy-and-hold.  s i t e o f what the f i l t e r  The n e g a t i v e -16%  compared  Hence, i f we d i d the oppo-  t o l d us t o do,  l a r g e r r e t u r n than expected.  i n absolute  we  should have a .  Once again the study r e v e a l e d  t h a t with i n c r e a s e d charges these p r o f i t s would be  reduced.  Conclusion Fama and Blume s t a t e t h e r e appears t o be both p o s i t i v e and n e g a t i v e dependence but not o f the magnitude to enchance p r o f i t s , hence the random walk theory i s s t i l l of  reality.  s t r o n g evidenc  22  CHAPTER  METHOD OF  Data  closing March  data  1963  the  and  by  of  a  the  an the as  the  289  stocks  end  the  security  first  Investment  IPR's),  during  study  that  the  year  425  securities  the  end  of  Forty-five  period.  or  were  to  done  have to  an  the  names  or  upward  companies  suspended  data  drift  was  done  over  to  by  (hereinafter  data  the  reinstated.  T h i s was  relative, i n the  delisted not  period  period  the  Matrix.  company  f o r the  10  at  monthly  changed  tend  performance  f o r each  VSEM  These  p e r i o d were  was  the  subsequently  bankrupt  Performance  investment  listed.  that  prices  thing  the  presently trading  went  of  on  Throughout  were  securities  either  consisted of  listed  1973.  consolidation  data  study  a l l stocks  securities  112  Since time  in this  February  425  and  through  on  to  of  consisted period  used  price  total  in  RESEARCH  Used  The  a  3  the  over  develop  computing  referred 120  to  periods  covered. An  IPR  month, of  the  (P  i s the  ),  month,  price  divided (  p t  +  1  ) •  of  into  a  the  The  at  price  the  formula P  IPR  secuirty  =  t  by  rate  t a k i n g the  of  r e t u r n f o r any  product  of  the  would  beginning  security  at  of  the  the  end  be:  1  P  The  +  of  the  t  period of  time  may  be  a p p r o p r i a t e IPR's minus  calculated 1.0.  The  rates  of  return  used  in this  study  were  calculated  by  this  method. "The  use  of  changes  measure  of  return  walk  literature.  several it  ways.  less  in  price  log  price  e  change  differencing month,  justified  i n percentages  Similarly,  Thus  results  the  on  or  cumulative  earn  i f he  had  held  etc.  up  12 0 m o n t h s .  the  IPR  the  monthly  market  price  as  tells  And  than  us  for  one percent carried  returns to  price."  e  f o r one  an  for  each  investor  month,  would  the  (5)  calculated what  •  or  two  would months,  be:  t+i for  IPR's  a whole  was  formula  CIPR  The  IPR  change  percentage  identical  i n log  security The  the  one-period  changes  The  the  fifteen  essentially  security.  price  , tests  cumulative  P  for  return.  of  in  purposes,  shorter  i n excess  out  based  that  one-period  unusual.  tests  note  random  f i f t e e n percent,  are  yielded  be  for current  intervals  returns  the  I t can  i s approximately or  as  i n the  But  than  price  e  i s common  i s s u f f i c i e n t to  changes  to  in log  and  2 to  i =  CIPR's were  assuming  equal  n  also  weight  calculated f o r each  for  relative  change. P where I  P  o K  P K  n  given Price  years  O  base year Price number o f index items  24  To equal  clarify,  dollars  security the if  the  of  smaller  number  security no  ilarly, IPR's that or  i n f l u e n c e on  extent  IPR  IPR  was  IPR  Serial  as  are  the  (stock  market  security divided means was  was  that  can  This  i s to  index of  was  based  not  by  the  i n the  i t started trading  again.  that  than  those  of  the  felt  on  the  particular  sum  Sim-  of  the  i f IPR's  for  not  trade month,  index  the  was  each  security for a  months The  to  data  had  compute  the  been  converted  serial  into  correlation  lag of  1 month,  of  serial  IPR's  the  until  next  coefficient  2 months,  and.up  to  for 6  inclusive. definition  i s given  below.  the  correlation  ....  month),  month.  particular market  be  during  that  security did  included  only  trade  number  that  insure  index.  If a  i t during  one  influence  will  the  month.  did  available for  not  the  consisted  i f a  size  no  differently  part  market  during  data,  a  calculated for  step  u  the  behave  Thus,  place  Correlation  Once  (P )  for  f o r the  This  stock  they  trading  p r i c e data  time  that  missing  month.  such  index.  their  the  the  dollar  firms  had  then  market  i n v e s t o r would  purchases.  companies  f o r each  no  the  an  large  stocks  monthly  s e c u r i t y he  i t s absolute  on  monthly  of  that  of  the  The  of  earned  stocks  to  assumes  i n each  because  return  only  this  coefficient  Cov(X ,X t  p  k  (sx )  (sx  t  where  X  = IPR  t  X  t + k  S  The out  on  t + k  t + k )  fc  IP\  =  )  f o r k = 1,  + k  = standard  computer u s i n g the n£XY  4,  5,  6.  c o e f f i c i e n t s were c a r r i e d  following -  3,  deviation  a c t u a l computation of the  the  2,  formula:  SXSY  P, k \l[(nSX )  (SX) ]  2  where  2  n  =  number of  X  =  IPR  Y  =  I P R  I(n£Y ) 2  -  (27Y) ] 2  observations  t  t k +  The two  c o e f f i c i e n t of c o r r e l a t i o n i s a measure of the  variables  covary.  S e r i a l c o r r e l a t i o n measures the  of a time s e r i e s of data to move i n c y c l e s or t r e n d s .  way tendency Hence  high c o e f f i c i e n t s should i n d i c a t e t h a t the p r i c e changes imply some form of dependency.  Conversly, a c o e f f i c i e n t  approximating zero would i n d i c a t e l i t t l e dependency i n p r i c e changes. Runs T e s t s In the event t h a t  s e c u r i t y p r i c e s i n the data do  some form of dependency which the detect,  have  s e r i a l correlations did  runs t e s t s were i n s t i t u t e d .  Security  not  p r i c e changes  26  might  be  random most  coefficients, significant are  of  however,  trend  the  time  there  may  factor.  thus be  Runs  yielding  occasions  tests  should  low  correlation  where  there  determine  is  i f  there  any.  Definition  A the  of  run  a  can  Run  be  defined  same d i r e c t i o n  whenever Thus  a  the  run  sequence price 15,  could  of  giving  price us  It  6  is  obtained  of  the  the  of  price  For  observed; would  of  sign.  only  changes.  changes  sequence  same  next  consist  was  a  A  run  change  one  is  price  example,  15,  price  20,  20,  be  +5,  0,  compare  the  number  changes  is  determined  different.  change  or  a  large  i f the  following  25,  15,  +5,  18,  -7,  in  -3,  16,  +1,  and  -1,  runs. possible  with  random.  formula  of  price  sequence  the  were  sign  or  as  to  what w o u l d This  was  be  expected  done w i t h  the  of  runs  i f the  price  use  the  of  actually changes following  (6). 3 M  =  [N(N+1)  - _£^  2 ±  ]  /N  i=l where M  =  total  expected  N  =  total  number  N^=  Runs were to  see  i f they  independence.  the  number  calculated were  of  of  for  consistent  number price  price  a l l of with  of  runs  changes  changes  the the  of  stocks  each  in  assumption  the of  a  sign.  data  T e s t i n g Independence With F i l t e r The  pure form of the  security  Rules  random walk theory s t a t e s  p r i c e changes are  independent of each o t h e r .  e f f i c i e n t market h y p o t h e s i s i s concerned more w i t h assumption t h a t average by  s u p e r i o r p r o f i t s cannot be  analyzing existing  c o r r e l a t i o n t e s t s and of dependency but  information.  T h i s means t h a t  i c a n t enough to earn h i g h e r p r o f i t s than normal.  s a r i l y random. be the  One  e x i s t e n c e of  I f the and  rule that  can  assumes  security  r i s e s at l e a s t x percent,  u n t i l i t ' s p r i c e drops a t  u n t i l the  long p o s i t i o n  and  assume a  p r i c e r i s e s at l e a s t x percent.  moves i n a p a r t i c u l a r d i r e c t i o n by e x i s t s that  least  p r i c e decreases x  f i l t e r r u l e assumes t h a t once a s e c u r i t y ' s  probability  neces-  Rule  p e r c e n t or more, l i q u i d a t e any  The  A random  trends.  x percent from a subsequent h i g h ; when the  short p o s i t i o n  signif-  to t e s t i f above average p r o f i t s  p r i c e of a s e c u r i t y  h o l d the  a degree  an e f f i c i e n t market i s not  earned i s to employ a mechanical t r a d i n g  D e f i n i t i o n of F i l t e r  buy  way  The  the  dependency i n p r i c e changes  walk i m p l i e s e f f i c i e n c y but  ...  the  earned on  runs t e s t s might i n d i c a t e  i s the  that  the  price  at l e a s t x p e r c e n t  t r e n d i n that  direction  the  will  continue. The in size  f i l t e r r u l e was from:  applied  to the  data f o r f i l t e r s  rangi  28 x equal t o : .005 .01 .02 .05 .10 .20 .25 .50 An example o f how t h i s technique was a p p l i e d i s i l l u s t r a t e d below.  Transaction  c o s t s and d i v i d e n d s were excluded.  mining companies do not g i v e d i v i d e n d s  Most  so the r e s u l t s w i l l not  be i n f l u e n c e d to any great degree, however, the omission of t r a n s a c t i o n c o s t s c o u l d have a s i g n i f i c a n t i n f l u e n c e on the results, particularly  f o r the small f i l t e r s ,  frequency o f t r a n s a c t i o n s .  because o f the  Hence the omission  of transaction  c o s t s w i l l b i a s the r e s u l t s upwards i n f a v o r of the f i l t e r t  Action Signal*  Price  1  1.00  2  1.05  3  Buy  P r o f i t / (Loss)  rule.  Return  1.10  4  1.20  5  1.30  1.80 - 1.10  6  1.50  = .70  7  2.00  1.30 = 118?  8  Sell  & go short  1.80  9  1.50  10  1.25  11  1.00  12  Buy and go long * f i l t e r s i z e o f 10%  "  1.20  1.80 - 1.20 =  -  6 0  1.10  29  In the example the r e t u r n  f o r the f i l t e r would be 118%  compared t o 20% f o r a buy and h o l d p o l i c y . The  f i l t e r r u l e i s an a r b r i t r a r y a p p l i c a t i o n and assumes  t h a t the i n v e s t o r can buy and s e l l the s e c u r i t y a t the time and p r i c e t h a t the f i l t e r commands. always t r u e .  In p r a c t i s e t h i s i s not  The f i l t e r r u l e i n i t s pure a b s t r a c t  form w i l l  i n d i c a t e whether p r i c e changes are independent o r not.  As  a r e s u l t i t might p o s s i b l y r e f u t e the random walk theory but not  the e f f i c i e n t market h y p o t h e s i s .  The r e s u l t s however,  should g i v e some i n d i c a t i o n as t o the p r o f i t a b i l i t y o f a t r a d i n g rule. Measure o f Risk In comparing the. r a t e s o f r e t u r n earned on the TSE w i t h those earned on the VSEM some c o n s i d e r a t i o n the r i s k assumed i n each case.  must be given t o  F o r purposes o f a n a l y s i s i n  t h i s study the standard d e v i a t i o n o f r e t u r n s was used as a surrogate f o r r i s k .  S =  N £ X -  The f o l l o w i n g formula was used:  2  I  2 - ( X X)  (N - 1) The  c o e f f i c i e n t o f v a r i a t i o n was a l s o c a l c u l a t e d such  that: S CV = — — X  The  c o e f f i c i e n t o f v a r i a t i o n i s necessary t o determine  the r e l a t i v e v a r i a t i o n i n r e t u r n s between groups of data with v a r y i n g means. S t a t i o n a r i t y o f Returns One p a r t o f the weak form h y p o t h e s i s s t a t e s t h a t the r e t u r n s generated from s u c c e s s i v e  p r i c e changes a r e i d e n t -  ically distributed. "Identically distributed i s a technical s t a t i s t i c a l phrase which means the numbers a l l conform t o some g i v e n bability distribution.  pro-  Since the p r o -  b a b i l i t y d i s t r i b u t i o n s of h i s t o r i c a l  rates  o f r e t u r n tend t o be s t a t i o n a r y f o r any given  s e c u r i t y , t h i s i n d i c a t e s t h a t the  r a t e s o f r e t u r n f o r those s e c u r i t i e s a r e identically  distributed."(8)  In February o f 1973 there were 289 s e c u r i t i e s t r a d i n g . Only 25 o f these had complete p r i c e data f o r the t e n years under o b s e r v a t i o n .  T h i s simply  maintained the same corporate As  means t h a t 25 companies  name f o r the e n t i r e 10 y e a r s .  a r e s u l t they were used as a sample to t e s t the assumption  t h a t h i s t o r i c a l r a t e s o f r e t u r n tend t o be s t a t i o n a r y over time. The  companies were f i r s t d i v i d e d down i n t o f i v e , 2  year p e r i o d s  and l a t e r i n t o two, 5 year p e r i o d s .  p e r i o d the mean r e t u r n and standard  For each  deviation of returns  were determined t o see i f there had been any change i n e i t h e r o f these two measures.  I f the mean r e t u r n and/or  31  the  standard  returns  deviation  are  not  changed  stationary  i t would  and  indicate  therefore,  are  that  not  the  identically  distributed. The  major  distributions the  expected  will  be.  implication i s that  return  This  developing  Calculation  of  Rather  than  The  and  be  would  the  accuracy  stationary  accurately  aid  predict  the  portfolio  a  combinations  of  security  of  in  model  of  securities.  Return  arithemetic  i s obtained  m e a n was  what  managers  Markowitz-Sharpe  Mean R a t e  taking  from  c h a r a c t e r i s t i c s of  efficient  geometric  drawn  more  risk  Geometric  greater  used.  and  p o r t f o l i o s along space  is  can  knowledge  risk-return  periods,  we  to  mean o f  i f the  derived  the  various  geometric  using  the  mean  following  formula:  Average n  If it  was  R  the  monthly =  rate  number  average  of  t+12  where  (1.0  =  R  =  +  the  R )  monthly  t  A/IPR  months  annual  calculated with  .rvy  =  1  2  in  return  t  IPT  for  the  +  1  . . .  period  equation:  1.0  geometric  t  X  IPR  t + n  period  following  -  X  mean.  was  required  32  CHAPTER FOUR FINDINGS  Serial  Correlation  Serial correlation  c o e f f i c i e n t s were generated f o r 4 8  s e c u r i t i e s f o r a p e r i o d o f 10 y e a r s . calculated findings  The c o e f f i c i e n t s were  f o r monthly changes w i t h l a g s up t o 6 months.  are d e t a i l e d  i n table  Fama, (6) has shown t h a t  I I and summarized i n t a b l e I I I . f o r large  sample sizes.,  even  though the c h a r a c t e r i s t i c exponent <K o f the u n d e r l y i n g P a r e t i a n process i s g r e a t e r than 1, the c o e f f i c i e n t s are  consistent  correlation The  The  and unbiased estimates o f the t r u e  stable  generated  serial  i n the p o p u l a t i o n .  number o f s i g n i f i c a n t c o r r e l a t i o n s  a t the .05 l e v e l  ranged from 18.7% o f the t o t a l sample f o r a l a g o f one month to 6.2% f o r l a g s o f 2 and 3 months.  The l a r g e s t  was f o r the f i r m NGD f o r a l a g o f 1 month. s t a t i s t i c was a - .3868.  The r e s u l t i n g  The g r e a t e s t degree o f c o r r e l a t i o n  appears f o r a l a g o f 1 month. was  coefficient  The average  (mean) c o e f f i c i e n t  .1192 compared w i t h .0680 f o r a l a g o f 3 months.  Once  again except f o r t = 3, the m a j o r i t y o f the c o e f f i c i e n t s had negative.signs.  F o r a l a g equal t o 6, 31 o f 48  correlations,  or 64.5%, were n e g a t i v e . I t was i n t e r e s t i n g t o note t h a t when t e s t s involving  f o r dependence  s e r i a l c o r r e l a t i o n were run on f i r m s t h a t  ceased t o  trade d u r i n g the p e r i o d , the r e s u l t s were q u i t e s i m i l a r .  A  t o t a l o f 41 f i r m s f o r v a r y i n g p e r i o d s o f time were observed  33  and  as i s i n d i c a t e d i n t a b l e I I I and  s i g n i f i c a n t c o r r e l a t i o n s was  IV the percentage of  o n l y 11.3%  f o r t = 1,2,...6;  versus 11.06% f o r the a c t i v e f i r m s . The  s i g n o f the c o e f f i c i e n t s tended t o f o l l o w  same p a t t e r n as w e l l . c o e f f i c i e n t was  However, the average s e r i a l c o r r e l a t i o n  s i g n i f i c a n t l y higher  T h i s can be e x p l a i n e d on average w i t h the  f o r a l l values of t.  by the s m a l l e r number of  appears to be t h a t there  is l i t t l e  r e t u r n s generated i n one  p e r i o d and  and  some f u t u r e p e r i o d . 1.42%  observations  inactive firms.  Based on the r e s u l t s thus f a r a t t a i n e d the  in  the  For the  suggestion  dependence between the the r e t u r n s  generated  a c t i v e f i r m s between  of the movement i n lagged p r i c e changes can  .46% be  used to e x p l a i n the v a r i a t i o n i n the c u r r e n t p r i c e change. In terms of d e c i p h e r i n g  p r o f i t a b l e t r a d i n g r u l e s based  h i s t o r i c a l p r i c e changes, s e r i a l c o r r e l a t i o n g i v e s i n s i g h t and would appear to add Market Hypothesis.  strength  to the  on  little  Efficient  TABLE I I Monthly  Serial Correlation  C o e f f i c i e n t s f o r Lags o f 1,2, (ten year time span)  Stock  1  2  3  BCC BR BSM CGQ CMNA COP CPG CRI CSR CST DVM GDC GIM GRL GRV MM MTW NCR NIN NOV NPM PB PDL . PEEL PSS QUT. RV SBC  .1333 .0390 -.1126 .0297 -.0223 .0050 .0845 -.2988* -.0510 -.1471 -.0912 -.0868 .0494 .1143 -.2179* -.1047 -.0277 -.0949 .0372 .3212* -.1253 .1855* .0033 -.0843 -.0910 -.2534* -.1385 -.1769  -.0349 .0976 -.0469 -.0927 .2016 .0057 .1132 .1604 -.2044* .1227 -.0840 -.0011 -.0260 -.0827 -.1631 -.0592 -.1001 .0336 -.1354 .2689* -.0247 .0114 -.0788 .0816 .1648 .0414 -.1183 -.1768  .0028 .0621 .0244 -.0020 -.0171 .1002 .2678* -.0823 .0162 -.1925* .0419 .0126 .0099 -.0486 -.0622 .0156 -.0245 -.0355 -.0099 .1256 .0155 .0967 .1150 -.0965 .1249 -.0418 .1646 .0183  Lag  6 Months  4  5  -.0381 .0894 -.0570 .0199 .0168 -.0787 .0079 -.0226 -.0258 .0754 .0061 -.0192 -.1638 .0262 .3133* .0038 -.2350* .0737 .0325 .1641 -.0316 .2552* -.1701 .0761 .1171 -.0115 -.0121 -.0610  .0373 .0249 .1641 -.0569 .0185 -.0555 -.1113 -.0556 .2340* -.0663 -.2480* -.0311 . 0089 -.1209 -.0709 . 0433 .0178 -.0502 .0165 .0124 -.0413 .0428 .0509 -.0396 -.0780 .0736 -.0215 -.2576*  6 .0333 -.0917 -.0255 -.0954 .0569 -.0737 -.0660 -.1453 .0222 -.0785 -.1339 .0217 -.0606 -.2070 -.1305 .0629 .0563 -.2506 -.2475 .0057 -.1399 .018 3 .0767 -.0658 .0278 -.1004 -.1018 .2146  TABLE I I (continued) Monthly S e r i a l C o r r e l a t i o n  1 SCH SRD SS TR TRJ TWT VN WMI  NEW  -.0962 -.1382 .2400* -.0587 -.0519 .0210 -.1644 .1343  2  C o e f f i c i e n t s f o r Lags o f 1,2, (ten year time span) 3  Lag  .1231 .1128 -.0712 -.0548 .0658 .0286 -.1266 .0553 -.0191 . 0520 .0589 -.0261 -.0028 -.0330 .0531 -.1917 * * C o e f f i c i e n t i s twice  4 -.0942 -.1310 -.0478 -.1199 .0425 -.0265 -.0917 -.0040  ATS CCD CYD DVN JY JRC LTL'A' NGD PPT RHM SLO TMX  1 -.2121* -.1121 .2406* .0603 .1027 .0241 -.1169 -.3868* .1465 .1085 .1040 .0754  2  3  .0429 -.0720 -.0478 -.1137 -.0284 -.1081 .0921 -.0214 -.0599 -.1146 -.0503 -.0477 .0510 -.0136 .1609 -.2145* -.1720 .0080 .0656 .0403 -.1070 -.0057 .0101 -.0280 * C o e f f i c i e n t i s twice  5  6  .0442 -.0832 -.1347 . 0024 .0189 -.0677 .1855* -.1465  -.0040 .0931 -.0685 .0425 -.0223 -.0767 -.2514* .0292  i t s computed standard  Monthly S e r i a l C o r r e l a t i o n C o e f f i c i e n t s f o r Lags o f 1,2, (eight year time span);  Stock  , 6 Months  4  error  6 Months  5  -.1098 -.0271 .0585 -.1656 -.0495 -.0290 -.1143 -.1213 -.0842 -.0059 -.0327 .0327 .0297 -.0218 .0528 -.0168 -.3051* -.0420 -.2078 -.1861 .199 .1809 -.2784* .0532 i t s computed standard  6 .0065 -.0924 -.0120 .0555 -.0674 -.1072 -.0088 -.0863 -.2115* -.2459* -.0562 .0551 error  TABLE I I I Summarization o f R e s u l t s o f S e r i a l C o r r e l a t i o n  1  2  3  4  Coefficients  5  6  no. o f n e g a t i v e & p o s i t i v e signs  26(-) 28(-) 23(-) 27(-) 29(-) 3K-) 22( + ) 20( + ) 25( + ) 21( + ) 19( + ) 17( + )  % o f negative signs  54.1  58.3  47.9  56.2  60.4  64.5  % of negative signs (inactive)  60. 9  46.3  46.3  60.9  63.4  63.4  18. 7  6.2  6.2  10.4  10.4  14.5  17.0  4.8  7.3  7.3  14.6  17.0  .0680  .0865  .0744  .0875  .1622  .1846  .1775  .1934  Percentage o f significant correlations* for inactive firms * *  Average c o e f f i c i e n t .1192 .0838 i n a c t i v e firms .2062 .1579  _• . . • r™^ : ^ 5 • *approximately twice the standard e r r o r **absolute value <t  —•  Monthly  TABLE IV S e r i a l C o r r e l a t i o n C o e f f i c i e n t s f o r Lags o f 1,2,  6 Months  I n a c t i v e Firms Stock AET AKN BAP BRX BTL CDT CHH CMAN CTH CVM DIN EYB FMI GBX GDR GLS GLW GPU IBL IMR JAY KAM KONEW KOP LBM MGC MRX NAI NHL NKR  # of Observations 91 72 21 27 29 41 65 58 114 3 13 33 73 15 27 28 26 41 15 22 79 107 21 110 15 92 31 25 16 8  ^ ^ ^ ^ ^ ^ 1 -.0078 -.0486 .1739 .0380 -.3772* -.3014 .0909 -.0885 -.1968* .9810* -.1717 -.0498 -.0063 -.3480 -.3711 -.0491 .1499 .017.7 -.0908 -.1834 -.3687* -.0469 .0434 .2386* .1610 .0903 -.2565 -.2669 -.3407 -.1660  Lag  2  3  -.0062 •.0196 .1848 -.0525 -.1130 .0760 .0846 -.1980 .0225 1.0 .0520 -.2437 .0052 .0520 .1985 -.0499 -.2683 .0071 -.2339 -.1967 .0078 -.0312 -.3274 .0213 .0652 .2025* .0599 -.0190 -.1693 -.6297  -.0041 .1174 -.0426 -.1031 .1600 .1878 -.0736 .0464 -.0242 0 .6500* .2791 -.1053 .2574 / -.1361 -.0519 -.4412* .0073 .0602 .2807 -.0796 .0513 .1478 -.0371 .3428 -.0583 -.1240 -.2022 .2117 -.3189  4  5  6  -.0059 -.0917 -.2237 -.0428 -.5188* -.4110* .0320 -.0444 -.0793 0 -.1743 -.2041 .0884 -.3288 -.2588 -.0541 -.2803 .0075 .1627 .1607 .1245 .0480 -.0194 -.1575 .1289 -.0945 .1976 .2473 -.4589 .8536*  -.0191 -.0822 -.1031 -.1963 .4586* .1292 -.0028 -.0017 .0784 0 -.2594 -.1385 -.1541 .2878 .4909* -.0565 .0085 -.1828 -.0540 .0151 -.2070 .0038 .2494 -.1149 -.5293* -.1400 -.4075* -.1994 .5305* -.2326  -.0052 .0249 -.2427 -.3803 -.0640 -.1975 .0416 -.0017 -.0597 0 .0700 -.0941 .0389 -.3925 -.4568* • .4349* .5155* .0047 -.5089 -.4062 -.0576 -.0123 .0447 -.0595 -.5825 -.1713 .1595 -.4024* -.0095 -.7495*  TABLE IV Monthly S e r i a l C o r r e l a t i o n  #  Stock NLC NRX PRM RXM SEM SML" SSD SUH VNS WLM WTM  (Continued)  C o e f f i c i e n t s f o r Lags o f 1,2, I n a c t i v e Firms  O f  Observations 21 23 24 30 17 33 10 33 48 12 25  1  2  3  .1697 -.1894 -.2174 .4108* .0812 -.3206 .1111 -.2606 .3339* -.4058 .2338  -.0902 -.1490 -.0093 .134 9 -.3837. .0187 .1125 .1814 .0801 .5858* .1319  -.2043 .3671 .0975 .1424 -.2049 -.3443* .1125 .2131 .0655 .1228 -.0146  * Coefficient is  LAG  6 Months  4  5  5  -.3369 -.1437 -.1985 .0021 -.15.7.0 .2111 .1429 -.0961 .1308 -.4397 -.0291  -.0713 -.0143 .1544 -.0783 .2283 -.0285 .1667 -.0595 .0693 .8082* -.0883  -.0057 .1941 -.0540 . 0336 -.0479 -.0635 .2000 -.0043 .0329 -.5857* .3375  twice i t s computed standard e r r o r  39  Runs T e s t s Runs t e s t s were conducted on the sample stocks u s i n g the f o l l o w i n g formula: M  =  [N(N+l) -  ^ ^  n /N] 2  i=l  1  where N i s the t o t a l number o f p r i c e changes, numbers of p r i c e changes o f each  and the n^ are the  sign.  Table V summarizes the r e s u l t s o f the Runs T e s t .  Of a l l  the f i r m s t e s t e d the percentage d e v i a t i o n between expected and a c t u a l number o f runs averaged 8.6 p e r c e n t , with o n l y 6 f i r m s out o f 4 8 showing 15 p e r c e n t .  a percentage d e v i a t i o n g r e a t e r than  Although the c a l c u l a t i o n s were not a p p l i e d t o  a l l the f i r m s i n the sample,  u s i n g a B e r n o u l l i process w i t h  P( + )# P ( ) , and P(0) on a few o f the f i r m s i n d i c a t e d t h a t the -  number o f expected p o s i t i v e , n e g a t i v e and no change runs corresponded c l o s e l y w i t h the a c t u a l d i s t r i b u t i o n of runs. Fama (6) suggested t h a t the percentage d i f f e r e n c e between a c t u a l and expected number of runs would be a good measure t o determine the amount o f dependence i n the observed data, hence the s t a n d a r d i z e d o r Z-value was. not c a l c u l a t e d . Twenty-nine  out o f f o r t y - e i g h t s e c u r i t i e s y i e l d e d  runs  which were below what would have been expected, s u g g e s t i n g perhaps a s m a l l t r e n d f a c t o r .  Whether one c o u l d suggest t h a t  t h i s supports the r e s u l t s o f the s e r i a l c o r r e l a t i o n however i s i n c o n c l u s i v e .  coefficients  There appeared t o be some n e g a t i v e  c o r r e l a t i o n o r downtrend i n terms o f the number of companies e x h i b i t i n g negative c o e f f i c i e n t s .  40  I t i s i n t e r e s t i n g to note t h a t those  f i r m s t h a t ceased  t r a d i n g d u r i n g the p e r i o d d i d not behave i n a s i m i l a r f a s h i o n . Of the 4 2 i n a c t i v e f i r m s o n l y 14 had  fewer runs than was  The d i s t r i b u t i o n of runs f o r both a c t i v e and  expected.  i n a c t i v e firms  were s i m i l a r , with p o s i t i v e runs o c c u r i n g about as f r e q u e n t l y as negative runs.  The  a b s o l u t e percentage d i f f e r e n c e between  expected and a c t u a l number o f runs was For the 42 f i r m s t e s t e d , the spread f o r the i n a c t i v e f i r m s versus companies.  8.6  significantly  approximated 16.02  percent  higher. percent  f o r the a c t i v e  Upon o b s e r v a t i o n i t appeared t h a t the i n a c t i v e  f i r m s f o l l o w e d a more c y c l i c a l p a t t e r n .  P o s i t i v e changes  were more apt to be f o l l o w e d by negative  changes.  This i s  to some degree by the g r e a t e r number of  negative  confirmed  c o r r e l a t i o n c o e f f i c i e n t s f o r a l a g o f t = 1. evidence  Once again  the  suggests t h a t the amount o f dependency i s small  and  not s i g n i f i c a n t l y i n d i c a t i v e of non-randomness.  TABLE V Total  Actual  and Expected  Numbers  Monthly Stock  Expected  Actual  BCC BR BSM CGQ CMNA COP CPG CRI CSR CST DVM GDC GIM GRL GRV MM MTW NCR NIN NOV NPM PB PDL PEEL PSS QUT RV SBC SCH SRD SS TR TRJ TWTNEW VN WMI  66.4622 78.042 76.9328 73.0336 78.9496 72.78 6 7 . 87 79.16 69.33 73.58 66.61 7 1 . 35 62.56 74.74 80.26 73.86 73.87 72.24 76 . 05 67.12 69.70 77.62 76. 56 73.47 78.88 71.37 78.36 72.33 71.75 75.12 65.10 75.82 72.40 62.03 72.32 68.41  66.0 46.0 81.0 63.0 71.0 71.0 65.0 64.0 58.0 81.0 70.0 70.0 59.0 75.0 77.0 78.0 73.0 75.0 69.0 65.0 75.0 72.0 73.0 82.0 70.0 83.0 75.0 76.0 71.0. 78.0 68.0 67.0 73.0 57.0 71.0 66.0  ATS CCD CYD DVN JY  54.71 62.15 59.50 62.22 63.62  59.0 56.0 64.0 ' 61.0 69.0  o f Runs  f o r One-Month  inflections  Period  Runs  -  0  +  -  0  . 007 .696 - .050 .159 .112 .025 .044 .237 .196 - .092 - .048 .019 .060 - .003 . 042 - .053 . 012 - .037 .102 .033 - .071 .078 .049 - .104 .127 - .140 .045 - .048 .011 - .037 - .043 .132 - .008 .088 .019 .037  51 42 56 58 33 59 61 49 28 55 60 52 65 56 42 51 58 57 53 64 58 47 44 58 50 53 46 59 61 56 64 40 56 67 59 53  7 50 30 17 50 17 9 37 69 17 7 13 3 20 39 18 19 15 22 9 11 25 23 18 .32 13 36 16 16 21 6 26 15 3 16 9  61 27 33 44 36 43 49 33 22 47 52 54 51 43 38 49 42 47 44 46 50 47 52 43 37 53 35 44 42 42 49 50 48 49 44 57  29 16 34 28 21 31 29 26 21 35 30 30 28 31 28 27 29 33 29 29 32 29 27 36 29 32 28 32 31 35 30 28 30 27 30 28  7 14 22 8 23 12 7 15 19 13 7 9 3 19 21 17 16 12 12 9 10 14 17 17 16 12 21 16 11 15 6 10 11 3 13 8  30 16 25 27 27 28 29 23 18 33 33 31 28 25 28 34 28 30 28 27 33 29 29 29 .2 5 39 26 28 29 28 32 29 32 27 28 30  - .073  52 46 56 55 53  6 20 12 11 14  40 31 34 40 38  27 23 29 27 32  6 9 10 10 10  26 24 25 24 27  %Diff.  .109 - .070 .020 - .078  +  TABLE Total  Actual  and Expected  V  (continued)  Numbers  Monthly Stock JRC LTL'A NGD PPT RHN SLO TMX  1  Expected  Actual  64.91 66.47 67.68 6 2 . 38 57.10 55.28 64. 36  67.0 65.0 69.0 60.0 49.0 46.0 52.0  o f Runs  f o r One-Month  Inflections %  Diff.  -.031 .023 -.019 -.039 .165 .202 .238  Period  Runs  -  0  +  -  0  +  61 29 43 40 47 43 44  12 26 32 25 10 10 27  39 47 27 29 39 39 27  29 25 27 23 21 20 22  10 12 17 16 8 9 11  28 28 25 21 20 17 19  43  TABLE Total  Actual  VI  a n d E x p e c t e d Numbers o f Runs Inactive Firms  f o r One-Month  Stock  Expected  Actual  AET . AKN . BAP . BRX . BTL . CDT . CHH . CMAN. CTH . CVM . DIN . EYB . FMI . GBX . GDR . GLS . GLW . GPU . IBL . IMR . JAY . KAM . KONEW KOP . LBM . MGC . MRX . NAI . NHL . NKR . NLC . NRX . PRM . RXM . SEM . SML . SSD . VNS . WLM . WTM . YUK . SUH .  22.45 4 3 . 84 12.36 13.85 12.05 24.28 33.19 19.85 68.86 3.50 3. 86 16.07 40.97 4.42 16.50 6.36 11.90 6.62 9.13 7.43 46.92 64.43 1 3 . 82 58.52 6.45 47.95 19.93 1 7 . 85 10.65 5.00 1 2 . 33 9. 80 14 .28 18.48 1 2 . 22 13.96 4.40 20.55 5.80 17.231 2.71 19.76  21 44 13 15 14 27 35 13 73 4 4 18 42 7 21 5 12 5 9 9 59 59 16 29 6 53 24 18 12 6 12 11 17 17 8 16 4 20 8 14 3 23  %  Periods  Differ .069 .003 .049 .076 .140 .100 ..052 .527 .057 .125 .036 .107 .025 . 367 .214 .273 .008 .324 .014 .175 .205 .092 .136 1.018 .076 .095 .169 .009 .113 .167 .028 .109 .160 . 087 .528 .128 .100 .028 .275 .231 .095 .141  44  F i l t e r Trading A filter  Rule r u l e i s a mechanical t r a d i n g r u l e , where by i t  i s b e l i e v e d t h a t stock p r i c e s , or more s p e c i f i c a l l y changes in  stock p r i c e s f o l l o w c e r t a i n d i s c e r n i b l e p a t t e r n s .  Once a  stock p r i c e i s i n motion i t w i l l continue to move i n the same d i r e c t i o n long enough and  c o n s i s t e n t l y enough to generate  p r o f i t s which h o p e f u l l y are g r e a t e r  than a simple buy  and  hold  policy. As mentioned i n Chapter 2, Alexander had t e s t i n g of the previous  filter  r u l e , and  done  considerable  a f t e r correcting for biases  s t u d i e s , concluded t h a t a f t e r t r a n s a c t i o n and  in  dividend  c o s t s , s u f f i c i e n t p r o f i t s would not be generated to beat a and  hold p o r t f o l i o .  Table VII summarizes the r e s u l t s  when a f i l t e r r u l e , w i t h f i l t e r  s i z e s ranging  buy  obtained  from .5% t o  50%,  was . a p p l i e d to the monthly p r i c e changes f o r f o r t y - f i v e securities.  In a l l cases the f i l t e r  average, negative filter  s i z e of two  of 20%.  The  r e t u r n s ranging percent,  r u l e generated, on  from a minus 121.0% f o r a  to a minus 4.1%  for a f i l t e r  reader i s r e f e r r e d to Table V I I I where the  r a t e of r e t u r n f o r each s e c u r i t y i s t a b u l a t e d  and  purchased at the b e g i n n i n g of the p e r i o d and  for  The  filter  been  h e l d f o r the  T h i s was  the average  t r a n s a c t i o n c o s t s were a p p l i e d as w e l l as  d i v i d e n d adjustments. per  total  bottom of the t a b l e d i s p l a y s the mean r e t u r n  a l l of the s e c u r i t i e s i n the sample.  r e t u r n before  size  compared w i t h  what the p a r t i c u l a r stock would have earned i f i t had  duration.  the  There were s l i g h t l y more negative  than p o s i t i v e .  The  any returns  median number o f p o s i t i v e r e t u r n s  45  was  20 or approximately 44%.  T h i s corresponded very c l o s e l y to  the percentage o f p o s i t i v e r e t u r n s f o r a l l 415 f i r m s i n the data.  TABLE V I I Summarization  .005 No. o f p o s i t i v e (total  o f 45)  short  long  position  positions  positions of positive  for  a l lfirms  .01  .02  .05  .10  .20  .25  .50  B&H*  21  20  20  18  22  20  13  16  17  23  23  23  20  23  23  13  12  18  18  16  17  21  18  11  13  (109.0). (112.6)  (loss)  no.  (121.0)  (90.3)  (33.8)  (4.1) (83.0)  (82.7)  (84.9)  (61.4)  (62.1)  (50.0)  (22.7)  (10.9)  (43.6)  (34.1)  (24.0)  (51.2)  (58.9)  (40.3)  (11.1)  6.8  (39.4)  (48.6)  185  182  184  175  171  174  155  145  96  96  96  82  62  37  30  17  returns  (415)  aver. no. o f t r a n s a c t i o n s per f i l t e r *  Tests  returns  mean p e r c e n t r e t u r n p e r filter (loss) mean p e r c e n t r e t u r n o n short positions (loss) mean p e r c e n t r e t u r n o n long  Rule  returns  No. o f p o s i t i v e on  of F i l t e r  returns  No. o f p i s i t i v e on  of Findings  Buy a n d H o l d  Portfolio  29.9  In comparing the s h o r t and long p o s i t i o n s the data i n d i c a t e s t h a t the long p o s i t i o n s were more p r o f i t a b l e , i n terms o f o v e r - a l l mean r a t e o f r e t u r n and number o f p o s i t i v e r e t u r n s per f i l t e r .  T h i s can be v e r i f i e d by examination o f Table IX  which compares the r e t u r n s generated f o r both the short and long p o s i t i o n s per stock as w e l l as the o v e r - a l l mean r e t u r n for  each f i l t e r  s i z e f o r a l l s e c u r i t i e s combined.  the number o f p o s i t i v e r e t u r n s c l o s e to one another.  However,  f o r both p o s i t i o n s were r e l a t i v e l y  For a f i l t e r  to be the most s u c c e s s f u l f i l t e r ,  s i z e o f 20%, which appeared  the mean r a t e o f r e t u r n was  a p o s i t i v e 6.8% f o r the long p o s i t i o n .  These same s e c u r i t i e s  under a buy and hold p o l i c y generated a mean r a t e o f r e t u r n o f over 29 It returns  percent. i s s i g n i f i c a n t t o note t h a t the number o f p o s i t i v e f o r a l l 415 s e c u r i t i e s i s c l o s e t o 50.percent f o r the  total for a l l filter  sizes.  I n d i c a t i n g t h a t the l i k e l i h o o d  o f any p a r t i c u l a r f i r m earning  a p o s i t i v e r e t u r n i s not  s i g n i f i c a n t l y g r e a t e r than the p o s s i b i l i t y o f e a r n i n g  a  negative  return. Alexander, as w e l l as Fama and Blume (7), found  there  was evidence o f p e r s i s t e n c e or p o s i t i v e dependence i n very short-term  p r i c e movements.  By short-term  or even i n t e r - d a i l y p r i c e movements.  they meant d a i l y  Since the data i n t h i s  paper c o n s i s t e d o f monthly p r i c e movements, t h i s might e x p l a i n why the r e s u l t s are s i g n i f i c a n t l y d i f f e r e n t from t h e i r  studies.  I t a l s o c a s t s s e r i o u s doubts as t o the v a l i d i t y o f u s i n g monthly p r i c e data.  In order  f o r the f i l t e r  i t must c a t c h a l l movements i n the p r i c e .  t o be e f f e c t i v e ,  Monthly p r i c e changes  TABLE V I I I F i l t e r T r a d i n g Rules as Compared t o a Buy and Hold P o l i c y Filter Stock  .005  .01  .02  BCC BR BSM CGQ CMNA COP CPG CRI CSR CST DVM GDC GIM GRL MM MTW NCR NIN NOV NPM PDL PEEL PSS QUT RV SBC SCH SRD SS  1.410 2,556 1.808 1.212  -.130 2.457 1.808 1.212  .346 2. 605 1. 808 1.187  2.048 . 390 .247 -.428 -3.556 . 849 -4.730 1.360 3. 947 -1.400 1. 953 .655 1. 452 5.660 -1.481 .871 -1.467 2.124 -8.056 -5.960 .686 -2.756 -10.400 -.303  2.048 .390 .166 .682 -3.556 .849 -4.541 1.067 3.947 -1.400 1.953 .655 1. 452 5.660 -1.481 . 337 -1.467 1.992 -8.056 -5.960 .686. -2.756 -10.400 .667  Size .25  . 50  B&H  .05  .10  .20  -2.4 60 1.790 -1.038 2.612  1.635 1.741 -.885 1.400  -2.656 1.211 -1.115 -.900  -3.044 1.000 -.808 .414  3.667 .452 1.556 -1.067  6.226 .308 .103 1.357  1.290 1.513 . 390 -.878 -.014 .096 . 830 1.830 -3.556 -2.889 1.068 1.068 -4.541 -3.703 .348 .101 3.947 3.947 -1.800 -.400 1.953 1.739 -.379 .655 1.452 1.167 5.132 9.434 -1.481 -1.037 .124 .374 -1.467 -1.462 3.642 4. 358 -7.278 -5.056 -5.960 -3.760 .514 1.486 -2.000 -5.378 -10.400 -12.000 . 848 .545  -1.076 4.488 .241 1.317 -2.667 .808 -5.373 1.258 2.526 -4.818 2.096 .793 1.024 8.604 -3.630 1.162 1. 333 5. 992 -1.944 -.010 .371 -5.810 -9.000 3.636  .555 9.585 .667 1.510 -8.333 .298 -2.795 1. 653 -.174 2.067 1.662 -1.483 1.929 12.151 -1.704 2.060 1.926 5.710 -.050 -1.120 -1.175 .222 -11.400 .924  1.173 10.634 . 809 1.208 -7.333 -.440 -2.205 .203 -1.333 .600 1.690 -3.621 .905 11.660 -2.963 1.735 . 741 2. 617 -2.550 3.980 -2.100 -.130 -7.200 -7.030  .922 2. 604 0.000 .733 -.571 -.355 -3.282 2.441 1.200 4.667 1. 592 -.379 -.810 5.509 1.333 -.091 -.687 1.963 1.545 .900 -1.980 -.444 -3.500 1.750  .143 . 607 .413 1. 214 1.8571 .560 .895 5.263 .471 1.500 .096 1.125 .560 3". 647 3.474 2.055 .828 . 298 1.438 .600 .548 .148 1.250 2.759  TABLE V I I I Filter  Trading  Rules  (Continued)  a s Compared t o a Buy Filter  Stock  .005  .01  .02  .05  and H o l d  Policy  Size  .10  .20  TR TRJ TWTNEW VN WMI ATS CCD CYD DVN JY JRC NGD PPT RHM SLO TMX GRV  .533 -14.167 5.869 1.500 2. 362 -1.659 .441 4.045 2.233 1.525 -.565 -4.250 1.305 4.111 4.246 2.192 -2.750  .533 -14.167 5.869 1.500 2.499 -1.659 .441 4.045 2.233 1.525 -.565 -4.250 1.416 4.111 4.246 2.356 -2.750  .533 -16.611 3.174 1.500 2.3.52 -1.659 .441 3.985 2.033 1.525 -.565 -4.250 1.093 3.381 4.277 2.740 -2.750  .267 -3.944 4.043 1.500 2.423 -1.098 .147 3.258 .267 1.875 .913 -4.450 .960 3.698 4.031 2.795 -1.812  .133 9.056 3.522 .800 1.370 -.902 .088 5.470 2.433 . 900 2.696 -4.350 .952 2.032 3.431 2.000 -2.938  -1.867 17.500 2.959 2.000 .220 -.805 . 353 4.076 .800 .600 2.575 -1.364 1.527 1.190 3.754 -.712 -2.529  Average  -109.0%  -112.6%  -121.0%  -90.3%  — 33.8 %  -4.1%  .25  .50  1.156 -.400 12.389 -.929 -.739 -5.250 -3.200 .800 .602 .291 -.707 -2.317 .324 .029 1.637 -.409 . 800 1.371' .075 — 1 . 4 5 0 .711 . 875 -.879 -1.061 1.752 .70 8 1.127 -2.349 3.292 2.585 -2.521 -.110 -5.059 -4.250 -83.0%  -82.7%  B&H 2.000 2. 5 7 1 1.438 .909 .791 .268 .206 .095 .964 .225 .261 .2812 .522 .667 3.385 .493 .5185 29.9%  bury from view a l l the d a i l y p r i c e changes. i g n o r i n g the f i l t e r  Hence we a r e  r u l e d u r i n g the month when i n e f f e c t  there may have been s i g n i f i c a n t p r i c e changes t h a t would have a c t i v a t e d the f i l t e r w e l l before the end o f the month. However, s i n c e the e n t i r e study has u t i l i z e d monthly  data,  there appears t o be a c o n s i s t e n t p a t t e r n d i s p l a y e d i n a l l tests.  Namely, s e c u r i t y p r i c e changes, when viewed from an  economic p e r s p e c t i v e , appear t o move i n a random manner.  51  TABLE Returns  G e n e r a t e d From  IX  Short  and  Filter Short BCC BR BSM CGQ COP CPG CRI CSR CST DVM GDC GIM GRL GRV MM MTW NCR NIN NOV NPM PDL PEEL PSS QUT RV SBC SCH SRD SS TR TRJ TWTNEW VN WMI ATS CCD CYD DVN JY JRC NGD PPT RHM SLO TMX Average  Long  -191. 4 104. 9 82. 7 1. 3 80. 0 -1. 2 -8. 5 -78. 9 -250. 0 17. 1 -282. 4 -226. 9 176. 3 159. 3 -145. 0 92. 9 17. 2 54. 7 166. 0 -196. 3 -53. 8 -113. 3 91. 4 -466. 6 -328. 0 10. 0 -160. 0 -1700 i . -136. 3 -40. 0 -827. 7 243. 4 50. 0 83. 0 -96. 3 11. 7 193. 9 66. 6 65. 0 -54. 3 -235. 0 39. 1 172. 2 2 0 .,0 84. 9  232. 4 50. 7 -1. 9 20. 0 24. 8 59. 8 -66. 9 -63. 9 -205. 5 -32. 2 -290 . 5 262. 9 118. 4 -215. 6 105. 0 2. 3 -51. 7 -9. 5 300. 0 -51. 8 40. 9 -133. 3 20. 9 -438. 8 -368. 0 -41. 4 -215. 5 -1700 i . 6. 0 -6. 6 -688. 0 243. 4 0. 0 53. 4 -169. 5 -67. 6 110. 6 56. 6 -13. 7 -100. 0 -290. 0 -8. 6 138. 8 304. 6 34..2  - 8 4 . ,9  - 2 4 . ,0  Short  Positions  Size .05  .02  .01  005  Stock  Long  Long  Short  Long  Short  144. 5 -268. 4 45. 6 100. 0 -1. 9 82. 6 20. 0 1. 2 24. 8 80. 0 59. 8 -1. 2 -12. 5 -70. 9 -76. 6 -91. 5 -250. 0 -205. 5 -32. 2 17. 1 -271. 6 -279. 7 -241. 5 248. 3 118. 4 176. 3 -159. 3 -215. 6 -145. 0 -105. 0 2. 3 92. 9 2 5 1 . 7 17. 54. 7 09. 5 300. 0 166. 0 -51. 8 -196. 3 14. 2 -80. 5 -113. 3 -133. 3 12. 5 86. 6 -466. 6 -438. 8 -328. 0 -368. 0 1 0 . 0. - 4 1 . 4 -160. 0 -215. 5 -570. 0 -570. 0 54 . 5 087. 8 -40. 0 -6. 6 -827. 7 -688. 0 243. 4 243. 4 0. 0 50. 0 60. 0 89. 8 -96. 3 -169. 5 -67. 6 11. 7 110. 6 193. 9 56. 6 66. 6 -13. 7 65. 0 -54. 3 -100. 0 -235. 0 -290. 0 44. 6 -3. 0 138. 8 171. 4 304. 6 20. 0 42. 4 93. 1  -244. 6 107. 4 82. 6 0. 0 42. 0 -1. 2 -21. 5 -15. 9 -250. 0 28. 0 -272. 9 -277. 5 176. 3 -159. 3 -165. 0 92. 9 17. 2 54. 7 139. 6 -196. 3 -91. 1 -113. 3 169. 1 -427. 7 -328. 0 1. 4 -122. 2 -570. 0 93. 9 -40. 0 -983. 3 108. 6 50. 0 82. 5 -96. 3 11. 7 190. 9 56. 6 65. 0 -54. 3 -235. 0 28. 5 135. 7 21. 5 1 1 2 . .3  179. 2 53. 0 -1. 9 18. 7 -13. 6 -59. 8 -79. 8 -1. 0 -205. 5 -21. 2 -281. 0 212. 3 118. 4 -215. 6 115. 0 2. 3 -51. 7 -9. 5 273. 5 -51. 8 3. 6 -133. 3 95. 0 -400. 0 -368. 0 -50. 0 -177. 7 -570. 0 48. 4 -6. 6 -811. 0 108. 6 0. 0 48. 3 -169. 5 -67. 6 107. 5 46. 6 -13. 7 -100. 0 -290. 0 -19. 2 91. 2 306. 1 61. 6  -384. 9 66 . 6 -59. 6 71. 2 55. 0 -64. 6 -16. 0 34. 0 -216. 6 28. 0 -231. 0 -289. 8 176. 3 -112. 5 -95. 0 82. 6 -34. 4 40. 4 354. 7 -174. 0 -78. 7 -119. 2 205. 0 -316. 6 -218. 0 50. 0 -286. 6 -650. 0 -78. 7 -53. 3 -316. 6 152. 1 -100. 0 86. 0 -68. 2 -2. 9 154. 5 -3. 3 82. 5 19. 5 -245. 0 21. 9 1 5 1 ..5 16. 9 115. 0  -51. 2  -62. 1  -58. 9  -50. 0  - 6 1 .,3  Long 38. 8 12. 3 -144 . 2 90. 0 -3. 8 -123. 1 -74. 4 48. 9 -172. 2 -21. 2 -239. 1 200. 0 118. 4 -168. 7 -45. 0 -8. 6 -103. 4 -23. 8 488. 6 -29. 6 16. 1 -126. 9 130. 8 -288. 8 -258. 0 -1. 4 -351. 0 -650. 0 63. 6 -20. 0 -177. 7 152. 1 -150. 0 51. 8 -141. 4 -82. 3 71. 2 -13. 3 3. 7 -28. 2 -300 . 0 25. 8 107. 1 286. 1 6 4 .. 3 - 4 0 .,3  52  TABLE Returns  G e n e r a t e d From  IX  Short  and  Filter .10  Stock Short BCC BR BSM CGQ COP CPG CRI CSR CST DVM GDC GIM GRL GRV MM MTW NCR NIN NOV NPM PDL PEEL PSS QUT RV SBC SCH SRD SS TR TRJ TWTNEW VN WMI ATS CCD CYD DVN JY JRC NGD PPT RHM SLO TMX Average  -180. 1 0. 0 -51. 9 1. 2 -63. 9 203. 6 -13. 4 4. 5 -205. 5 15. 0i -309. 6 -217. 9 105. 2 -168. 7 -309. 1 100. 0 24. 1 33. 3 313. 2 -303. 7 -43. 6 16. 6 286. 6 -161. 1 -31. 0 -5. 7 -309. 5 -500. 0 60. 6 -60. 0 333. 3 126. 1 15. 0 33. 4 -58. 5 -5. 8 265. 1 -31. 6 33. 7 108. 6 -240. 0 21. 4 68. 2 2. 3 7 5 . ,3  - 2 2 . ,7  Long Size  .20 Long  243. 6 0. 0 -136. 5 38. 7 -143. 6 145. 1 -62. 4 27. 2 -161. 1 34. 2 -327. 7 243. 8 47. 3 -225. 0 -272. 7 9. 2 -44 . 8 -30. 9 447. 1 -159 . 2 59. 9 16. 6 212. 5 -133. 3 -70. 0 -57. 1 -371. 4 -500. 0 203. 0 -26. 6 472. 2 134. 7 -35. 0 3. 5 -131. 7 -85. 2 181. 8 -41. 6 -45. 0 60. 8 -295. 0 -26. 3 23. 8 2 4 0 . ,1 24. 6 - 1 1 . ,1  Short  Positions  .25 Long  -330. 0 41. 1 -65. 3 -112. 8 17. 4 450. 0 -3. 5 20. 4 -488. 8 -7. 1 -180. 0 -118. 6 -43. 4 -147. 0 53. 3 75. 3 -89. 6 78. 5 490. 5 -207. 4 91. 1 51. 8 272. 8 -60. 0 -86. 0 -80. 0 -3. 7 -620. 0 -390. 0 -160. 0 755. 5 97. 8 75. 0 -22. 7 -53. 6 7. 3 195. 4 76. 6 18. 7 105. 0 -81. 8 50. 2 26. 2 18. 5 -60. 3  -35. 5 -17. 8 -146. 1 -77. 1 -61. 9 408. 5 -29. 8 30. 6 -444. 4 -63. 1 -198. 7 183. 8 -73. 9 -205. 8 53. 3 -9. 2 -151. 7 14. 2 624. 5 -62. 9 14 . 9 40. 7 198. 1 -45. 0 -126. 0 -137. 5 -74. 0 -600. 0 223. 3 -126. 6 894. 4 97. 8 25. 0 -55. 3 -121. 9 -72. 1 112. 1 33. 3 -60. 0 52. 5 -154. 5 0. 2 -6. 4 27. 7 - 1 0 9 .,5  - 1 0 . ,9  6. 9  Short  .50 Long  Short  Long  -74. 4 -330. 0 0. 0 0. 0 -50 . 0 -130. 7 -11. 4 -47. 1 -18. 7 36. 1 459. 7 503. 6 -19. 1 0. 0 20. 7 0. 0 -438. 8 -394. 4 -44. 0 -100. 0 -148. 8 -171. 5 79. 6 -159. 3 -100. 0 -145. 8 -273. 5 -332. 3 -20. 0 -20. 0 -6. 8 75. 8 -196. 5 -258. 6 -38. 1 28. 5 600. 0 464. 1 -270. 3 -125. 9 61. 0 12. 0 -18. 5 -7. 4 -32. 7 104. 3 -185. 0 -160. 0 139. 0 169. 0 -126. 2 -183. 7 -94. 4 -18. 5 -360. 0 -360. 0 -472. 7 -330. 3 -53. 3 -86. 6 638. 8 500 . 0 -86. 9 -86. 9 -35. 0 15. 0 -36. 2 -3. 6 -129. 3 -197. 6 5. 9 -73. 5 -28. 7 -112. 1 -15. 0 -5. 0 85. 0 -7. 5 -32. 5 20. 0 -57. 6 -130. 3 11. 5 6 1 . ,5 -9. 5 2 3 . ,0 16. 9 - 4 0 . ,0 -150., 6 - 2 0 1 . 4  0. 0 5. 2 69 . 4 -106. 1 265. 0 116. 0 0. 0 0. 0 -75. 0 -37. 6 -220. 9 -47. 4 33. 3 -231. 2 193. 3 73. 0 -34. 4 -57. 1 158. 4 -70. 8 -54. 5 -71. 8 4. 6 0. 0 -75. 0 -16. 3 -31. 4 -225. 0 -58. 3 0. 0 -121. 4 -358. 3 -185. 0 -12. 8 -51. 2 - -8.8 75. 0 46. 7 -95. 0 28. 0 -66. 6 0. 0 -157. 1 - 4 . .6 - 3 0 .,1  266. 7 -60. 0 -13. 8 -72. 7 -335. 0 44. 3 0. 0 -26. 6 -82. 1 -97. 8 207. 2 -27. 1 -13. 3 -293. 7 173. 3 -17. 7 -100. 0 111. 9 292. 4 104 . 1 -54. 5 -96. 8 91. 5 54. 0 . 90.0 -181. 6 -112. 9 -225. 0 133. 3 15. 6 -71. 4 -266. 6 -235. 0 -39. 6 -119. 5 -79. 4 ^5. 0 -9. 7 -150. 0 -57. 0 -139. 3 -29. 2 -177. 7 2 3 3 . .8 - 8 0 . ,8  -39. 4  - 3 4 . ,1  - 4 8 . ,6  - 4 3 . ,6  53  Stationarity In theory  of  keeping states  Returns with  that  the definition  the returns  Initially,  i t was  securities  conformed  t o a normal  completely  described  b y two moments;  and  further Fama  to  a stationary  the  by r e s e a r c h e r s  (6) a n d M a n d e b r o t symetric  the standard  measure  of risk.  true  be i d e n t i c a l l y that  distributed.  the returns  d i s t r i b u t i o n which t h e mean  d i s t r i b u t i o n s had f i n i t e  by  Thus  felt  must  o f a random walk, t h e  and  variance.  (14) s u g g e s t e d  that  d i s t r i b u t i o n with  Recent  infinite  i t s effectiveness  As sample  sizes  are increased deviation  be  studies  r e t u r n s ..conformed .  loses  the standard  could  variance,  deviation  population,  from  variance. a s an  accurate  t o approximate  will  increase  erratically. A  good  absolute  substitute  deviation,  f o r the standard  (MAD).  tribution  of returns  according  to the following  MAD  Therefore,  f o r t h e sample  deviation  i s t h e mean  i n describing  stocks,  t h e MAD  the diswas  used  formula:  -2  =  i=l where  r^_  r  The each.  data  F o r each  describes The to  was  =  =  divided  period  rate  of  return  mean  rate  into  two t i m e  t h e mean  of  return  a n d MAD  periods were  of five  years  calculated.  Table  the results. mean  determine  stationary  a n d MAD whether  over  time.  were  calculated  f o r t h e two t i m e  or not the d i s t r i b u t i o n of returns As Table  X indicates,  periods were  out of thirty  firms  X  TABLE  X  Comparison o f S h i f t B e t w e e n Mean M o n t h l y R a t e o f R e t u r n a n d MAD f o r P e r i o d M a r . 1 9 6 3 t o F e b . 1 9 6 8 & M a r . 1 9 6 8 t o F e b . 1 9 7 3  Firm BCC BSM CGQ COP CPG CRI CST DVM GDC GIM GRL GRV MM MTW NCR NIN NOV NPM PB PDL PEEL PSS QUT RV SBC SCH SRD SS TRJ TWTNEW *  Mean  MAD  1. 0 2 1 5 1. 0 0 6 0 • 9997 1. 0 0 4 1 1. 0 2 7 1 .9 9 2 6 1. 0 5 7 0 1. 0054 1. 0 1 3 7 1. 0 1 3 2 1. 0 1 8 1 1. 0 3 5 6 1. 0 3 5 5 .9 8 1 7 1. 0 6 1 8 1. 0 1 9 7 1. 0 0 0 7 1. 0 3 3 1 1. 0 1 5 2 1. 0 0 4 6 1. 0 1 0 1 1. 0 2 1 2 1. 0 2 7 2 1. 0 1 4 2 1. 0 0 0 6 1. 0 1 8 7 1. 0 6 5 4 1. 0 2 4 3 1. 0 6 0 5 1. 0 4 1 0  coefficient  of  . 0660 .1457 .1188 .0714 .1718 .0535 .2212 .1069 .1763 .0831 .1497 .1709 .1380 .1282 . 2006 .1384 .1284 .1635 .0871 . 0578 .1262 .1159 .1328 .0679 .0786 .1473 .2263 .1240 .2216 .1593 variation  Mean 1 .0056 .9746 1 .0352 .9795 1 .0204 .9963 1 .0400 1 .0051 1 .1478 1 .0275 1 .0053 1 .0326 1 .0102 1 . 0175 1 .0029 .9959 1 .0740 1 .0318 1 .0322 1 .0198 1 .0077 .9800 1 .0025 1 .0135 1 .0413 .9799 1 .0096 1 . 0175 1 .0193 1 .0087  MAD .0882 .1236 .1411 .0976 .1941 .0312 .2531 .1232 . 3449 .0968 . 1424 .1751 .1790 .1741 .1492 .0993 .2283 .1595 .1272 . 0727 .1661 .0883 .1068 .1669 .2206 .116 3 .1663 .1197 .1599 .1548  CV(1)*  CV ( 2 ) *  .2.069 24.283 396.0 17.415 .6.339 7.229 3.881 19.796 5.569 6.295 8.270 4 . 800 3. 887 7.005 3.246 7.025 183.4 4.939 5.730 12.560 12.495 5.467 4.882 4.782 131.0 7.877 3.460 5.103 3.663 3.885  1 5 . 75 4. 866 4. 008 4. 7 6 1 9. 514 8. 432 6. 328 2 4 . 157 2. 334 . 3.520 2 6 . 86 8 5. 3 7 1 1 7 . 548 9. 949 5 1 . 448 2 4 . 219 3. 085 5. 0 1 5 7 3. 950 3. 670 21. 571 4. 4 1 5 4 2 . 720 1 2 . 363 5. 3414 5. 786 1 7 . 322 6. 840 . 8.2 8 5 1 7 . 793  55 t e s t e d o n l y seven appeared t o d i s p l a y any s t a b i l i t y with to t h e i r mean r e t u r n .  E i g h t firms showed an i n c r e a s e  respect  i n the  mean r e t u r n w h i l e f i f t e e n firms showed a n o t i c a b l e drop i n average r e t u r n .  S i m i l a r l y , there were no i n s t a n c e s where t h e  computed c o e f f i c i e n t s o f v a r i a t i o n (CV) remained the same.  From  t h i s i t was concluded t h a t there was no r e l a t i o n s h i p between the mean and MAD f o r a l l the f i r m s t e s t e d , i n d i c a t i n g not o n l y a r e the d i s t r i b u t i o n o f r e t u r n s n o n - s t a t i o n a r y  but t h e i r shape  changes as w e l l . Thus i t would appear upon t h i s cursury  examination t h a t the  s e c u r i t y p r i c e changes do not completely conform t o a random walk. However, as was s t a t e d e a r l i e r , an e f f i c i e n t market does not r e q u i r e a random walk but a random walk would be a good i n d i c a t o r of  efficiency. Had  the d i s t r i b u t i o n o f r e t u r n s as t e s t e d , proved t o be  s t a t i o n a r y , then we would have been able t o make p r o b a b i l i t y statements about the percentage p r i c e changes to be expected i n the f u t u r e , and the h i s t o r i c a l mean r e t u r n and standard d e v i a t i o n would have p r o v i d e d  us with a good estimate o f the  f u t u r e expected r i s k and r e t u r n . "The past  As Fama s t a t e s :  random walk model does not say, however, t h a t information  i s o f no value  t r i b u t i o n s of future returns.  i n assessing Indeed s i n c e  disreturn  d i s t r i b u t i o n s are assumed to be s t a t i o n a r y through time, past r e t u r n s a r e the best information.  source o f such  The random walk model does say, however,  t h a t the sequence,  (or the o r d e r ) , o f the past  returns  i s of no consequence i n a s s e s s i n g d i s t r i b u t i o n s o f f u t u r e r e t u r n s . " (5)  56 The  shift  explained business  i n mean  i n that cycle. an  the The  VSEM  shows  IPR  This  decline  i n the  last  year  of  the  This  study  market  d i d not  described  by  i t s mean  returns  a  The  that  this  test  was  Table  The  was  index  one  be  complete  f o r the  evident  deviation.  standard beyond  lowest  the  to  conformed  of  or  and  to  into  this  see  can  scope  of  whether  a normal  monthly  .8310.  grouped  results  whether which  1.3222 a n d  entire study.  for  the  IPR's  not be  security completely  I t was the or  not  the  by  study. monthly  distribution. f o r the  period  range  of  seven  class  intervals  are  felt  present  The  grouping  returns  IPR's  detailed  in of  below  were  between equal in  XI.  Fitting Limits  a Normal  Normal  The  normal  respective z  whether  the  XI  Curve  Curve  .8310-.90117 .90117-.9713 .9713-1.0415 1.0415-1.1116 1.1116-1.1818 1.1818-1.2519 1.2519-1.3222  the  cover  distribution  TABLE  Class  to  particularly  conducted  VSEM  subsequently  size.  monthly  ascertain  was  h i g h e s t and  respectively, were  normal  f o r the  appear  firms might  study.  a  However,  d i d not  sample  .8930 f o r t h e l a s t m o n t h o f t h e  of  to  writer  data  f o r the  cumulative  conformed  the  returns  to Observed  Frequencies  Data  Observed  8 29 43 28 5 2 4  9 25 37 30 14 3 1 curive  f r e q u e n c i e s were  - values  normal  curve  f o r the provides  Frequencies  class a  obtained  by  boundaries.  reasonably  good  computing To  confirm  f i t to  the  57 o r i g i n a l d i s t r i b u t i o n the c h i - square f i t was  used i n accordance  l e v e l of s i g n i f i c a n c e of  i=l  t e s t - o f goodness of  w i t h the f o l l o w i n g formula, a t a .05:  e. 1  where n  =  actual frequencies  e  =  expected  frequencies  2  A v a l u e of X  =4.17  was  o b t a i n e d i n d i c a t i n g t h a t the  observed  d i s t r i b u t i o n c o n s t i t u t e s a sample from a p o p u l a t i o n having a normal d i s t r i b u t i o n .  58  Risk  of  and  Return  The  previous  determining  independently that  these  used  to  a  our  buy  of  a  on  and  the  information,  news  they  equal  monthly compared and  its  the  market  of  we  price  is  no  above  is  could  reached This  complete  freely,  rationally  i n  changes  generally  what  have  the  recognized  and the  be  the  problem  move  information which  Market.  there  fluctuate  security  sum o f  returns  rate  a  of  with  can  attained f i r s t  with  is  dissemination are  be  level  d e f i n i t i o n  there  a  i n  pred-  of  great  interpretation  XII as  was  return  standard  period  for  each  month.  and  reward  which on  used  the  this  as of  for  VSEM  average  the  across monthly  measure  risk.  monthly  i n  an  of  any  and  rate  independent  securities returns  observation  the  measure  of  of  return  would  the  be  standard  v a r i a b i l i t y  Therefore, standard  w i l l  the  average  deviation for  of  the  were  TSEM  deviation.  displays  the  i n  behave  movements  Based  good  the  prices  their  protfolio  hence,  Table  risk  profit  distributed.  deviation returns,  i t  TSEM  receive.  then  normally  If  Return  primarily with  security  Efficient  acting  and  dealt  contain  policy,  an  individual  a  not  another.  hold of  Risk  have  movements  prices  investors  manner  one  or  assumption  many  If  sections  trading  definition  icated  VSEM V e r s u s  whether  price  earn  naive  of  well  as  Table for  the  the  number  XIII  both  actual  the  of  monthly  returns  firms  included  indicates VSEM  and  the  (IPR) i n  relationship  TSEM.  for  the  index  between  59  CHAPTER  INTERPRETATION  General  Statement  The the  securities trading  As  was  months,  negative being  smaller to  be  quite  tests  also  as  verify  significant,  then  expected. this  type  W h a t was  expected  periods  runs  or  there  number  averaged  by  there  of  were Large of  the  data  used a  Had  the  to  for  earn  naive  a  buy-  this  only  few  significant  for  coefficients  alternating returns this  a  lag  of  were  patterns  followed  dependency  coefficients.  by appeared The  runs  alternating pattern have  filter  i n d i c a t e d more  rules  runs  should  have  picked  derived  from  those  pattern. the  information  were  would of  were  Except  the  low  t e s t s would  was  bankrupt  the  be  changes.  magnitude  fact.  unexpected  have  can  weakly^efficient  price  attained with  signs  there  consistent  would  lagged  The  the  went  which  shows  returns.  this  that  Yet  the  evidenced  firms  changes.  of  Furthermore, of  the  historical  be  price  perhaps  etc.  low  study  lagged  i n the  been  out  the  majority  returns  to  of  Changes  between  generated  could  p r i c e movements  strategy.  Price  indicating  conform  that  information  expected,  the  RESULTS  i n d i c a t e the  Stocks  says  above what  of  correlations 3  no  investment  Correlation  study  Mining  which  contain  profit  and-hold  this  Vancouver  hypothesis,  NUMERICAL  Findings  findings of  Listed  market  of  OF  FIVE  delisted have  been  significant 11.3%  which  during  the  some t r e n d  period. i n the  One price  correlations for a l l was  equivalent  to  the  60  active with  firms.  the  prices  can  uations of  use  An of  be  between  as  the  above these  well.  the  two  yet  series  the  they  the  barriers of  of  the  of  firms  only  price  action  barriers  value  of  the  are security.  as  decline  moves  as  randomly  value  of  for, or  within  the •  l a r g e f o r the  account  Thus,  bankruptcy  barriers  absolute  twice  the  fluct-  investor operates.  s t i l l  average  s t i l l  security  Through  nearing  reflecting  The  the  naive  price  possible  c o n s t r a i n e d random  value.  the  approximately  3.7%  suggests  intrinsic  those  security  could  be  investors reflecting  below  value  of  He  might  inactive  explain,  movement.  Tests  From point,  both  statistical appear  imply  previous  monthly  indicates security  there  i s no  prices  historical with  departure.  and  price  sample  were  performance  dependence  superior performance price  group  prices  runs  average  investment  is little  data.  The  consensus are  movements.  negative The  and  there  t h a t would  studying  the  a  i t would  changes  runs  two  was  approximately  Runs  and  (3).  intrinsic  constraints.  coefficients firms,  a  true  levels  However,  these  as  explain this  model  (informed)  intrinsic  declines,  for  the  experienced  In  to  Cootner's  viewed  around  established  attempt  based  Comparing  the  no  number  positive  2 7.18  and  2 8.18  market  price be  had  making  the  major  number or and  of  by  process  trend  information other  suggested of  could  regarding on  in  stand-  in than  positive  significant negative  respectively.  runs  61  The  implication  correlation slightly no  from  a  pure  and  random  from  runs  the  tests  series  results  is  their  of  although  the they  similarity  depart  suggests  Tests  techniques  were  successive  rules  were  costs  and  argued  price  were  i s obviously  not  were  included  losses  Even  from  returns,  without  indicated  that  changes.  For  earning  a  not  the  there any  was  From  Hence,  or  firm or  had  dependencies of  the  argued  considering point  sizes  would  statistical costs  the  of  view  was  negative  costs  have  increased.  viewpoint, and  pattern  there  trading  transaction  i f transaction  discernible  return  results  investor  transaction  particular  positive  when  an  correlation  complicated the  a l l filter  no  serial  Alexander,  relevant  theoretical  including  and  possible  case. to  tests  However,  prices.  this  purely  to  startling.  security  the  runs  changes.  dividends  a  that  insensitive  e v e n more  movement o f  of  drawn  departure.  Technicians  in  be  coefficients  significant  Filter  to  dividends, in  about  return  filter  price an  for  even any  chance  filter  size.  Stationarity  It appeared  was  of  pointed  to  be  MAD  for  each  did  not  appear  decline as  well.  in  Returns  out  l i t t l e  be  returns,  the  previous  relationship  individual to  in  security.  stationary and  the  as  shape  chapter  between The  the  mean  there return  d i s t r i b u t i o n of  evidenced of  that  the  by  the  and  returns  average  distribution  changes  62  Upon in  examination  t h e mean  19 67 TSE  the market, showed  showed  a rather  also  bears  The  firms  that  That  i s , many  well  below  study  could  themselves  per  Hence  of  stock,  make  penny  The of the  d i d the relative  f o r many o f t h e  observation  be c l a s s i f i e d  Subsequently  the  majority  as s p e c u l a t i v e  stocks.  trading  many  that  at a price  fo these  resulting i n increases  t h e t r a n s i t i o n was  stocks  a market  be s u b j e c t  the  speculative  from  range  firms  i n the price  speculative  to  i n the risk characteristics  to significant nature type  to valuation  and  reward  and  that  by  'promoters'  price  changes.  of mining  stocks,  ventures,  suggests  does  hence  not hold.  they  trying are or  Because o f  i . e . , the anticipation that  the traditional  Trade-offs  between  f o r i n d i v i d u a l s e c u r i t i e s do n o t n e c e s s a r i l y  the spin  assigning  securities  are influenced  i n a particular security,  a l l or nothing  approach  in  from  r e s u l t i n g i n a change  can  of  1973  to  the security. Many  to  to  for. t h e  1968  stocks  i s why  so r a d i c a l l y  o f t h e s e c u r i t i e s were  established  stable  Index  from  mining  answering  appear  a dollar.  share.  needs  change  I t would  under  Metal  by comparison.  f o r the total  1963  the period  The i n t e r v a l  performance  the decline  fact out.  i n returns  securities? of  this  question  variation  index  From  by t h e Base  imporvement.  sluggish  market  f o r the period,  c a n be e x p l a i n e d .  as measured  steady  cumulative VSE  return  o f t h e market  of a roulette  probabilities.  tend  t o be e i t h e r  wheel  might  The i m p o r t a n t boom o r b u s t  be more thing  risk exist  appropriate  i s these  ventures.  Once  63  the boom, (or b u s t ) , occurs then perhaps the r i s k c h a r a c t e r i s t i c s change.  Thus the i n d i v i d u a l s e c u r i t y being  studied i n period 1  with i t s average r e t u r n and MAD might be e n t i r e l y d i f f e r e n t i n p e r i o d 2 with a new r i s k / r e w a r d The  relationship.  r e s u l t s would i n d i c a t e t h a t p r o b a b i l i t y statements  about f u t u r e expected r e t u r n s and v a r i a b i l i t y o f r e t u r n s cannot be made, b u t , they do not i n d i c a t e t h a t the r e t u r n s as they are being  generated a r e not s u f f i c i e n t l y non-random  as t o comply w i t h the e f f i c i e n t market  hypothesis.  TABLE Monthly  Rates  March  1963  XII  of Return  for  to February  Market 1973  Months 5  Year 1  10  8  6  10  11  12  0.0 0  1.142 68  1.102 71  .943 73  .959 77  .976 78  .979 80  .999 81  .970 82  1.009 83  1.169 84  1.019 86  1.062 86  1.322 86  1.065 87  1.039 88  1.058 87  1.044 88  1.074 91  1.048 91  1.053 93  1.003 93  1.104 98  .970 98  .9924 98  1.035 100  .996 103  .860 104  .997 106  1.019 107  .943 108  1.054 111  1.263 112  1.016 116  1.107 117  .973 120  .955 119  1.108 127  .8839 140  .945 143  .990 145  .942 148  .922 150  .990 150  .966 152  1.018 155  1.145 155  1.088 156  .946 153  1.025 152  .956 152  .989 152  1.063 153  1.055 153  .994 157  .968 158  .989 161  1.040 165  1.111 167  .976 171  .980 167  1.016 169  1.096 170  1.093 171  1.001 176  1.048 178  1.084 182  1.101 181  1.093 185  1.032 191  1.252 195  1.117 196  .951 190  1.089 192  1.043 196  .831 200  .919 201  1.011 204  .953 206  1.054 209  .968 213  1.033 219  .946 221  .946 210  .884 214  .889 216  1.006 217  .977 223  1.026 228  .998 231  1.001 231  .993 233  .964 237  1.091 236  1.020 238  1.021 231  1.077 235  .927 236  .919 241  .957 244  .932 245  .968 246  .877 251  .955 253  1.136 254  1.312 254  1.038 258  .985 239  1.188 243  .879 252  1.005 263  .939 273  1.002 274  .984 277  .868 278  1.025 281  .942 286  1.222 288  1.060 289  ,  .961 206-  65  TABLE Comparison  of Risk  XIII  and Return  Mean  *  Std. Deviation  C.V.*  .9%  4.7%  5.875  VSEM  1.7%  8.6%  6.014  In  TSEM.  of the returns  Yet with greater  returns  was  coefficient  place  also  Market  their  much  to  maximize risk  their  return  f o r a given  level  (p),then  folmula ratios  The r e l a t i v e  variation  by t h e l a r g e r  under  words  level  of return.  can borrow  The a c t u a l  consideration.  f o r both  portfolio  In other  of a ten year  i t i s possible  i n equilibrium which they  of risk  I f we  or lend  i s deemed  will  Substituting  attempt  o r minimize  assume t h a t i n  t h e two  interest rate  government  t o determine  markets.  pure  investors  a t the pure  t h e r e l a t i o n s h i p between  can change.  to the rate  that  f o r a given  of  interest  states  portfolio.  a l l investors  period  outperformed  r i s k i n e s s t h e VSEM  as evidenced  i n the market  equilibrium  equal  t h e VSEM  of returns.  greater  theory  money  be an e f f i c i e n t  portfolios  to absolute  variability  to  their  respect  generated,  of variation.  Capital will  of variation  terms  displayed of  Return  a n d TSEM  TSEM  coefficient  the  f o r VSEM  bond into  during the  rate  market was s e t the time  following  thereqard-to-variability  66  A  L  "  P  P  (f P A. P  =  average  P  =  actual  (f p  =  variability  where  The .1314 it  result  for  the  is  Table the  market  the  IPR  for  of  firms  in  the  the  Table  XII,  be  firms the  the  that  This  was  this  market  by  would  the  the  only  would  firms  have  TSEM and  dominant  cumulative row  and  lending  portfolio  the  felt  incur been at  such  were  these  an  time  not  the  In  to 68 This  index removed  inactive  period.  purchasing the  impact  their  from  firms  entire  until  their of  333.  firms.  investor,  losses  removed, the  to  with  289  number  securities  begin  throughout that  68  cumulative  delisted include  of  i t  with  the  the  compare  indices  concludes in  from  returns  represents  contains number  should  i n mind  occured  row  reader Both  monthly  numbers  rate  to  had  of  constant  were  be  view  the  borrowing  second  that  mandatory  portfolio If  or  would  rate  for  the  first  XII  fact  bankrupt  the  the  returns.  Table  impact  .1064  Generally  the  XIV  market  market  both  the  Table  done w i t h  period.  while  at  I t was  their  The  increased  monthly  went  on  market.  however,  index.  market  i n the  of  for  portfolio.  data  period  explained that  TSEM  return  interest  VSEM becomes  portfolio.  clarify  securities,  the  of  of  combining  presents  portfolio to  can  to  each  used  order  the  that  XIV  for  so  By  superior  pure  coefficient  VSEM.  i s apparent  and  is a  rate  end on  of the  delisting.  67  Subsequently i n the f o l l o w i n g month the market index would show a s i g n i f i c a n t improvement. unrealistic.  T h i s , i t was  f e l t , would be  TABLE XIV Cumulative Monthly Rates o f Return f o r Market March 1963 to February 1973 Months 6  Year  10  8  10  11  12  0.0 0  1.142 68  1.240 71  1.156 73  1.092 78  1.043 79  1.014 82  997 84  944 85  934 87  1.075 88  1.080 90  1.456 90  1. 337 92  1. 368 93  1.387 95  1.493 96  1.471 98  1.498 104  1.547 104  1.609 106  1.626 106  1.721 112  1.612 113  1.584 114  1.588 118  1.523 124  1.272 125  1.268 127  1.264 131  1.167 132  1.190 136  1.447 . 138  1.419 143  1.521 146  1.450 149  1.344 150  1.461 158  1.208 171  1.123 174  1.106 176  1.051 179  .981 181  .944 181  .876 185  .898 188  1.010 188  1.090 189  1.014 186  1.035 185  1.006 185  1.006 186  1.068 187  1.119 187  1.097 191  1.054 192  1.043 195  1.116 199  1.212 201  1.185 205  1.192 202  1.199 204  1.290 205  1.339 206  1.290 211  1.323 213  1.418 217  1.504 216  1.634 221  1.678 227  1.018 231  1.243 232  2.058 226  2.213 228  2.236 233  1.905 237  1.735 - 239  1.781 242  1.716 244  1.696 244  1.773 237  1.707 251  1.679 258  1.610 260  1.286 249  1.165 253  1.019 255  1.037 256  1.008 262  1.039 267  1.052 270  1.013 270  1.052 272  1.006 277  1.062 277  1.159 279  1.163 272  1.195 276  1.066 277  1.035 282  .957 285  992 286  947 287  . 816 292  .791 294  889 295  1.140 295  1.087 29 9  1.022 281  1.067 285  .990 305  .953 315  948 317  904 320  .781 322  .778 325  768 330  . 913 294  . 866 332  .893 333  69  R e l a t i o n s h i p Between the VSEM and The  cursory  examination g i v e n i n the p r e v i o u s  would i n d i c a t e that the simply  folklore.  TSEM  f o l k l o r e surrounding the VSEM i s  Contrary  r i s k i n e s s of the two  chapter  to what was  expected the  markets were q u i t e s i m i l a r .  relative  The  conclusion  to be drawn i s t h a t an i n v e s t o r on the average i s not much g r e a t e r r i s k by  assuming  i n v e s t i n g i n the VSEM versus the TSEM  r e l a t i v e to the r e t u r n s  generated.  In f a c t i f one  subscribes  to C a p i t a l Market Theory, w i t h the a b i l i t y t o borrow and  lend  funds at the r i s k f r e e r a t e , the i n v e s t o r c o u l d become more e f f i c i e n t by  i n v e s t i n g i n the VSEM.  This conclusion  i s based s o l e l y on the r e l a t i o n s h i p d i s -  p l a y e d between mean r e t u r n and and  does not c o n s i d e r  depth of the two  other  Lorie  d e v i a t i o n of  returns  f a c t o r s such as the breadth  markets and how  IMPLICATIONS FOR Hamilton and  standard  and  t h i s would e f f e c t m a r k e t a b i l i t y .  INVESTMENT MANAGEMENT (13)  s t a t e t h a t the most  general  i m p l i c a t i o n o f the e f f i c i e n t market h y p o t h e s i s i s t h a t most s e c u r i t y a n a l y s i s i s l o g i c a l l y incomplete and v a l u e l e s s . study centred reference  This  only on the b e h a v i o r of s e c u r i t y p r i c e s , without  to fundamental i n f o r m a t i o n .  The  conclusion  to  be  drawn from the s e r i e s o f t e s t s conducted i s t h a t p r i c e data i n i t s e l f w i l l not y i e l d s u f f i c i e n t i n f o r m a t i o n speculative p r o f i t s .  The  Technician  i s wasting h i s time.  be  i s t h a t he  to generate  i m p l i c a t i o n f o r the C h a r t i s t o r Patterns  found i n p r i c e changes, they can a l s o be  randomly generated s e r i e s of numbers, but  may  found i n a  they w i l l not  provide  70  sufficient Hamilton  information  (13),  Efficient  for p r e d i c t i v e purposes.  effectively  Market  summarize  the  Lorie  and  implication of  the  Theory:  "There i s a c u r i o u s paradox. In o r d e r f o r the h y p o t h e s i s t o be t r u e , i t i s n e c e s s a r y f o r many i n v e s t o r s to d i s b e l i e v e i t . That i s , market p r i c e s w i l l p r o m p t l y and f u l l y r e f l e c t what i s k n o w a b l e a b o u t t h e c o m p a n i e s whose s h a r e s are traded o n l y i f i n v e s t o r s seek to earn s u p e r i o r r e t u r n s , make c o n s c i e n t i o u s a n d c o m p e t e n t e f f o r t s t o l e a r n a b o u t t h e c o m p a n i e s whose s e c u r i t i e s a r e t r a d e d , and a n a l y z e r e l e v a n t i n f o r m a t i o n p r o m p t l y and p e r c e p t i v e l y . I f t h a t e f f o r t were abandoned, the e f f i c i e n c y of the market would deminish rapidly."  LIMITATIONS  Monthly  Data  Using in  the  rule  monthly  results  results  effectively investor could  daily the Runs  if  the  study.  subject  to  a l l of  have  been  created  observed  and  also  daily  to.  much  investor to changes  In  a  the  inherent  price  trading  Monthly  changes  signals,  the  weaknesses  filter  criticism.  earlier  initiate  of  particular,  Thus  for a l l of  given  number  serious  the  access  a  to  that buy  the  filter  earlier.  l a r g e r sample  would  an or  during  tests  data  sell,  month  have  Using  refined  size.  Tests This  and  this  hides  price  data  are  would  have  enabling  of  data  no the  study  attempt series  concentrated was  was  made t o random,  only  look  at  f o r both  on  the  the  total  number  positive  number of  and  runs  of  runs  expected,  negative  runs.  71  This  study  i s further  changes  were  changes  followed  was  of  not looked  the sign  that  much  this  limited at.  by large  i n that That  daily  of the successor  of this  additional  the sequence.of the  i s , were  large  price  changes  change.  I t was  research  daily  price  a n d i f so what felt,  was b e y o n d  however,  the scope  study.  AVENUES  OF F U R T H E R  RESEARCH  Seasonality The The  study  concentrated  correlation  to  s i x months  in  the data  prices Still  tests  there  upon  should  the results  months  when  Table stocks  t o make  indicates  that  t h e market  of  followed  Variation  o f up  decision.  whether  behave  there  information  Perhaps the year.  were  some  i n some p r e d i c t a b l e  f o r t h e combined  the ten year  results  period,  there  a heavy  were  Advances  and  Declines  M  A  M  J  J  A  S  D  100%  60  22  90  40  40  30  70 L 20  0 40  N  Advances  50  70  Declines  0%  40  77  10  60  60  70  30  80  60  50  30  F  J  some  concentration  XV  i n Market  fashion.  of a l l the  declines.  TABLE Seasonal  a period  t o one complete  appeared t o have  by  movements.  t o be s i g n i f i c a n t  upwards  might  over  m o n t h s when  over  not indicate  prices  price  a trading  lagged  would  i n t h e sample  advances  that  d i d not appear  been  stock XV  indicated  which  have  on s h o r t - r u n  72 The month o f January had a p o s i t i v e r e t u r n throughout the study,  f o l l o w e d by A p r i l with  90% o f the p r i c e changes  being p o s i t i v e and August and December with 70%.  These  t e n t a t i v e r e s u l t s would i n d i c a t e a s i g n i f i c a n t ' seasonal factor.  By the e l i m i n a t i o n o f c y c l i c a l s e c u l a r and i r r e g u l a r  f l u c t u a t i o n s a seasonal t h i s seasonal  index c o u l d be developed t o measure  impact upon the r e t u r n s .  D i s t r i b u t i o n o f P r i c e Changes The  p r e l i m i n a r y f i n d i n g s o f t h i s paper suggest t h a t  f u r t h e r r e s e a r c h i s needed i n a s s e s s i n g the d i s t r i b u t i o n o f p r i c e changes.  The r e s u l t s o f chapter  four i n d i c a t e t h a t  s e c u r i t y r e t u r n s a r e not s t a t i o n a r y over time. f a c t the case,  If this i s i n  i t becomes d i f f i c u l t t o assess the r i s k / r e w a r d  characteristics of individual s e c u r i t i e s .  However, i t c o u l d  be p o s s i b l e t o measure the r e l a t i o n s h i p i n d i v i d u a l have t o the market.  securities  We c o u l d measure t h e i r v o l a t i l i t y t o  the market, and d e s c r i b e t h e i r r i s k u s i n g the s l o p e . c o e f f i c i e n t . Mechanical T r a d i n g  Rules  Of the f o r t y - f i v e f i r m s t e s t e d , t h i r t y - f o u r s e c u r i t i e s performed the buy-and-hold p o r t f o l i o f o r some f i l t e r The  out-  size.  obvious problem, however, was t h a t there was no c o n s i s t e n c y  i n which f i l t e r was a p p r o p r i a t e .  Only f i v e stocks c o n s i s t e n t l y  out performed the buy-and-hold s t r a t e g y f o r a l l f i l t e r I f the o p p o s i t e o f what the f i l t e r  d i c t a t e d had been  i t might have been p o s s i b l e t o improve the r e s u l t s . study  i n t h i s area might uncover some c l u e s .  sizes.  followed, Further  Perhaps i n s t e a d  73  of measuring the percentage p r i c e change, a moving average o f the stock p r i c e changes c o u l d be used.  74  REFERENCES  1.  S i d n e y S. A l e x a n d e r . " P r i c e Movements i n S p e c u l a t i v e Markets: T r e n d s o r Random W a l k s . " I n d u s t r i a l Management R e v i e w , v o l . 2, n o . 2, (May 1 9 6 1 ) , p p . 7-26.  2.  . " P r i c e Movements i n S p e c u l a t i v e Markets: T r e n d s o r R a n d o m W a l k s . No. 2," p r i n t e d i n "The Random C h a r a c t e r o f S t o c k M a r k e t Prices." C a m b r i d g e , M.I.T., 1964.  3.  P. H. C o o t n e r , " S t o c k P r i c e s : Random V e r s u s S y s t e m a t i c C h a n g e s , " I n d u s t r i a l M a n a g e m e n t R e v i e w , v o l . 3, n o . 2, pp. 24-25, S p r i n g 1962.  4.  G e o r g e W. D o u g l a s . "Risk i n the E q u i t y Market: An Emperical A p p r a i s a l o f Market E f f i c i e n c y . " Unpublished P h . D. d i s s e r t a t i o n , Y a l e U n i v e r s i t y , 1967.  5.  E u g e n e F. Fama. " E f f i c i e n t C a p i t a l Markets: A Review o f T h e o r y and E m p e r i c a l Work," J o u r n a l o f F i n a n c e , v o l . 2 5 , n o . 2, (May 1 9 7 0 ) , p p . 383-417.  6. Journal  of  __. "The B e h a v i o r o f S t o c k M a r k e t Prices," B u s i n e s s , v o l . 38, ( J a n u a r y 1965), pp. 24-105.  7.  and M a r s h a l l Blume. " F i l t e r Rules and Stock Market T r a d i n g P r o f i t s , " Journal of Business, 39 ( S p e c i a l S u p p l e m e n t , J a n u a r y 1 9 6 6 ) , p p . 2 2 6 - 4 1 .  8.  Jack Clark F r a n c i s . "Investments: Analysis M c G r a w - H i l l Book Company; 1972, pp.537.  9.  Ibid.,  pp.  and  Management,"  554  10.  C. W. J . G r a n g e r a n d 0. M o r g e n s t e r n . "Spectral Analysis o f New Y o r k S t o c k M a r k e t P r i c e s , " K y k l o s , v o l . 16 (1963), pp. 1-27.  11.  M i c h a e l C. J e n s e n . "Risk, the P r i c i n g of C a p i t a l Assets, and the E v a l u a t i o n o f Investment P o r t f o l i o s , " Journal o f B u s i n e s s , v o l . 4 2 , n o . 2, ( A p r i l 1 9 6 9 ) , p p . 167-247.  12.  B e n j a m i n F. K i n g . "Market and I n d u s t r y F a c t o r s i n S t o c k P r i c e B e h a v i o r , " J o u r n a l o f B u s i n e s s , v o l . 39, (January 1966), pp. 139-190.  13.  J a m e s H. L o r i e , M a r y T. H a m i l t o n . T h e o r i e s a n d E v i d e n c e , " R i c h a r d D. I l l i n o i s , 1973, pp. 98.  "The S t o c k Market, I r w i n , I n c . , Homewood,  75  14.  B e n o i t Mandelbrot. "The V a r i a t i o n of C e r t a i n S p e c u l a t i v e P r i c e s , " J o u r n a l o f B u s i n e s s , v o l . 36, (October, 1963), pp. 394-419.  15.  A r n o l d B. Moore. "Some C h a r a c t e r i s t i c s o f Changes i n Common Stock P r i c e s , " i n Paul H. Cootner, The Random Character o f Stock Market P r i c e s , Canbridge, Mass., The M.I.T. P r e s s , 1964. pp. 139-61.  16.  M. F. M. Osborne. "Brownian Motion i n the Stock Market," Operations Research, v o l . 7, (March - A p r i l , 1959), pp. 145-73.  17.  Harry V. Roberts. "Stock Market P a t t e r n s and F i n a n c i a l Analysis: M e t h o d o l o g i c a l Suggestions," J o u r n a l o f Finance, v o l . 15, no. 1, (March 1959), pp. 1-10.  18.  W i l l i a m F. Sharpe. " P o r t f o l i o Theory and C a p i t a l Markets," New York, McGraw-Hill Book Co., 1970, pp. 82.  19.  I b i d . , pp.  83.  76  APPENDIX Firms Used In Study ATS  A r l i n g t o n S i l v e r Mines L t d .  BCC  Bethlehem Copper Corp. L t d .  BR  B r a l o r n e Can F e r Resources L t d .  BSM  Blue S t a r Mines L t d .  CCD  C a s s i a r C o n s o l i d a t e d Mines L t d .  CGQ  Cariboo Gold Quartz Mining Co. L t d .  CMNA  Coleman C o l l i e r i e s L t d . 'A'  COP  Coast Copper Co. L t d .  CPG  Copper Ridge Mines L t d .  CRI  Craigment Mines L t d .  CSR  C a s s i a r Asbestos Corp. L t d .  CST  C o n s o l i d a t e d Standard Mines L t d .  CYD  Croyden Mines L t d .  DVM  D o l l y Varden Mines L t d .  DVN  Dundee Mines L t d .  GDC  Granduc Mining Co. L t d .  GIM  Giant Mascot Mines L t d .  GRL  General Resources L t d .  GRV  Grandview Mines L t d .  JY  J e r s e y C o n s o l i d a t e d Mines L t d .  JRC  J e r i c h o Mines L t d .  LTL'A MM MTW  1  Lytton Minerals Ltd. M i n e r a l Mountain Mining Co. L t d .  . . . . . . Mt. Washington Copper Co. L t d .  77  NCR  New  NGD  Norgold  NIN  New  NOV  Northwest Ventures L t d .  NPM  New  PB  Pend  PDL  Placer  PEEL  Peel  Resources L t d .  PPT  Pine  Point  PSS  Peso  Silver  QUT  Quatsino  RHM  Rolling  RV  Reeves  MacDonald  SBC  Silbak  Premier Mines L t d .  SCH  Sileurian  SLO  Slocan  Ottawa  SRD  Silver  Ridge Mining  SS  Silver  Standard  TMX  Texmont  TR  Transcontinental  TRJ  Trojan  TWT  NEW  . . . .  Cronin  Babine Mines L t d .  Mines L t d .  Indian  Mines L t d .  Privateer Oreille  Mines L t d . Mines  and  Development  Metals  Co. L t d .  Ltd.  Mines L t d . Mines L t d .  Copper Hills  -  Gold  Copper  Mines L t d .  Mines L t d .  Mines L t d .  Chieftain  Mining  Co. L t d .  Mines L t d . Co. L t d .  Mines L t d .  Mines L t d . Resources L t d .  Consolidated  Torwest Resources  Mines L t d .  (1962) L t d .  VN  Vananda  Explorations Ltd.  WMI  Western  Mines L t d .  78  PROGRAM  Michigan  Terminal  TO RUN F I L T E R  System  Fortran  RULE  G(41336)  COMMON/A1/IFELT,CRRT, MRRT, R T T , P S E R C T , P F T , NUMLAG, NUMY, CONSNT, F E L T E R 1,XP (10),ITITLE(60,5) REAL F l ( 1 2 , l l ) , P ( 1 3 2 ) , R R ( 1 3 2 ) , R ( 1 3 2 , 2 ) , D O U B R R ( 1 2 , 1 1 ) R E A L RUN (132),DOUBRN(12,11),CRET(132),DOUBCR(12,11),E(3) REAL DCUMS(12,11),CUMSUM(132),COR(12),MRRK(132)DDMRRK(12,11) REAL LPROF,SPROF INTERGER YEAR (11),LASTY,JSTART/1/,NEG,POS,ZERO,RNEG,RPOS, *LASTR,RZERO,ICUM(132),DDICUM(12,11),ICORC(12) * SCC/9/,MRR/8/,CRR/7/,CRRM/2/,MRRM/3/,IMRK(132),DDIMRK(12,11), * N I ( 3 ) , N R ( 3 ) , R T / 4 / , P C R R , PMRR, P A G E L / 6 0 / , C O N S N T , T Y / 1 9 / , P F , P F T , *CRRT, MRRT, F E L T E R , F R / 1 / EQUIVALENCE (NEG,NI(1)),(ZERO,NI(2)),(POS,NI(3)), *(RNEG,NR(1)),(RXERO,NR(2)),(RPOS,NR(3)), *(EXPECT,E(1)),(ACTUAL,E(2)),(DTFF,E(3)) EQUIVALENCE (F1,P),(RR,DOUBRR),(RUN,DOUBRN),(CRET,DOUBCR), *(ICUM,DDICUM),(DCUMS,CUMSUM),(MRRK,DDMRRK),(IMRK,DDIMRK) LOGICAL*1 EOF/.FALSE./,MISS/.FALSE./,START,NEGONE,STAR/'*'/,BLK/' 1 V , *LOGM REAL * 8 FIRM(11) , L A S T F J / ' 9 9 9 ' / / B L A N K S / DATA R U N ( l ) / 0 . / , R R ( l ) / 0 . 0 / , C R E T ( 1 ) / 0 . 0 / DATA BBLOG/'BB'/,SSLOG/'S'/,BLOG/'B'/ 1  '/  C C PF=PFT C C READ ( T U , 2 4 ) NUMLAG FORMAT(12) DO 9 8 3 k = l , 5 READ(TU,333) (ITITLE(J,K),J=l,60) WRITE(0,444) (ITITLE(J,K),J=l,60) 444 FORMAT(' ' , 3 0 A 4 , / , I X , 3 0 A 4 ) 333 FORMAT(60A4) 983 CONTINUE IFELT=9 DO 1 4 2 k - 1 , F E L T E R KK=IFELT+K WRITE(KK,338)K,XP(K) 338 F O R M A T ( ' 1 * * * * F I L T E R R U L E S * * * * ' , 4 X , ' T Y P E = ',12,3X, *'PRECENTAGE = ' , F 9 . 4 , / / , *1X,'**FIRM ',8X,'PROFIT*,IX,'RETURN RATE',3X,'SHORT',IX, *3X,'LONG',3X,'START',2X,'FINISH',1X,'TOT..BOR', *2X,'.MIN.'',3X,-.MAX.',3X,'RANGE',1X,'#_BUYS',1X,'#_SELLS',/) 14 2 CONTINUE DO 10 1 = 1 , 1 0 0 0 WRITE(6,243) 243 FORMAT (1X.,131 (' = ') ) LASTY=-1  24  177  13 17 8  12 34 0 8 88 C  IF IF  (EOF) GOTO 9999 (1-1) 177,178,177 NUMY=NUMY+1 LASTY=YEAR(NUMY) LASTFJ=FIRM(NUMY) DO 13 K=l,12 Fl(K,1)=F1(K,NUMY) YEAR(1)=YEAR(NUMY) FIRM(1)=FIRM(NUMY) DO 11 J=JSTART,11 JKEEP=J FIRM(J)=BLANKS READ(5,12,END=340) (Fl(K,J),K=1,12),FIRM(J),YEAR(J) F0RMAT(12F6.3,A7,I1) GOTO 8 88 EOF=.TRUE• CONTINUE IF (J.EQ.l) GOTO 9 31 IF (LASTFJ.NE.FIRM(J).OR.ECF) GOTO 7  C HERE WE DETERMINE WHEN TO PROCESS THE CURRENT FIRM C . . 931 LASTY=YEAR.(J) LASTFJ=FIRM(J) 11 CONTINUE 7 JSTART=2 NUMY=JKEEP-1 IZ=NUMY*12-1 IZI=IZ+1 NSTAR=0 RRSUM=0 PF=PF+1 C C THE MINIMUM FELTER UNIT IS "IFELT"+1 C WRITE(6,413) FIRM(1),I 413 FORMAT( ***',A7,3X,'(',14,')') DO 415 K=l,120 IF(P(K).EQ.O.O) GOTO 415 KSTART=K GOTO 515 415 CONTINUE 515 DO 32 J=l,FELTER WRITE(6,242) 242 FORMAT(IX,100('*') ) NEGONE=.FALSE. ITYPE=1 BORROW =0.0 BUY = 0.0 IIS=0 IIB=0 TBOR=0.0 ORIG=0.0 LPROF=0.0 SPROF=0.0 1  80  430  290 291 C C WE C  241 292  C C C C C  293 C  TXMAX = P ( K S T A R T ) TXMIN = P ( K S T A R T ) IXX=IZ1 LOGM=BLK DO 31 K = K S T A R T , I Z I I F ( P ( K ) . G T . O . O ) GOTO 430 IZ.Z=K LOGM=STAR PLAST=0.0 GOTO 4 73 K1=K+1 I F ( P ( K ) .EQ.0.0) P ( K 1 ) = P ( K ) I F ( P ( K ) . G T . T X M A X ) TXMAX=P(K) I F ( P ( K ) . L T . T X M I N ) IXMIN = P ( K ) GOTO (291,292,293),ITYPE I F (P ( K ) - T X M I N ) / T X M I N . L T . X P (J).) GOTO GET HERE  I F WE  HAVE  300  BOUGHT.  IIB=IIB=1 BUYPR=P(K) ORIG=BUYPR BUY=BUYPR XMSOS=BUYPR WRITE(6,241) XP(J),BUT,BUYPR,BLOG,XMSOS,SPROF,TXMIN,TSMAX,BORROW,K 1START,K,ITYPE,IZl XMIN = P (K) XMAX=P(K) ITYPE = 2 FORMAT(1X,3F10.4,A2,5F10.4,4I10) GOTO 300 I F ( P ( K ) . G T . S M A X ) SMAX = P ( K ) I F ( ( S M A X - P ( K ) ) / X M A X . L T . X P ( J ) ) GOTO 300 IIS=IIS+1 G E T HERE I F WE A R E ABOUT TO S E L L , I N T H I S C A S E , WE BORROW SOME S T O C K AND AMOUNT  SELL  THE  EQUIVALENT  BORROW = P ( K ) SELLPR=P(K) LPROF=LPROF+SELLPR-BUYPR XMSOS=XMSOS-SELLPR BUY=0. WRITE(6,241) XP(J),BUY,SELLPR,SSLOG,XMSOS,LPROF,XMIN.XMAX,BORROW,K 1START,K,ITYPE,IZ1 XMAX = P ( K ) XMSOS=XMSOS+BORROW TBOR=TBOR+BORROW XMIN=P (K) ITYPE = 3 GOTO 300 I F ( P ( K ) .LT.XMIN) XMIN =P (K) I F ( ( P ( K ) - X M I N ) / X M I N . L E . X P ( J ) ) GOTO #))  81  C C C  GET THE  HERE I F WE BROKER FOR  A R E ABOUT TO BUY BACK AND L E N D I N G US SOME STOCK  REPAY  IIB=IIB+1 BUYPR=P(K) BUY=P(K) SPROF=SPROF+BORROW-BUYPR BORROW=0.0 W R I T E ( 6 , 2 4 1 ) XP ( J ) , BUY, BUYPR,.BBLOG , XMSOS, S P R O F , XMIN, XMAX, BORROW, KS 1TART,K,ITYPE,IZ1 XMIN=P (K) XMAX=P(K) ITYPE=2 300 CONTINUE 31 CONTINUE PLAST=P(IZ1) 4 73 TEMP=0. IZ1=IZZ IF(ITYPE.EQ.2)TEMP=PLAST-BUY PROFIT = TEMP+(LPROF+SPROF) FRR=0.0 I F ( O R I G . N E . 0 . 0 ) FRR=1.+PROFIT/ORIG RANGE=TXMAX=TXMIN KK=IFELT+J I F (PF.GT.PAGEL) CALL RESET(PF,KK,5) W R I T E ( K K , 1 4 3) L O G M , F I R M ( 1 ) , I , P R O F I T , F R R , S P R O F , L P R O F , O R I G , P L A S T , *TBOR,TXMIN,TXMAX,RANGE,IIB,IIS 14 3 FORMAT(IX,A1,A7, (',13,')',F8.3,IX,F9.3,IX,F9.3,IX,7(F7.3,IX),216) WRITE(6,642) FIRM(l),XP(J),PROFIT,XMSOS,BORROW,BUY,TXMIN,TXMAX,P(I 1Z1),LPROF,SPROF,FRR,ORIG,TBOR 642 F O R M A T ( I X , A 7 , ' P E R = ' , F 1 0 . 4 , P R O F I T = ' , F 1 0 . 4 , ' X M S O S = ' , F 1 0 . 4 , ' BORROW 1=',F10.4, BUY=', * F 1 0 . 4 , ' TXMIN='F10.4,' TXMAX= ,F10.4,/, F(IZl)= ,F10.4, *' L P R O F = ' , F 1 0 . 4 , SPROF=',F10.4, R A T E OF RETURN= ,F10.4, *' O R I G = ' , F 1 0 . 4 , ' T O T A L BORROWED = ' , F 1 0 . 4 ) 32 CONTINUE 10 CONTINUE 9 9 9 9 RETURN END 1  1  1  1  1  1  1  1  1  82  SUBROUTINE R E S E T ( I P A G E , I U N I T , I N D E X ) INTEGER FELTER,CONSNT,TSERC(60),TCUM(60),TRUNT(60),TMON(60) COMMON/A1/IFELT,IT(5),NUMLAG,MUMY,CONSNT,FELTER,XP(10),ITITLE(60.5 1) EQUIVALENCE(ITITLE(1,1),TCUM(1)), (ITITLE(1,2),TMON(l)), *(ITITLE(1,3),TRUNT(1)),(ITITLE(1,4),TSERC(1)) C C C C C C  THIS NEXT  SUBROUTINE TRSETS PAGE.  THE  PAGE  COUNTER AND  THEN  S K I P S TO  THE  GOTO ( 1 0 , 1 0 , 3 0 , 3 0 , 3 0 ) , I N D E X I P A G E = I T ( I N D E X ) + NUMY + CONSNT GOTO 100 30 IPAGE = IT(INDEX) + 1 100 CONTINUE GOTO ( 1 1 , 2 1 , 3 1 , 4 1 , 5 1 ) , I N D E X 11 WRITE(IUNIT,TCUM) GOTO 20 0 21 WRITE(IUNIT,TMON) GOTO 200 31 WRITE(IUNIT,TRUNT) GOTO 200 41 .! W R I T E ( I U N I T , T S E R C ) N U M L A G , ( K , K = l , N U M L A G ) GOTO 200 51 DO 142 K = l , F E L T E R KK=IFELT+K WRITE(KK,338)K,XP(K) 338 F O R M A T ( 1 * * * * F I L T E R R U L E S * * * * ,4X, T Y P E = ' , I 2 , 3 X , *'PERCENTAGE = ' , F 9 . 4 , / / , *1X,'**FIRM ',8X,'PROFIT',IX,'RETURN RATE',3X,'SHORT',IX, *3X,'Long',3C,'START',2X,'FINISH',IX,'TOT..BOR*, *2X,'.MIN.•,2X,'.MAX.',3X,'RANGE',1X,'#_BUYS',1X,'#_SELLS',/) 142 CONTINUE 200 CONTINUE WRITE(0,2)IPAGE,IUNIT,INDEX,IT(INDEX),CONSNT,NUMY 2 FORMAT(' ',6110) RETURN END  10  1  1  1  83  PROGRAM  TO  COMPUTE:  RUNS T E S T S , S E R I A L C O R R E L A T I O N C O E F F I C I E N T S , R A T E O F M A T R I C E S F O R MONTHLY AND C U M U L A T I V E R E T U R N S .  C C C C C C C C C C C C C  RETURN  T H I S PROGRAM P E R F O R M S A N A L Y S I S ON S T O C K Q U O T A T I O N S O V E R T H E P E R I O D O F S T U D Y ( A B O U T 10 y e a r s ) . A L T H O U G H T H E PROGRAM I S S I M P L E AND NOT TO B E T A K E N S E R I O U S L Y F O R T H E I N V E S T O R , I T DOES HOWEVER I L L U S T R A T E SOME IMPORTANT P O I N T S .  HERE  ARE  THE V A R I A B L E S USED  F1(i,j) P(K) RR(K)  IN THE  PROGRAM  T H E F I R M S S T O C K Q U O T E S F O R Y E A R J F O R MONTH I . T H E SAME A S A B O V E , B U T A S A L I N E A R A R R A Y . T H E R A T E S O F R E T U R N S , P I C K E D UP FROM P ( T + 1 ) / p ( t ) .  C  D O U B R R ( I , J ) . . . t h e r a t e s o f r e t u r n s a s a two d i m e n s i o n a l a r r a y .  C C C  FIRM(J) YEAR(J) CRET(K)  C  D O U B C R ( I , J ) . . . t h e cumulative r a t e s o f r e t u r n s a s a two  C C C C  NUMLAG COR(K) CUMSUM(K)  T H E NAME O F T H E F I R M A S READ W I T H T H E T H E YEAR OF T H E QUOTATIONS. T H E CUMULATIVE RATES OF RETURNS  YEAR  D I M E N S I O N A L ARRAY E Q U A L S T H R E E , F O R T O T A L NUMBER O F L A G S C O N S I D E R E D . 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 FOR T H E K'TH L A G . C U M U L A T I V E R A T E O F RETURN M A T R I X ( M A R K E T ) .  C  D C U M S ( I , J ) . . . . t h e same except i n two dimensions.  C C C C C C C C C C C C C C C C C C C C C C C  MRRMK(K) MONTHLY R A T E S O F R E T U R N S ( M A R K E T ) . D D M R M K ( I , J ) . . . S A M E A S A B O V E , E X C E P T I N TWO DIMENSIONS SCC SERIAL CORRELATION C O E F F I C I E N T S . MRR MONTHLY R A T E S O F R E T U R N S CRR CUMULATIVE RATES OF RETURNS. CRRM C U M U L A T I V E R A T E S O F R E T U R N S ON T H E M A R K E T . MRRM MONTHLY R A T E S O F R E T U R N S ON T H E M A R K E T . RT RUN T E S T S . FR F E L T E R OUTPUT UNIT. CWB COMPANY WENT B R O K E . TU T H E U N I T FROM WHICH T H E T I T L E S A R E R E A D . DEL T H E C O M P A N I E S D E L E T E D D U E TO BAD D A T A . SUMMRY A SUMMARY U N I T . DEBUG A DEBUGGING UNIT. PCRR L I N E / P A G E COUNTER FOR CUMULATIVE RATES O F RETURNS. PMRR L I N E / P A G E C O U N T E R F O R MONTHLY R A T E S O F R E T U R N S . PRTC L I N E / P A G E C O U N T E R F O R RUN T E S T S . PSERC L I N E / P A G E COUNTER FOR S E R I A L C O R R E L A T I O N . CONSNT R E Q U I R E D TO C A L C U L A T E T H E E X P E C T E D NUMBER O F L I N E S TO B E P R I N T E D F O R T H E C U M U L A T I V E AND MONTHLY R A T E S O F R E T U R N S . FELTER.. T H E NUMBER O F F E L T E R P E R C E N T A G E S . XP(10) THE F E L T E R PERCENTAGES.  U U U U U U U U U U U U LP LP LP LP  84  C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C  NI(3) NR(3) SUMNI ACTUAL E I (3)  TF TF TF TF TF  THE I N F L E C T I O N S ( - , 0 , + ) T H E RUNS (-,0, + ) . SUM OF T H E I N F L E C T I O N S . SUM O F T H E RUNS. T H E P E R C E N T A G E S OF T H E I N F L E C T I O N S (-,0,+). ER(3) T H E P E R C E N T A G E S OF T H E RUNS (-,0, + ) . TRUNT O B J E C T T I M E FORMAT (RUN T E S T S ) . TMON O B J E C T T I M E FORMAT (MONTHLY MARKET R E T U R N S ) . TCUM O B J E C T T I M E F O R M A T ( C U M U L A T I V E MARKET R E T U R N S ) . TSERC OBJECT TIME FORMAT(SERIAL CORRELATIONS). SKIPL(2) O B J E C T T I M E FORMAT. FOR S K I P P I N G L I N E . NUMTIT NUMBER OF T I T L E S FOR O B J E C T T I M E FORMAT. IBROKE COUNTER FOR COMPANIES T H A T WENT BROKE. IDEL COUNTER F O R COMPANIES D E L E T E D . KSTART T H E MONTH I N WHICH T H E F I R S T P R I C E A P P E A R E D . PS T A R T P (KSTART). PSTORE T H E V A L U E OF T H E L A S T NON M I S S I N G P R I C E . LOGICAL VALUES L O G B . . . . S E T TO S T A R FOR BROKE COMPANIES STAR "*" . BLK " ".  BLOCK  DATA  PSERT CRRT  T I T L E P A G E L E N G T H FOR S E R I A L C O R R E L A T I O N S . T H E T I T L E P A G E L E N G T H FOR C U M U L A T I V E R A T E S OF RETURNS. MRRT S I M I L A R FOR MONTHLY R A T E S OF RETURNS RTT T I T L E P A G E L E N G T H FOR T H E RUN T E S T S . CONSNT T H E OVERHEAD ON P R I N T I N G A F I R M S RETURN R A T E S . FELTER T H I S V A R I A B L E I S T H E NUMBER OF F E L T E R P E R C E N T A G E S T H A T WE A R E C O N S I D E R I N G . F E L T A ( I O ) . . . . T H I S I S AN ARRAY OF F E L T E R P E R C E N T A G E S . NUMLAG T H E # OF L A G S FOR S E R I A L C O R R E L A T I O N S .  INTEGER CRRT,RTT,CONSNT,FELTER,NUMLAG,PSERCT COMMON/P1/PAGEC(10),SKIPL(2) COMMON/A1/CRRT,MRRT,RTT,PSERCT,NUMLAG,NUMY,CONSNT,FELTER, 1 F E L T A (10 ) ,.ITITLE.(60,5) DATA CRRT/3/,MRRT/3/,RTT/6/,CONSNT/8/,FELTER/2/, *NUMLAG/3/,PSERCT/6/ DATA S K I P L / ' ( ' ' ''',')'/,FELTA/.005,.01,.02,.05,.25,.5/ END  85  C C C C C C C C  TITLE  INDEX  1) CUMMULATIVE R A T E OF R E T U R N S . 2) MONTHLY R A T E OF RETURNS 3) RUN T E S T S . 4) S E R I A L C O R R E L A T I O N C O E F F I C I E N T S . COMMON/P./PAGEC(10),SKIPL(2) COMMON/A1/CRRT,MRRT,RTT,PSERCT,NUMLAG,NUMY,CONSNT,FELTER, *XP(10),ITITLE(60,5) R E A L F l ( 1 2 , l l ) , P ( 1 3 2 ) , R R ( 1 3 2 ) , R ( 1 3 2 , 2 ) , D O U B R R ( 1 2 , 1 1 , ) , E I (3) ,ER * (3) , * RUN(132),DOUBRN(12,ll),CRET(132),DOUBCR(12,11),E(3) , * DCUMS(12,11),CUMSUM(132),COR(12),MRRK(132),DDMRRK(12,11), * RMEAN(12,11) INTEGER YEAR(11),JSTART/1/,NEG,POS,ZERO,RNEG,RPOS, * L A S T R , R Z E R O , I C U M ( 1 3 2 ) , D D I C U M ( 1 2 , 1 1 ) , I C O R C ( 1 2 ) , ONE/1/, * SCC/9/,MRR/8/,CRR/7/, CRRM/2/,MRRM/2/,IMRK(132),DDIMRK(12,11), *NI(3),NR(3),RT/4/,PCRR,PMRR,PAGEL/60/,CONSNT,CWB/1/,IDEL/0/, *CRRT,MRRT,RTT,FELTER,FR/1/,TU/19/,PSERC,PSERCT,DEBUG/0/,DEL/3/, * TRUNT(60),TMON(60),TCUM(60),TSERC(60),PAGEC,PRTC,SUMMRY/2/ EQUIVALENCE(ITITLE(1,1),TCUM(1)),(ITITLE(1,2),TMON(1)), *(ITITLE(1,3),TRUNT(1)),(ITITLE(1,4),TSERC(1)) LOGICAL*l EOF/.FALSE./,MISS/.GALSE./,START,NEGONE,FLOG(8), 1STAR/ * /,LOGB, *BLK/' / REAL*8 F I R M ( 1 1 ) , L A S T F J / ' 9 9 9 ' / , B L A N K S / '/ EQUIVALENCE ( N E G , N I ( 1 ) ) , (ZERO,NI(2)),(POS,NI(3)), *(RNEG,NR(1)), RZERO,NR(2)), RPOS,NR(3)), *(EXPECT,E(1)),(ACTUAL,E(2)),(DIFF,E(3)), *(FIRM(l),FLOG(l)), * (F1,P),(RR,DOUBRR),(RMEAN,RUN,DOUBRN),(CRET,DOUBCR), *(ICUM,DDICUM),(DCUMS,CUMSUM),(MRRK,DDMRRK),(IMRK,DDIMRK) DATA R U N ( 1 ) / 0 . / , R R ( 1 ) / 0 . 0 / , C R E T ( 1 ) / 0 . 0 / , I B R O K E / 0 / , P S T O R E / 0 . 0 / 1  1  1  1  C C C 555 24  444 333 9 83 798  984  HERE  WE  INITIALIZE  AS  WELL A S  READ  IN  TITLES.  WRITE(DEBUG,555) FORMAT('1****DEBUG UNIT****',///) R E A D ( T U , 2 4 ) NUMLAG FORMAT(12) DO 983 K = l , 4 READ(TU,333) (ITITLE(J,K),J=1,60) WRITE(DEBUG,444) (ITITLE(J,K),J=l,60) FORMAT( ',30A4,/,IX,30A4) FORMAT(60A4) CONTINUE DO 798 K = l , 1 0 PAGEC(K)=l DO 984 K = l , 1 2 1 IMRK(K)=0 MRRK(K)=0.0 ICUM(K)=0 CUMSUM(K) =0.0 ICUM(K) = 0 1  86  C C S E T T H E L I N E COUNTERS TO T H E T I T L E L E N G T H S , AND P A G E COUNTERS C TO 1. C PCRR=CRRT PMRR=MRRT P R T C = RTT PSERC=PSERCT C C C A F T E R T H E I N I T I A L I Z A T I O N , WE P R I N T OUT T H E T A B L E H E A D I N G S ON C T H E . V A R I O U S U N I T NUMBERS. C C WRITE(SCC,TSERC) ONE,NUMLAG,,(K,K=l,NUMLAG) WRITE(CWB,882) 882 FORMAT ('1***THE FOLLOWING COMPANIES WENT B R O K E * * * '",//, *'**FIRM**',12X,'MONTH ,4X,'YEAR',//) WRITE(DEL,8888) 8888 FORMAT. ('1***THE FOLLOWING COMPANIES WERE D E L E T E D FROM T H E 1SURVEY',//, *'**FIRM**',12X,'MONTHS I N STUDY',//) WRITE(MRR,TMON) ONE W R I T E ( C R R , T C U M ) ONE W R I T E ( R T , T R U N T ) ONE DO 10 1 = 1 , 1 0 0 0 LASTY=-1 I F ( E O F ) GOTO 9 9 9 9 I F (1-1) 177,178,177 177 NUMY=NUMY+1 LASTFJ=FIRM(JKEEP) DO 13 K = l , 1 2 13 F1(K,1)=F1(K,JKEEP) Y E A R (1 ):=YEAR ( J K E E P ) FIRM(1)=FIRM(JKEEP) 178 DO 1 1 J = J S T A R T , 1 1 JKEEP=J FIRM(J)=BLANKS READ(5,12,END=340) (Fl(K,J,K=1,12),FIRM(J),YEAR(J) 12 F0RMAT(12F6.3,A7,I1) GOTO 888 340 EOF=.TRUE. 888 CONTINUE I F ( J . E Q . l ) GOTO 9 3 1 I F ( L A S T F J . N E . F I R M ( J ) . O R . E O F ) GOTO 7 C C HERE WE D E T E R M I N E WHEN TO P R O C E S S T H E CURRENT F I R M . C 9 31 LASTFJ=FIRM(JKEEP) 11 CONTINUE 7 JSTART=2 NUMY=JKEEP-1 IZ=NUMY*12-1 IZ1=IZ+1 NSTAR=0 RRSUM=0 1  87  C C C C C C C C C C C C C C C C C C C  H E R E S T A R T WITH T H E R A T I O S C A L C U L A T E T H E RUNS.  T H E RUNS  I N THE P R I C E S A R E C A L C U L A T E D I N T H E FOLLOWING  WAY.  1. T H E F I R S T P O S I T I V E RUN I S NOT COUNTED, T H I S I S DUE TO T H E F A C T T H A T I F T H E STOCK OPENS I T ' S RUNNING VALUE I S MEANINGLESS I N THIS CASE. 2. C O N S E Q U E N T L Y , T H E RUN OF ZEROS B E F O R E T H E O P E N I N G OF T H E STOCK A R E NOT COUNTED. FURTHERMORE, T H E ZEROS I N T H E M I D D L E OF T H E S T O C K S L I F E ( M I S S I N G DATA) DO NOT COUNT A S P A R T O F A N E G A T I V E RUN, RATHER T H E Y COUNT A S A ZERO RUN.  RR(1)=0 MON=0 NEG=0 POS=0 ZERO=0 RNEG=0 RZERO=0 RPOS=0 IMISS=0 MISS=.TRUE. NEGONE=.FALSE. START=.FALSE. LOGB=BLK KSTART=-1 IF(P(K).EQ.0.0) DO 15 K = 1 , I Z IF(P(K).EQ.0.0) C C C 609  " R R " ( R A T E OF R E T U R N S ) , AND A L S O  FIND THE F I R S T  IMISS=IMISS+1 IMISS=IMISS+1  LISTING  K1=K+1 IF (P(K))  O F T H E STOCK  93,92,91 C C WE G E T HERE I F T H E COMPANY WENT BROKE. IN THIS CASE EVERYTHING C FROM HERE ON I N I S ZERO, AND WE BRANCH OUT OF T H E L O O P . C 93 I F ( N E G O N E ) GOTO 94 CALL GETMON(YEAR,K,IK,IMON,IYEAR) KWB=K WRITE(CWB,4 72) FIRM(l),I,IMON,IYEAR 4 72 FORMAT(4X,A7,IX,'(',14,')',4X,16,2X,16) IBROKE=IBROKE+l LOGB=STAR NEGONE = .TRUE. 94 DO 16 K I = K , I Z 1  88  16 1112 91  654 92  40  47  41 50  60  70  RUN(KI)=0.0 RR(KI+1)=0.0 CRET(KI+1)=0.0 P(KI)=0.0 DO 1 1 1 2 K K = k , 1 2 0 ICUM(KK)=ICUM(KK)+1 GOTO 1 5 1 I F ( P ( K 1 ) . L T . 0 . 0 ) GOTO 93 MON=MON+l I F ( P ( K ) . N E . 0 . 0 ) PSTORE=P(K) I F ( S T A R T ) GOTO 654 KSTART=K PSTART=P(K) START=.TRUE. RUN(K1) = ( P ( K 1 ) - P ( K ) ) I F ( . N O T . S T A R T ) GOTO 800 I F ( P ( K 1 ) . E Q . 0 . ) GOTO 4 7 I F ( K . E Q . K S T A R T ) GOTO 40 MISS=.FALSE. RUN(Kl) = P ( K 1 ) - PSTORE GOTO 41 PSTORE=P(K) MISS=.TRUE. GOTO 4 1 MISS=.TRUE. R U N ( K l ) = 0.0 GOTO 60 IF(RUN(K1)) 50,60,70 NEG=NEG+1 I F ( R U N ( K ) . G E . 0 . ) RNEG=RNEG+1 GOTO 80 ZERO=ZERO=l I F ( R U N ( K ) . N E . 0 . ) RZERO=RZERO+l GOTO 80 POS=POS+l I F ( R U N ( K ) . L E . 0 . ) RPOS=RPOS+l CONTINUE CONTINUE  80 800 C C C NOW F I G U R E T H E C U M U L A T I V E R A T E S OF RETURNS AND C R A T E S OF RETURNS C C I F ( K . N E . K S T A R T ) GOTO 15 3 RR(K) = 0 CRET(K) = 0 153 I F ( P ( K 1 ) . N E . 0 . 0 ) GOTO 702 R R ( K 1 ) = 1.0 CRET(Kl) = CRET(K) I F ( K . N E . S T A R T ) GOTO 7 0 1 RR(K1)=1. CRET(Kl)=l. GOTO 7 0 1 702 I F ( K S T A R T . E Q . - 1 ) GOTO 704  T H E MONTHLY  89  701  703  704 15 151 C C C C C C C C C C C C  533  R R ( K 1 ) = (P ( K D / P S T O R E CRET(Kl) = P(K1)/PSTART I F ( K S T A R T . E Q . - l ) GOTO 704 RRSUM=RRSUM+RR(Kl) NSTAR=NSTAR+1 I F ( K S T A R T . E Q . - l ) GOTO 704 CALL GETMON(YEAR,K,II,IK,IMON,IYEAR) I F ( C R E T ( K l ) . E Q . 0 . ) GOTO 70 3 CUMSUM(IK) = C R E T ( K l ) + C U M S U M ( I K ) ICUM(IK) = ICUM(IK) + 1 I F ( R R ( K 1 ) . E Q . 0 . 0 ) GOTO 704 IMRK(IK)=IMRK(IK)+1 MRRK(IK) = MRRK(IK) + R R ( K l ) ' CONTINUE CONTINUE I F ( K S T A R T . E Q . - l ) GOTO 4 09 2 RRMEAN=RRSUM/FLOAT(NSTAR)  HERE  WE  P R I N T OUT  THE  RESULTS  HERE WE P R I N T OUT T H E HEADINGS FOR T H E V A R I O U S F I L E D E S T I N A T I O N S . (MONTHLY R A T E S OF RETURNS ...MRR,CUMULATIVE R A T E S OF RETURNS..CRR) WE A L S O CHECK TO S E E I F WE N E E D TO R E S E T T H E P A G E S .  PCRR = NUMY + CONSNT + P C R R PMRR = NUMY + CONSNT + PMRR PRTC = 1 + PRTC PSERC = 1 + PSERC IF(PCRR.GT.PAGEL) CALL RESET(PCRR,CRR,1) I F ( P R T C . G T . P A G E D C A L L R E S E T ( P R T C , RT, 3) I F (PMRR. GT. P A G E D C A L L R E S E T (PMRR, MRR, 2 ) IF(PSERC.GT.PAGED CALL RESET(PSERC,SCC,4) WRITE(MRR,533) FIRM (1),I,LOGB,RRSUM,NSTAR,RRMEAN,IMISS,(K,K=1,12) WRITE(CRR,533) FIRM (1),I,LOGB,RRSUM,NSTAR,RRMEAN,IMISS,(K,K=1,12) F O R M A T ( I X , / , I X , * * , A 7 , * (' , 1 4 , A l , ') , 1 4 X , *'SUM(P(T+l)/P(T)) = ,F10.4,2X, ,N = ,15,2X,',MEAN= ,F10.5, *4X, ,MISSING=',13,/, *8X,'*',35X, MONTHS ' , 1 0 X , / , *8X,'*',/,lX,132('*'),/, *2X,' Y E A R ' , 1 X , ' * • , 1 2 ( 4 X , I 2 , 4 X ) , 3 X , , / , 8 X , ,123 ( ' - ' ) , ' * ' ) FORMAT ( 8 X , * , 3 5 X , ' MONTHS ',/,8X, * , / , I X , 1 3 2 ( ' * ' ) , / , *2X,' Y E A R ' , 1 X , * ' , 1 2 ( 4 X , I 2 , 4 X ) , 3 X , * ' , / , 8 X , ' * ' , 1 2 3 ( ' - ' ) - ' * ' ) WRITE(6,32) LASTFJ,NUMY,(K,K=1,12) FORMAT('-FIRM = * * * * , A 4 , * * * * NUMBER OF Y E A R S I N STUDY =',15,// * 8 X , ' * ' , 3 5 X , ' MONTHS ,/,8X,'*',/,IX,132( *'),/, *2X, ' YEAR' ,1X, ,12 ( 4 X , 1 2 , 4X) ,3X, '*' ,/,8X, '"*' ,123 ( ' - ' ) , ' * ' ) DO 1 3 1 K = l , 1 0 KKEEP=K IR=12 YEAR(K)=YEAR(K)+1 WRITE(MRR,231) Y E A R ( K ) , ( D O U B R R ( L , K ) , L = 1 , I R ) 1  1  1  1  1  1  1  1  1  532  1  1  1  1  32  1  1  1  1  1  90 231  FORMAT(4Z,12,2X, *' ,3(3(IX,F7.4,2X) ,'/') ,3(IX,F7.4,2X), '*') WRITE(CRR,231) YEAR(K),(DOUBCR(L,K),L=1,IR) 321 FORMAT(3X,12,3X, *',IX,12(IX,F7.4,2X) ,2X, *',/,8X,•*' ,123X, '*') C WRITE(6,31) YEAR(K), (Fl(L,K),L=l,IR) C WRITE(6,321) YEAR(K),(DOUBRN(L,K),L=l,IR) 31 FORMAT(3X,12,3X,'*',IX,12(IX,F7.4,2X) ,2X,'* ,/,8X, '*',123X,'* ) IF (K*12.GE.IZ) GOTO 132 131 CONTINUE 132 CONTINUE WRITE(MRR,54) WRITE(CRR,54) 54 FORMAT(8X,125('*') ) C WRITE(6,30) NSTAR,KKEEP,MON,RRSUM,RRMEAN,NEG,RNEG.ZERO,RZERO, C *POS,RPOS C30 FORMAT(IX,//,' NUMBER OF GOOD RATIOS IS "NSTAR",NSTAR=',13,', , C * I 5 , ' YEARS STUDIES,',2X,15, MONTH''S CONSIDERED.',//, C *1X,'SUM OF ( P(T+1)/P(T) ) = ',F12.5,3X,',MEAN SUM = ', C *F12.5,//,1X,'NUMBER OF RUNS ANALYSIS,',//, C *IX,'INFLECTIONS: NEGATIVE = ',15,4X,'RUNS: NEGATIVE',17,/, C *15X,'ZERO = ' ,110,15X, .'ZERO = ',18,/, C *15X,'POSITIVE = ',16,15X,'POSITIVE = ',14,//) C C C NOW COMPUTE THE- EXPECTED NUMBER OF RUNS ACCORDING TO THE C FORMULA. C C EXPECT = (N*(N+l)-SUM((NI.I** 2)) / N C C C ACTUAL = 0. SUMNIR = 0 SUMNI = 0 DO 205 K=l,3 SUMNI = SUMNI + NI(K) SUMNIR= SUMNIR+ NI(K)**2 205 ACTUAL = ACTUAL + NR(K) EXPECT = SUMNI + 1, - SUMNIR/SUMNI IF(ABS(SCTUAL).GE..0001)GOT0294 DIFF = 0 GOTO 295 294 DIFF= (EXPECT=ACTUAL)/ACTUAL 295 CONTINUE DO 5 K=l,3 E I ( K ) = NI(K)/SUMNI 5 ER(K) = NR(K)/ACTUAL C C C PRINT C C 1) RUN TEST UNIT=RT C C WRITE(RT,579) LOGB,FIRM(1),I,(E(K),K=1,3),(NI(K),EI(K),K=1,3), *(NR(K),ER(K),K=1,3) 1  1  1  1  1  1  1  91 579 C C C C  FORMAT (IX,Al,A7, (',14, )',IX,2(2X,F8.4,IX), *3X,3(IX,'/',1X,I3,]X,F4.2,1X),1X,'/'/3('/',IX,13,2X,F4.2,2X)) 1  NOW  111 271  113  110 C C C C C C C C C 697 4092 4093 10  WE START THE  1  CORRELATIONS  IF(NEGONE) IZ=KWB DO 110 LAG=1,NUMLAG ICORC(LAG)=0. COR(LAG)=0.0 IZ1=IZ=1-LAG IC=0 XR1=0.0 XR2=0.0 DO 111 K=2,IZ1 IF (RR(K)*RR(K+LAG).EQ.0.0) GOTO 111 IC=IC+1 R(IC,1)=RR(K) R(IC,2)=RR(K+LAG) XR1=XR1+RR(K) XR2=XR2+RR(K+LAG) CONTINUE IF (IC-1) 110,110,271 XRl=XRl/FLOAT(IC) XR2=XR2/FLOAT(IC) RS=0 RSQ1=0 RSQ2=0.0 DO 113 K-1,IC RK1=R(K,1)-XR1 RK2=R(K,2)-XR2 RS=RS+RK1*RK2 RSQ1=RSQ1+(RK 1**2) RSQ2=RSQ2+RK2**2 RRT=RSQ1*RSQ2 IF (RRT.NE.0.) COR(LAG) =RS/SQRT(RRT) ICORC(LAG) = IC CONTINUE HERE 1) -2) 3)  WE. PRINT SERIAL CORRELATION COEFFICIENTS MONTHLY RATES OF RETURNS CUMULATIVE RATES OF RETURNS  UNIT=SCC UNIT=CRR UNIT=CRR  WRITE(SCC,697) LOGB,FIRM(1),1,(COR(L),ICORC(L),L=1,NUMLAG) FORMAT(IX,A1,A7,' ( ,14, ') ',IX.7(IX,'/ ,IX,F7.4,2X,13,2X)) GOTO 10 WRITE(DEL,4093) FIRM(1),I,IZ1 FORMAT(' **',A7,' * ,14,') ,9X,13) IDEL=IDEL+1 CONTINUE 1  1  1  1  92  9999 9  1=1-1 WRITE(SUMMRY,9) I , I B R O K E , I D E L F O R M A T ( 1 ' , / / , 1 X , '****THE T O T A L NUMBER OF•FIRMS. S T U D I E S WAS', *l4 " * * * * * ' , / , I X . ' * * * * T H E NUMBER OF COMPANIES G O I N T B R O K E = ' , I 4 , * / , I X . ' * * * * T H E NUMBER OF COMPANIES D E L E T E D FROM T H E D A T A = ' , I 4 ) 1  f  C C C C C C C C 859  54 3  54 4  857  564  WE  GET HERE  WHEN WE  ARE  1) C U M U L A T I V E R A T E S 2) MONTHLY R A T E S OF  FINISHED.  WE  PRINT  OF RETURNS (MARKET) RETURNS (MARKET)  OUT: UNIT=CRRM UNIT=MRRM  WRITE (MRRM, 859). F O R M A T ( ' 1 ****MONTHLY R A T E S OF R E T U R N S ( M A R K E T ) * * * * ' , / / ) WRITE(MRRM,532) (K,K=1,12) CALL CALCU(DDIMRK,RMEAN) DO 544 K=.,10 WRITE(MRRM,543) K,(DDMRRK(L,K),L=1,12),(DDIMRK(L,K),L=1,12), *(RMEAN(L,K),L=1,12) FORMAT .(2X, 1 2 , 3X, ' * ' , I X . 12 ( 1 X , F 7 . 2 , 2X) , 2X, ' * • ,/., *8X, ' *•' ,1X,12 ( 3 X , I 5 , 2 X ) ,2X, ' *• , / , * 8 X , , 1 X , 1 2 ( 1 X , F 7 . 4 , 2 X ) , 2 X , • * ' , / , 8 X , ' * • , 1 2 3,'*') CONTINUE WRITE(MRRM,54) WRITE(CRRM,857) FORMAT('1****CUMULATIVE RATES OF RETURNS(MARKET)****',//) WRITE(CRRM,532) (K,K=1,12) C L A L CALCU(DCUMS,DDICUM,RMEAN) DO 564 K = l , 1 0 WRITE(CRRM,543) K,(DCUMS(L,K),L=1,12),(DDICUM(L,K),L=1,12), CONTINUE WRITE(CRRM,54) RETURN END  93 SUBROUTINE GETMON(YEAR,K,II,IK,IMON,IYEAR) C C C  THIS SUBROUTINE GETS THE MONTH AND YEAR GIVEN ANY K. INTEGER YEAR(10),IYEAR(1),IMON(l),11(1),IK(1) II(l)=MOD(K 12) I F ( I I (1) .EQ.O) II(1)=12 IMON(l)=II(l)+l IYEAR (10 = YEAR( ( (K-D/12+1) ) IK(l)=IMON(l)+IYEAR(l)*12 RETURN END f  94  12 10 11  SUBROUTINE CALCU(XX,IX,XMEAN) REAL XX(12,11),XMEAN(12,11) INTEGER IX(12,11) DO 11 K=l,10 DO 10 J=l,12 IF(IX(J,K=0.0 XMEAN(J,K=0.0 GOTO 10 XMEAN(J,K) = XX(J,K)/FLOAT(IX(J,K)) CONTINUE CONTINUE RETURN END  95  non  SUBROUTINE RESET(IPAGE,IUNIT,INDEX) INTEGER PAGEC,CONSNT,TSERC(60),TCUM(60),TRUNT(60),TMON(60) COMMON/A1/IT/(4),NUMLAG,NUMY,CONSNT,FELTER,XP(10),ITITLE(60,5) COMMON/P1/PAGEC(10),SKIPL(2) EQUIVALENCE(ITITLE(1,1),TCUM(1)),(ITITLE(1,2),TMON(l)), *(ITITLE(1,3),TRUNT(1)),(ITITLE(1,4),TSERC(1))  C c  THIS SUBROUTINE RESETS THE PAGE/LINE COUNTERS AND THEN TO THE NEXT PAGE. PAGEC(INDEX)=PAGEC(INDEX)=1  /-I  10 30 100 11 21 31 41 200 2  GOTO (10,10,30,30),INDEX IPAGE = IT(INDEX) + NUMY + CONSNT GOTO 100 IPAGE = IT(INDEX) + 1 CONTINUE GOTO (11,21,31,41),INDEX WRITE(IUNIT,TCUM) PAGEC(INDEX) GOTO 200 WRITE(IUNIT,TMON) PAGEC(INDEX) GOTO 200 WRITE(IUNIT,TRUNT) PAGEC(INDEX) GOTO 200 WRITE(IUNIT,TSERC) PAGEC(INDEX),NUMLAG,(K,K=l,NUMLAG) WRITE(IUNIT,SKIPL) CONTINUE WRITE (0,2)IPAGE,IUNIT,INDEX,IT(INDEX),CONSNT,NUMY FORMAT(' ***RESET ***',6I10) RETURN . END  

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