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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 WEAK FORM OF THE E F F I C I E N T MARKET. HYPOTHESIS AND ITS APPLICATION TO THE VANCOUVER LISTED MINING STOCKS by RICHARD BUIS B.B.A., U n i v e r s i t y o f O r e g o n , 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION "~~ i n t h e D e p a r t m e n t o f Commerce and B u s i n e s s A d m i n i s t r a t i o n We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA MAY, 1976 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree l y ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is for f i nanc ia l gain sha l l not be allowed without my wr i t ten permission. Department of The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date AJ/9Y7, /?76 i ABSTRACT The purpose of t h i s study was to test the hypothesis that security p r i c e changes for the L i s t e d Vancouver Mining Stocks conform to the weak form of the E f f i c i e n t Market Hypothesis. B r i e f l y stated t h i s hypothesis asserts that current prices f u l l y r e f l e c t the information implied by the h i s t o r i c a l sequence of pric e s . If such i s the case i t would not be possible for an investor to enhance his investment performance by studying previous successive price changes. In order to determine whether t h i s hypothesis i s applicable to the L i s t e d Vancouver Mining Stocks a series of tests were performed on the monthly pr i c e data for the period, March 1963 to February 1973. The method of investigation consisted of a number of seperate and d i s t i n c t experiments. I n i t i a l l y the monthly price changes were s e r i a l l y correlated for various differe n c i n g i n t e r v a l s to determine the degree of dependency i n the price changes. Following t h i s procedure, trend anal-y s i s was performed to measure the number of runs or patterns in the price changes and to compare these re s u l t s with what could be expected i f the series was random. The i n d i v i d u a l stocks were also subjected to a trading rule, refered to as f i l t e r i n g , to see i f a mechanical trading rule could out perform a buy and hold p o l i c y . F i n a l l y an analysis was performed to determine i f security price changes were i d e n t i c a l l y d i s t r i -buted and whether they were stationary over time. I n a l l c a s e s t h e r e a p p e a r e d t o b e l i t t l e d e p e n d e n c e i n p r i c e c h a n g e s . B o t h t h e s e r i a l c o r r e l a t i o n a n d r u n s t e s t s y i e l d e d r e s u l t s c o n s i s t e n t w i t h a r a n d o m w a l k t h e o r y . F i l t e r r u l e s a p p l i e d t o t h e d a t a g e n e r a t e d r e s u l t s v a s t l y i n f e r i o r t o t h e b u y a n d h o l d p o r t f o l i o s , s u g g e s t i n g t h a t o n c e a m o v e i s i n i t i a t e d t h e r e i s e v i d e n c e t o i n d i c a t e t h a t i t d o e s n o t n e c e s s a r i l y p e r s i s t . T h e d i s t r i b u t i o n o f p r i c e c h a n g e s t e n d e d n o t t o b e s t a t i o n a r y o v e r t i m e . W h e t h e r t h i s i m p l i e s s e c u r i t y r e t u r n s d o n o t c o n f o r m t o s o m e g i v e n p r o b a b i l i t y d i s t r i b u t i o n o r w h e t h e r t h e t i m e p e r i o d u n d e r s t u d y w a s u n r e p r e s e n t a t i v e w i l l r e q u i r e f u r t h e r s t u d y . T h e g e n e r a l c o n c l u s i o n t o b e d e r i v e d f r o m t h i s s t u d y i s t h a t p r i c e m o v e m e n t s o f t h e V a n c o u v e r L i s t e d M i n i n g S t o c k s c o n f o r m t o t h e w e a k f o r m o f t h e E f f i c i e n t M a r k e t H y p o t h e s i s . i i i TABLE OF CONTENTS Page LIST OF TABLES V Chapter 1 INTRODUCTION 1 Statement of Purpose 1 Need for the Research 2 Method of Research 7 Method of Analysis 9 Organization of Study 10 2 PREVIOUS CLOSELY RELATED RESEARCH 11 The Behaviour of Stock Market Prices by E. Fama 11 Price Movements i n Speculative Markets: Trends of Random Walks by Alexander . . . . 15 Additional Research by Alexander 17 Fama and Blume Study on F i l t e r Rules . . . . 20 3 METHOD OF RESEARCH 22 Data Used 22 S e r i a l Correlation 24 Runs Tests 25 Testing Independence with F i l t e r Rule . . . 27 Statio n a r i t y of Returns 30 i v C h a p t e r P a g e 4 FINDINGS 32 S e r i a l C o r r e l a t i o n 32 Runs T e s t s 39 F i l t e r T r a d i n g R u l e s 44 S t a t i o n a r i t y o f R e t u r n s 53 R i s k , a n d R e t u r n 58 5 INTERPRETATION OF NUMERICAL RESULTS 59 G e n e r a l S t a t e m e n t o f F i n d i n g s 59 I m p l i c a t i o n s f o r I n v e s t m e n t Management. . . . 69 L i m i t a t i o n s 70 Avenues o f F u r t h e r R e s e a r c h 71 REFERENCES 74 APPENDIX 7 6 L i s t o f F i r m s Used i n S t u d y 76 Computer Programs Used 7 8 V L I S T OF TABLES T a b l e ! Page I N o r t h A m e r i c a n T r a d i n g 5 I I M o n t h l y S e r i a l C o r r e l a t i o n f o r L a g s o f One T h r o u g h S i x Months 34 I I I S u m m a r i z a t i o n 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 C o e f f i c i e n t s 36 IV M o n t h l y 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 I n a c t i v e F i r m s . 37 V T o t a l A c t u a l and E x p e c t e d Numbers o f Runs f o r One - Month P e r i o d 41 V I T o t a l A c t u a l and E x p e c t e d Numbers o f Runs f o r One - Month P e r i o d f o r I n a c t i v e F i r m s 4 3 V I I S u m m a r i z a t i o n o f F i n d i n g s o f F i l t e r R u l e T e s t s . . . 46 V I I I F i l t e r T r a d i n g R u l e s as Compared t o a Buy and H o l d P o l i c y 4 8 IX R e t u r n s G e n e r a t e d f r o m S h o r t and L o n g P o s i t i o n s . . 51 X C o m p a r i s o n o f S h i f t Between Mean M o n t h l y R a t e o f R e t u r n and 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 & March 1968 t o F e b r u a r y 1973 . . . . 54 XI F i t t i n g a Normal C u r v e t o O b s e r v e d D a t a 56 X I I M o n t h l y R a t e s o f R e t u r n f o r t h e M a r k e t : March 1963 t o F e b r u a r y 1973; 64 X I I I C o m p a r i s o n s o f R i s k and R e t u r n f o r VSEM and TSEM 65 XIV C u m u l a t i v e M o n t h l y R a t e s o f R e t u r n f o r t h e M a r k e t : M a r c h 1963 t o F e b r u a r y 1973 68 XV S e a s o n a l V a r i a t i o n i n M a r k e t A d v a n c e s and D e c l i n e s 71 v i " I had two d o l l a r s and made one more someone s u g g e s t e d t h e VSE f o r e v e n more I f o l l o w e d h i s a d v i c e and t h o u g h t i t w o u l d s u f f i c e and now I f i n d I have no more." CHAPTER 1 INTRODUCTION STATEMENT OF PURPOSE The p u r p o s e o f t h i s s t u d y i s t o t e s t t h e h y p o t h e s i s t h a t s e c u r i t y p r i c e movements on t h e V a n c o u v e r S t o c k E x c h a n g e L i s t e d M i n i n g S e c t i o n c o n f o r m t o t h e weak f o r m o f t h e E f f i c i e n t M a r k e t H y p o t h e s i s . F u r t h e r m o r e , t h i s p a p e r w i l l a t t e m p t t o t e s t t h e h y p o t h e s i s t h a t t h e V a n c o u v e r S t o c k Exchange L i s t e d M i n i n g S e c t i o n i s a h i g h r i s k m a r k e t r e l a t i v e t o t h e T o r o n t o S t o c k E x c h a n g e . The d e f i n i t i o n o f t h e weak f o r m o f t h e E f f i c i e n t M a r k e t H y p o t h e s i s i s t h a t s u c c e s s i v e p r i c e c h a n g e s a r e i n d e p e n d e n t random v a r i a b l e s and t h a t t h e r e t u r n s a r e i d e n t i c a l l y d i s t r i b u t e d . S y m b o l i c a l l y , r a t e s o f r e t u r n a r e a m a r t i n g a l e i f E q . (1-1) i s n o t v i o l a t e d . E ( j R t + l l j V j R . t - l ' •-' i R t - n > = j R t where J R ^ - ~ r e t u r n f o r s e c u r i t y j a t p e r i o d t . E q u a t i o n (1-1) s t a t e s t h a t k n owledge o f h i s t o r i c a l r a t e s o f r e t u r n s u g g e s t o n l y t h a t t h e n e x t p e r i o d s r e t u r n w i l l e q u a l t h e l a s t p e r i o d s . S i n c e s e c u r i t y p r i c e s t e n d t o d r i f t upward o v e r t i m e t h e y i n e f f e c t r e p r e s e n t a s u b -m a r t i n g a l e p r o c e s s s u c h t h a t : E ( j P t + 1 j P t , JVt_ir • . - ., J P t _ n ) > J P t d - 2 ) where j P = p r i c e o f s e c u r i t y i n t i m e t . 2 T h r o u g h o u t t h e r e m a i n i n g p a p e r any r e f e r e n c e s t o t h e V a n c o u v e r S t o c k E x c h a n g e L i s t e d M i n i n g S e c t i o n w i l l be t h r o u g h t h e u s e o f t h e a b b r e v i a t e d f o r m VSEM. NEED FOR THE RESEARCH H y p o t h e s i s I T h e r e i s w i d e s p r e a d i n t e r e s t i n b o t h t h e a c a d e m i c and i n v e s t m e n t community w i t h r e s p e c t t o t h e E f f i c i e n t M a r k e t H y p o t h e s i s . S i m p l y s t a t e d t h i s h y p o t h e s i s e x p l a i n s t h a t c u r r e n t p r i c e s f u l l y r e f l e c t a l l a v a i l a b l e i n f o r m a t i o n w h i c h i m p l i e s t h a t s u p e r i o r i n v e s t m e n t r e s u l t s c a n n o t be o b t a i n e d c o n s i s t e n t l y s i m p l y by a n a l y z i n g e x i s t i n g i n f o r -m a t i o n . The c o n t r o v e r s y s t a r t e d i n 1959 when R o b e r t s ( 1 7 ) d e v e l o p e d a s e r i e s o f numbers c r e a t e d by c u m u l a t i n g random numbers w h i c h had t h e same v i s u a l a p p e a r a n c e as a t i m e s e r i e s o f s t o c k p r i c e s . He a l s o n o t e d t h a t t h e a c t u a l and s i m u l a t e d c h a n g e s i n w e e k l y s t o c k p r i c e s f o r a p e r i o d o f 52 weeks c o r r e s p o n d e d w i t h one a n o t h e r . Thus h i s work r a i s e d t e n a t i v e q u e s t i o n s as t o w h e t h e r s e c u r i t y p r i c e s i n .. f a c t d i d move i n a random f a s h i o n . F u r t h e r t e s t s by 0 s b o r n e ( 1 6 ) , M o o r e ( 1 5 ) , G r a n g e r and M o r g e n s t e r n (.10.) , p r o v i d e d a body o f e v i d e n c e t h a t s u g g e s t e d random movements i n s e c u r i t y p r i c e s . Some o f t h e more r e c e n t r e s e a r c h t h a t i s p a r t i c u l a r l y r e l e v e n t t o t h i s s t u d y w i l l be d i s c u s s e d i n g r e a t e r d e t a i l i n C h a p t e r 2. Most o f t h e e a r l y s t u d i e s on s t o c k p r i c e b e h a v i o r , were c o n c e r n e d w i t h t h e randomness o f p r i c e c h a n g e s and were a c c u m u l a t e d u n d e r t h e h e a d i n g o f t h e Random Walk T h e o r y . T h i s t h e o r y h a s s u b s e q u e n t l y become known as t h e Weak Form o f t h e E f f i c i e n t M a r k e t H y p o t h e s i s . A random w a l k i m p l i e s e f f i c i e n c y , however, a n e f f i c i e n t m a r k e t does n o t n e c e s s a r i l y mean t h a t s t o c k p r i c e s , ( o r r e t u r n s ) , move randomly.(5) The random w a l k t h e o r y assumes t h a t s u c c e s s i v e p r i c e c h a n g e s a r e i n d e p e n d e n t and t h a t t h e r e t u r n s a r e i d e n t i c a l l y d i s t r i b u t e d , s u c h t h a t : f ( J R t + 1 J R t - i ' • • • •» J R t _ n ) = f ( J R t ) d - 3 ) Where f (jR^_) = t h e p r o b a b i l i t y d i s t r i b u t i o n o f r e t u r n s f o r s e c u r i t y j a t p e r i o d t . The above e q u a t i o n i s n o t e x a c t l y t r u e i n t h a t s e c u r i t y p r i c e s a r e n o t i n d e p e n d e n t , o n l y n e a r l y s o . However, t h i s does n o t c o n f l i c t w i t h t h e e f f i c i e n t m a r k e t h y p o t h e s i s . The weak f o r m h y p o t h e s i s e f f e c t i v e l y s a y s t h a t h i s t o r i c a l p r i c e and volume d a t a f o r s e c u r i t i e s c o n t a i n no i n f o r m a t i o n w h i c h c a n be u s e d t o e a r n a t r a d i n g p r o f i t a b o v e what c o u l d be a t t a i n e d w i t h a n a i v e buy - and - h o l d i n v e s t m e n t s t r a t e g y . ( 8 ) The s e m i s t r o n g e f f i c i e n t m a r k e t h y p o t h e s i s s t a t e s t h a t m a r k e t s a r e e f f i c i e n t enough t h a t p r i c e s r e f l e c t a l l p u b l i c l y a v a i l a b l e i n f o r m a t i o n so t h a t o n l y a few i n s i d e r s c a n e a r n a p r o f i t w h i c h e x c e e d s what c o u l d be e a r n e d u s i n g a n a i v e buy - and - h o l d p o l i c y by t r a d i n g on s h o r t r u n p r i c e c h a n g e s . The s t r o n g l y e f f i c i e n t m a r k e t h y p o t h e s i s c l a i m s t h a t no one c a n c o n s i s t e n t l y e a r n a 4 p r o f i t o v e r what c o u l d be e a r n e d u s i n g a n a i v e buy - and -h o l d s t r a t e g y by t r a d i n g o n s h o r t r u n s e c u r i t y p r i c e movements b e c a u s e s e c u r i t y p r i c e c h a n g e s a r e i n d e p e n d e n t random v a r i a b l e s a n d no one h a s m o n o p o l i s t i c a c c e s s t o v a l u a b l e i n s i d e i n f o r m a t i o n . A g r e a t d e a l o f i n f o r m a t i o n has a c c u m u l a t e d o v e r t h e p a s t d e c a d e w i t h r e s p e c t t o t h e weak f o r m h y p o t h e s i s , however, most o f t h e s t u d i e s have been c o n d u c t e d on t h e New Y o r k S t o c k E x c h a n g e , (NYSE), w i t h r e l a t i v e l y c o n s i s t e n t r e s u l t s . P r i c e movements were s u b j e c t e d t o r i g o r o u s s c i e n t i f i c a n a l y s i s w i t h t h e r e s u l t b e i n g t h a t t h e weak f o r m h y p o t h e s i s i s g e n e r a l l y a c c e p t e d . T a b l e 1-1 i n d i c a t e s t h a t i n t e r m s o f t h e v a l u e o f t h e s h a r e s l i s t e d , t h e VSE i s e q u i v a l e n t t o .3% o f .the v a l u e o f s h a r e s l i s t e d on t h e NYSE, and i n t e r m s o f t h e number o f s h a r e s t r a d e d t h e VSE d i d a p p r o x i m a t e l y 13.5% o f t h e volume o f t r a n s a c t i o n s h a n d l e d by t h e NYSE. T h e s e two o b s e r v a t i o n s a l o n e w o u l d q u e s t i o n t h e v a l i d i t y t h a t t h e same c o n c l u s i o n s drawn f r o m s t u d i e s on t h e NYSE c o u l d be a p p l i e d w i t h o u t r e s e r v a t i o n t o t h e VSE. F u r t h e r -more, t h e l i s t i n g r e q u i r e m e n t s f o r t h e two e x c h a n g e s v a r y w i t h r e s p e c t t o t h e s i z e and f i n a n c i a l s t a t u s n e e d e d i n o r d e r t o be l i s t e d . Hence t h e t y p e o f s e c u r i t i e s b e i n g t r a d e d a r e s i g n i f i c a n t l y d i f f e r e n t f r o m t h o s e t r a d i n g on t h e NYSE as e v i d e n c e d by t h e h i g h , p r o p o r t i o n o f 'penny s t o c k s ' l i s t e d o n t h e VSE. TABLE 1 NORTH AMERICAN TRADING Excha n g e V a l u e S h a r e s (000) (000) 1973 1972 1973 1972 New Y o r k S t o c k E x c h a n g e $146 ,793, 295 160,177,580 4,375,224 4 ,593,889 A m e r i c a n S t o c k Exchange 11 ,007, 241 21,379,253 815,893 1 ,188,062 M i d w e s t S t o c k E x c h a n g e 8 ,131, 369 8,434,019 241,523 230,642 The T o r o n t o S t o c k E x c h a n g e 6 ,737, 076 6,258,153 663,856 635,886 P a c i f i c C o a s t S t o c k E x c h a n g e 6 ,359, 460 8,126,060 214,804 269,202 PBW S t o c k E x c h a n g e 4 ,394, 916 5,282,478 128,182 144 ,496 M o n t r e a l & C a n a d i a n S t o c k E x c h a n g e 2 ,173, 992 2,057,294 296,475 330,125 B o s t o n S t o c k Exchange 1 ,793, 047 1,562,882 42,193 38,605 V a n c o u v e r S t o c k Exchange 483, 271 784,103 592,745 906,053 D e t r o i t S t o c k E x c h a n g e 380, 588 362,790 10,686 9,844 C i n c i n n a t i S t o c k Exchange 118, 849 103,445 2,838 2,354 N a t i o n a l S t o c k Exchange 23, 952 112,448 7,530 15,912 C a l g a r y S t o c k E x c h a n g e 7, 123 6,493 10,215 12,208 Spokane S t o c k Exchange 6, 685 4,498 13,031 9,258 H o n o l u l u S t o c k Exchange 1, 897 3,990 260 565 I n t e r m o u n t a i n S t o c k E x c h a n g e 996 2,326 2,262 3,841 W i n n i p e g S t o c k E x c h a n g e 613 840 1,458 521 T o t a l s 188 ,414, 372 214,658,650 7,419,176 8 ,391,474 S o u r c e : 1973 Review, The T o r o n t o S t o c k Exchange 6 H y p o t h e s i s I I The VSE has h i s t o r i c a l l y d e v e l o p e d a f o l k l o r e o f b e i n g a h i g h r i s k m a r k e t , p a r t i c u l a r l y w i t h r e f e r e n c e t o t h e m i n i n g s e c u r i t i e s . T h i s p a p e r w i l l e i t h e r c o n f i r m o r deny t h e t r u t h i n t h e rumor by c o m p a r i n g t h e VSEM t o t h e T o r o n t o S t o c k E x c h a n g e , ( T S E ) . S i n c e most i n v e s t o r s a r e a d v e r s e t o r i s k i t i s r e a s o n a b l e t o s t a t e t h a t h i g h r i s k i n v e s t m e n t s a r e u n d e r t a k e n w i t h t h e e x p e c t a t i o n o f h i g h r e t u r n s . S t u d i e s were u n d e r t a k e n by D o u g l a s ( 4 ) where he e xamined t h e a n n u a l r e t u r n s o f a sample o f 616 s t o c k s between 1946 and 1963. The r e s u l t s i n d i c a t e d t h a t t h e r e was a h i g h d e g r e e o f p o s i t i v e c o r r e l a t i o n between t h e s t o c k r e t u r n s and t h e amount o f v a r i a t i o n i t d i s p l a y e d . On t h e a v e r a g e i t was shown t h a t i n v e s t o r s e a r n e d a h i g h e r r e t u r n by i n v e s t i n g i n h i g h r i s k s t o c k s t h a n i f t h e y h a d i n v e s t e d i n . low r i s k s e c u r i t i e s . F o r c o m b i n a t i o n s o f s e c u r i t i e s , ( p o r t f o l i o s ) , i t has b een f o u n d by J e n s e n ( 1 1 ) t h r o u g h t h e s t u d y o f m u t u a l f u n d s , t h a t f u n d s w i t h g r e a t e r r i s k as m e a s u r e d by t h e i r b e t a c o e f f i c i e n t s ( s y s t e m a t i c r i s k ) , w i t h t h e m a r k e t , had h i g h e r r e t u r n s t h a n f u n d s w i t h l e s s r i s k . I f we a l l o w a n i n v e s t o r t o i n v e s t o n l y i n t h e l i s t e d m i n i n g s e c u r i t i e s t h e n t h i s a v a i l a b l e l i s t o f s e c u r i t i e s r e p r e s e n t s h i s u n i v e r s e o f i n v e s t m e n t o p p o r t u n i t y . Hence, i f he were t o buy a l l t h e m i n i n g s t o c k s l i s t e d he has p l a c e d a l l h i s f u n d s a t r i s k . "The o p t i m a l c o m b i n a t i o n o f r i s k y s e c u r i t i e s i s t h a t e x i s t i n g i n t h e m a r k e t " ( 1 8 ) . I f one c o u l d assume t h a t m u t u a l f u n d s were e f f i c i e n t p o r t f o l i o s , 7 t h e r e t u r n s w o u l d a l s o be a l i n e a r f u n c t i o n o f t h e s t a n d a r d d e v i a t i o n . ( 1 9 ) T h e r e f o r e , t o t e s t t h e s e c o n d h y p o t h e s i s t h a t t h e VSEM i s a h i g h r i s k m a r k e t t h i s p a p e r w i l l compare t h e r e t u r n s g e n e r a t e d by t h e VSEM and t h e i r v a r i a b i l i t y , a s m e a s u r e d by t h e s t a n d a r d d e v i a t i o n , w i t h t h e r e t u r n s e a r n e d on t h e TSE. I n an e f f i c i e n t m a r k e t t h e r e s u l t s s h o u l d i n d i c a t e t h a t i f t h e VSEM i s a h i g h r i s k m a r k e t i t s h o u l d be c o m p e n s a t e d f o r by a v e r a g e h i g h e r r e t u r n s r e l a t i v e t o t h e TSE. METHOD OF RESEARCH D a t a U s e d The b a s i c d a t a u s e d f o r t h e a n a l y s i s i n t h i s s t u d y was s u p p l i e d by R o n a l d D. S. P o u l i e r , a f o r m e r g r a d u a t e s t u d e n t a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . M o n t h l y d a t a on t h e c l o s i n g p r i c e was c o l l e c t e d f o r a 10 y e a r p e r i o d f r o m M a r c h 1963 t o F e b r u a r y 1973. T h i s c l o s i n g p r i c e was o b t a i n e d f r o m t h e l a s t weekend summary o f t h e month as r e c o r d e d i n 'The P r o v i n c e ' n ewspaper. I f a p r i c e was n o t c o n t a i n e d i n t h i s summary, e a c h o f t h e p r e c e d i n g summaries were s u c c e s s i v e l y e x a m i n e d f o r a c l o s i n g p r i c e . I f a s i n g l e m o n t h l y p r i c e was q u o t e d i n t h e V.S.E. Review, w h i c h was u s e d as a c r o s s r e f e r e n c e , i t was u s e d . Any d i s -c r e p e n c i e s between t h e V.S.E. Review and t h e w e e k l y summary were r e s o l v e d by c h e c k i n g d a i l y s a l e s . 8 The d a t a c o n s i s t e d o f 425 co m p a n i e s i n t o t a l . However, some c l a r i f y i n g comments a r e n e e d e d . A l t h o u g h t h e l i s t o f company names e q u a l s 425 many o f t h e s e were i n f a c t t h e same company. O v e r 100 o f t h e co m p a n i e s i n t h e e a r l i e r p e r i o d s o f t h e s t u d y s u b s e q u e n t l y c h a n g e d t h e i r names v i a a c o n s o l -i d a t i o n . I n some i n s t a n c e s a change o f name o c c u r e d a s many as s i x t i m e s d u r i n g t h e t e n y e a r p e r i o d . I f a company c h a n g e d i t s t i c k e r t a p e symbol i t was t r e a t e d as a new company t o f a c i l i t a t e t h e c o m p u t a t i o n o f t h e ' i n v e s t m e n t p e r f o r m a n c e r e l a t i v e ' , (IPR).- Hence e a c h s t o c k was c h e c k e d t o i n s u r e t h a t i t i n f a c t d i d c h a n g e names and was t h e r e f o r e , t r a d i n g . I f a company was s u s p e n d e d o r d e l i s t e d and had n o t b e e n r e i n s t a t e d w i t h i n t h e p e r i o d s t u d i e d t h e r a t e o f r e t u r n was s e t e q u a l t o -100% a t t h e t i m e o f d e l i s t i n g . I t a p p e a r e d more r e a s o n a b l e t o assume t h a t an i n v e s t o r w o u l d l o s e h i s i n v e s t m e n t r a t h e r t h a n t o assume t h a t t h e l a s t p r i c e r e c o r d e d b e f o r e a s u s p e n s i o n o r d e l i s t i n g was t h e p r i c e a t w h i c h t h e i n v e s t o r s o l d . F o r months i n w h i c h a s e c u r i t y d i d n o t t r a d e no IPR was computed, as i t i s i m p o s s i b l e t o assume what t h e v a l u e o f a s e c u r i t y w o u l d be when t h e r e i s no m a r k e t f o r i t . A d d i t i o n a l I n f o r m a t i o n 1. A l l s e c u r i t i e s were g i v e n e q u a l w e i g h t s i n c o m p u t i n g m a r k e t movements. T h a t i s e q u a l w e i g h t s were a s s i g n e d t o e q u a l r e l a t i v e p r i c e c h a n g e s . 2. A l l s e c u r i t i e s were a d j u s t e d f o r s t o c k s p l i t s a n d s t o c k d i v i d e n d s . 9 3. P r i c e s were n o t r e s t r i c t e d t o r o u n d l o t p r i c e s a s some s t o c k s t r a d e d o n l y i n odd l o t s f o r e x t e n d e d p e r i o d s o f t i m e . 4. N e i t h e r t r a n s a c t i o n c o s t s n o r t a x e s a r e a c c o u n t e d f o r i n t h i s s t u d y . 5. D i v i d e n d s were e x c l u d e d f r o m t h e s t u d y . Most m i n i n g c o m p a n i e s do n o t g i v e d i v i d e n d s a s c a p i t a l i s r e t a i n e d f o r f u t u r e h i g h c o s t e x p l o r a t i o n . Many co m p a n i e s g i v e s t o c k d i v i d e n d s b u t t h i s h as been a c c o u n t e d f o r i n (2) a b o v e . METHOD OF ANALYSIS The method o f a n a l y s i s i s d e t a i l e d i n C h a p t e r 3 and i s o n l y b r i e f l y summarized h e r e . Computer programmes were w r i t t e n , ( d e t a i l e d i n a p p e n d i x ) , t o compute t h e r a t e o f r e t u r n p e r month f o r a l l . c o m p a n i e s i n t h e d a t a a s w e l l as t h e c u m u l a t i v e r e t u r n f o r e a c h s e c u r i t y . R a t e s o f r e t u r n were d e v e l o p e d f o r t h e VSEM a s s u m i n g e q u a l d o l l a r i n v e s t m e n t i n e a c h s e c u r i t y . The r e t u r n s on t h e VSEM were a l s o done on a c u m u l a t i v e b a s i s . The p r i c e c h a n g e s were t h e n s u b j e c t e d t o a number o f r i g o r o u s t e s t s t o d e t e r m i n e w h e t h e r t h e r e were any p r i c e d e p e n d e n c i e s . A programme was w r i t t e n t o compute t h e 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 p r i c e c h a n g e s o f one month w i t h l a g s o f one t o s i x months. A programme was a l s o w r i t t e n t o t e s t t h e number o f r u n s i n p r i c e c h a n g e s t o d e t e c t t h e p r e s e n c e o f o c c a s i o n a l non-random t r e n d s i n a s e r i e s o f p r i c e s . The 10 . number of runs observed were compared with the number of runs that would be expected from a sequence of t r u l y random numbers. F i n a l l y , since i t has been argued that these tests are not accurate enough to pick up s e n s i t i v e price movements, f i l t e r tests were conducted on the data for f i l t e r s ranging from .5% to 50%. ORGANIZATION OF THE STUDY The r e s u l t s of t h i s study are rather extensive i n that 425 stocks were observed, therefore, t h i s report presents only the summaries of the findings rather than the entire d e t a i l of the findings. Chapter Two presents a summary of some of the c l o s e l y related empirical research performed i n t h i s area. Chapter Three presents the detailed methodology used i n the research and the rationale underlying i t . Chapter Four presents the summarized findings of the research and Chapter Five comments on the influences, i m p l i -cations, and possible explanations of the findings. The l i m i t a t i o n s of the study as well as avenues for further research are also included i n Chapter.Five. CHAPTER 2 PREVIOUS CLOSELY RELATED RESEARCH THE BEHAVIOR OF STOCK MARKET PRICES(6) Professor Fama studies i n t h i s paper the theory of random walks i n security prices which i s based on the hypothesis that 1. Successive price changes are independent, and, 2. the price changes conform to some p r o b a b i l i t y d i s t r i b u t i o n . 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 for the price changes during time period t i s independent of the sequence of price changes during previous time periods. Fama goes to great lengths to show i n t u i t i v e l y how the random walk theory i s consistent with r e a l i t y . That i s , how the presence of sophisticated traders who can ascertain i n t r i n s i c values i n s e c u r i t i e s help to cause prices to move independently of t h e i r previous pr i c e . The implication of the Random Walk Hypothesis i s that the actions of the tech-nicians are f r u i t l e s s and that should there be discernable price patterns that may e x i s t , t h e i r actions c o l l e c t i v e l y would eliminate these price patterns. Likewise, for the fundamentalist, unless he can consistently, i n t e r p r e t new information i n such a manner as to earn higher p r o f i t s , his e f f o r t s w i l l also y i e l d him no more or no less than what the market i n general earns. 12 Tests for Independence A. S e r i a l Correlation Data - Dow Jones Ind u s t r i a l Averages -(end of 1957 to Sept. 26, 1962) 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 for d a i l y changes i n log prices were computed for each stock for lag 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 small (largest was .123) 2. Eleven c o e f f i c i e n t s for a lag of t = 1 were more than twice t h e i r standard error. However, i n most cases a c o e f f i c i e n t as small as .06 was more than twice i t s standard error. B. C o e f f i c i e n t s for 4, 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 small. 2. 23 out of 30 c o e f f i c i e n t s for d a i l y changes were po s i t i v e . 3. 21 and 24 c o e f f i c i e n t s for 4 day and 9 day differences were negative. Conclusions: There were no material dependencies i n price changes. The high degree of p o s i t i v e and negative signs for various series i s accounted for by the market influences(12) and i s not s u f f i c i e n t enough to imply the existence of p o r t f o l i o trading rules. C. Runs Tests Fama found the percentage difference between the actual and expected number of runs were quite small, i n d i c a t i n g l i t t dependence. S i m i l a r l y the difference between the actual and expected number of runs of a c e r t a i n sign are a l l very small. In addition there seems to be no important patterns i n the signs of the differences. For a l l the stocks, the expected and the actual d i s t r i b u t i o n s of runs by length turn 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 Price Changes Much of the current l i t e r a t u r e has suggested that the relevant d i s t r i b u t i o n of price changes i s Normal. This means that the d i s t r i b u t i o n i s rather f l a t i n the middle and has r e l a t i v e l y thin t a l e s . Fama argues, on the basis of emperical evidence and on t h e o r e t i c a l grounds, that 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 price changes conform better to a stable Paretian D i s t r i b u t i o n i n which there i s i n f i n i t e variance. Unlike Normal, where two parameters, (mean and standard deviation), f u l l y specify the d i s t r i b u t i o n , four parameters f u l l y specify a stable Paretian D i s t r i b u t i o n . c*. = measures height of extreme t a i l s , (<*- < 2 d i s t r i b u t i o n i s non-normal) ft = index of skewness £ = location parameter *y = defines the scale of a stable Paratian d i s t r i b u t i o n . For purposes of p o r t f o l i o analysis, a key property of stable Paretian d i s t r i b u t i o n s i s s t a b i l i t y . This means that: , 14 the values of the paremeters oc and remain constant under addition. Tests for Dispersion Frequency d i s t r i b u t i o n s were computed for a l l of the stocks, (price changes), i n the sample and t h e i r frequency of occurrence within given standard deviations of the mean. These results were compared with the unit normal. In a l l cases, some degree of leptokurtosis was present i n the securr. . i t i e s . The actual number of observations i n extreme t a i l s , (^2S, >3S, >4S, >5S), were also considerably higher than would be expected with a Normal Curve. Tests were conducted where the d a i l y f i r s t differences were regressed against a standardized variable such that: U - R Z = S where: Z = standardized variable st U = random variable (daily 1 * differences) R = mean S = standard deviation If data conformed to a Normal D i s t r i b u t i o n the graph would display a straight l i n e . However, i n a l l cases an S curve was generated confirming the results of the previous te s t s . The data was tested to see i f perhaps there was a mixture of d i s t r i b u t i o n s with possibly the same mean but d i f f e r e n t v a r i a n c e s , and a l s o i f t h e r e was n o n - s t a t i o n a r i t y e v i d e n t t o a c c o u n t f o r t h e d e p a r t u r e s f r o m n o r m a l i t y . I n b o t h c a s e s t h e e v i d e n c e i s a g a i n s t n o r m a l i t y . One Form o f Dependence M a n d e b r o t ( 1 4 ) s u g g e s t e d one p l a u s i b l e f o r m o f d e p e n d e n c e t h a t c o u l d p a r t i a l l y a c c o u n t f o r t h e l o n g t a i l s . Namely, t h a t l a r g e c h a n g e s i n p r i c e may t e n d t o be f o l l o w e d by l a r g e c h a n g e s . However, t h e s i g n o f t h e s e c o n d change a p p e a r s t o be random and o f f e r s no o p p o r t u n i t y f r o m an i n v e s t m e n t p o i n t o f v i e w t o enhance p r o f i t s . T h e s e l a r g e c h a n g e s a r e due t o t h e a d j u s t m e n t p r o c e s s i n t h e m a r k e t p l a c e . • I n c o n c l u s i o n , f r o m t h e v a r i o u s t e s t s p e r f o r m e d on t h e d a t a , i t was f o u n d t h a t t h e r e were no s e r i o u s d e p a r t u r e s f r o m i n d e p e n d e n c e i n s e c u r i t y p r i c e movements and t h a t a S t a b l e P a r e t i a n D i s t r i b u t i o n more f u l l y d e s c r i b e s t h e d i s t r i b u t i o n o f p r i c e c h a n g e s i m p l y i n g an i n f i n i t e v a r i a n c e . PRICE MOVEMENTS IN SPECULATIVE MARKETS: TRENDS ,OR RANDOM WALKS (1).. T h i s a r t i c l e a p p e a r s t o i n d i c a t e t h a t common s t o c k p r i c e s f o l l o w d i s c e r n a b l e p a t h s . A c c o r d i n g t o A l e x a n d e r , t h e s e t r e n d s c a n be b r o u g h t i n t o common v i e w by ' f i l t e r i n g ' o u t random v a r i a b i l i t y i n common s t o c k p r i c e s . The a r t i c l e i s b a s e d i n p a r t on a s t u d y done by M. G. K e n d a l l , The A n a l y s i s o f E c o n o m i c Time S e r i e s - P a r t I . P r i c e s , i n w h i c h he c a l c u l a t e d t h e f i r s t t w e n t y - n i n e l a g g e d s e r i a l c o r r e l a t i o n s o f t h e f i r s t d i f f e r e n c e s o f twen t y - t w o 16 time series representing speculative p r i c e s . In t h i s study Kendall asks the question: "How good i s the best estimate we can make of next week's price change i f we know t h i s week's price change and the changes of the past twenty-nine weeks and correspondingly for the monthly series?" Kendall found that generally the s e r i a l correlations i n d i -cated that stock prices tended to follow a random manner, even when in t e r v a l s were extended from one week to two, four, eight, and sixteen weeks. The a r t i c l e points out further studies that were done by Osborne(16) i n which he worked with the logarithms of price changes. He found that these logarithms were normally d i s t r i b u t e d with a standard deviation proportional to the square root of the length of the period, which i s c h a r a c t e r i s t i c of a random walk. In using logarithms of price changes Osborne found that the p r o b a b i l i t y of a change i n either d i r e c t i o n of a given amount i n the log of a price was equally l i k e l y , hence i t was no longer a 'Fair Game'. However, the differences at-tributed to the expectation of zero arithmetic gain or zero log gain are minimal and only deviate s i g n i f i c a n t l y over extremely long time periods. Alexander did further tests for randomness i n which he studied the number of runs that occured i n the weekly cash wheat prices at Chicago. He d i s t r i b u t e d the runs i n accordance with t h e i r duration and found that they conformed very c l o s e l y with what could be expected from a random group of data. However, when the same test was attempted on the 17 Standard and Poor's monthly composite stock price index, the resu l t s appeared to be inconsistent with the assumption of a random walk of equal p r o b a b i l i t y of r i s e or f a l l . By taking these r e l a t i v e frequencies into account he found the res u l t s did f i t the observed data quite well. The author concluded that the month to month movement of stock prices, at lea s t i n di r e c t i o n , i s consistent with the hypothesis of a random walk with an approximate 6 to 4 p r o b a b i l i t y of a r i s e . When Alexander applied f i l t e r rules to changes i n stock prices he found p r o f i t s , excluding commissions, could be earned. Results indicated that small f i l t e r s were superior to a buy-and-hold p o r t f o l i o . He concluded there are trends i n stock prices provided we are not dealing with f i n i t e uniform time periods. In speculative markets price changes appear to follow 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 introduced t h i s study by pointing out some c r i t i c i s m s that were raised against his previous research concerning f i l t e r i n g : 1. You cannot buy the averages. 2. By following the f i l t e r rule you negate your e f f o r t s . 3. Estimated p r o f i t s from the use of f i l t e r s were subject to bias exaggerating the p r o f i t a b i l i t y . 18 4. F i l t e r p r o f i t s a r e t h e c o n s e q u e n c e o f t h e f r e q u e n c y d i s t r i b u t i o n o f t h e d a i l y p r i c e c h a n g e s e v e n i f e a c h d a y ' s p r i c e change i s i n d e p e n d e n t o f t h e p r e c e d i n g d a y ' s . 5. A p p a r e n t p r o f i t a b i l i t y o f f i l t e r s s i m p l y r e f l e c t s t h e upward t r e n d i n p r i c e s . F o r c r i t i c i s m s one t h r o u g h t h r e e i t c a n be a r g u e d t h a t t h e y a r e n o t v a l i d . Namely: 1. You c a n buy t h e a v e r a g e s . 2. T h i s m i g h t be t r u e b u t we a r e n o t i n t e r e s t e d i n t h e p r a c t i c a l a p p l i c a t i o n o f f i l t e r s b u t w h e t h e r i n f a c t f i l t e r i n g t h e o r y n e g a t e s o r m o d i f i e s random w a l k t h e o r y . 3. A u t h o r i n p r e s e n t s t u d y a d j u s t e d f o r t h e s e b i a s e s , w i t h t h e r e s u l t t h a t p r o f i t s a r e r e d u c e d . C r i t i c i s m s 4 and 5 a r e e s s e n t i a l l y what t h e p r e s e n t s t u d y d e a l s w i t h . E m p i r i c a l F i n d i n g s 1928 - 1961 F i l t e r s r a n g i n g f r o m 1% t o 45.6% were u s e d . I f no c o m m i s s i o n s h a d t o be p a i d , a l l t h e f i l t e r s w o u l d h a ve made a p r o f i t . The most p r o f i t a b l e were t h e s m a l l e s t f i l t e r s . W i t h a 2% c o m m i s s i o n on e a c h t r a n s a c t i o n o n l y f i l t e r s o f 21.7% o r g r e a t e r show s i z e a b l e g a i n s o v e r c o m m i s s i o n s . O n l y t h e l a r g e s t , however, b e a t a b u y - a n d - h o l d p o l i c y . A l e x a n d e r m a i n t a i n e d i n h i s s t u d y t h a t n e i t h e r c o m m i s s i o n s n o r p r o f i t s f r o m a b u y - a n d - h o l d p o l i c y a r e r e l e v a n t f o r t h e 19 p u r p o s e a t h and. 'He was c o n c e r n e d w i t h a s c e r t a i n i n g w h e t h e r s t o c k p r i c e s move r a n d o m l y o r w h e t h e r o r n o t t h e r e a r e a p p a r e n t d e p e n d e n c i e s . Hence we s h o u l d be c o n c e r n e d w i t h c o m p a r i n g e x p e c t e d b e h a v i o r w i t h o b s e r v e d b e h a v i o r . To compare f i l t e r r u l e s w i t h a b u y - a n d - h o l d p o l i c y i s n e i t h e r h e r e n o r t h e r e . A r e p r o f i t s f r o m f i l t e r r u l e s e a r n e d s i m p l y as a r e s u l t o f t h e g e n e r a l upward t r e n d i n p r i c e s d u r i n g t h e p e r i o d s t u d i e d ? A c c o r d i n g t o A l e x a n d e r no. He f i r s t t e s t e d t h e a v e r a g e l o g a r i t h m i c p r o f i t p e r t r a n s a c t i o n a g a i n s t what we w o u l d e x p e c t f r o m t h e t r e n d f a c t o r i n h e r e n t i n t h e p r i c e movement. I t was f o u n d g e n e r a l l y t h a t f i l t e r s were more p r o f i t a b l e t h a n was t o be e x p e c t e d f r o m t h e i n f l u e n c e o f t h e t r e n d . S e c o n d l y t h e p e r i o d u n d e r s t u d y was s p l i t i n t o two s u b -p e r i o d s , 1928 - 1940 and 1940 - 1961. I n p a r t i c u l a r , t h e s u b - p e r i o d 1928 - 1940 showed p r o f i t s e v e n i n t h e a b s e n c e o f an upward t r e n d . T h i r d l y , he computed t h e p r o f i t s on t h e o r g i n a l p r i c e s by e l i m i n a t i n g t h e t r e n d f a c t o r and o n c e a g a i n f o u n d t h a t t h e f i l t e r s were s t i l l p r o f i t a b l e a l t h o u g h r e d u c e d somewhat. C o n c l u s i o n E v i d e n c e i n d i c a t e d by f i l t e r p r o f i t s r u n s s t r o n g l y a g a i n s t t h e h y p o t h e s i s t h a t f r o m 1928 - 1961 t h e movement o f t h e S t a n d a r d and P o o r ' s I n d u s t r i a l s i s c o n s i s t e n t w i t h a random w a l k w i t h d r i f t . 20 FILTER RULES AND STOCK-MARKET TRADING (7) This p a r t i c u l a r study was undertaken i n response to the res u l t s obtained by Alexander i n his paper. There appeared to be a number of areas that held some ambiguities, (cost of dividends, short term p o s i t i v e price change dependencies and intermediate term negative p r i c e dependencies), that prompted the authors to do further study with f i l t e r s . Alexander's f i l t e r technique was applied to series of d a i l y closing prices for each of the i n d i v i d u a l s e c u r i t i e s of the Dow-Jones Average s t a r t i n g about the end of 1957 to September 26, 1962. F i l t e r s were used ranging from .5% to 50%. Given these f i l t e r ranges various computations were performed on the data, namely computing returns before and a f t e r commissions, before and aft e r dividends, and average returns for both long and short positions. Generally under a l l situations the f i l t e r method produced vastly i n f e r i o r r esults r e l a t i v e to a buy-and-hold p o r t f o l i o . One variable Alexander f a i l e d to take into consideration was the e f f e c t dividends would have on a f i l t e r generated p o r t f o l i o . Div-idends declared when a stock was held short should be considered a cost, hence a reduction i n o v e r - a l l return. By taking dividends into account, the re s u l t s of Alexander's study might not have been as p o s i t i v e . Fama and Blume found that by adjusting for dividends they increased the average advantage of buy-and-hold over the f i l t e r technique by at least two percentage points. The study also indicated that the short positions taken by the f i l t e r technique produced i n a l l but one security, negative returns. On long positions 13 s e c u r i t i e s had a greater average return per f i l t e r than the corresponding returns from buy-and-hold. By averaging the returns.on a l l o the long positions however, yielded a lower return than a buy-and-hold. The authors found there was evidence of persistence or po s i t i v e dependence i n very small movements of stock pr i c e s , however, not enough to generate larger returns than a buy-and-hold p o l i c y once the increased commission charges were considered. Evidence of negative dependence i n intermediate s i z e -price movements was also found. For f i l t e r s larger than 1.5%, average losses on short positions exceeded i n absolute value the average returns from buy-and-hold. The negative annual average return on short positions was -16% compared with +9.8% for the buy-and-hold. Hence, i f we did the oppo-s i t e of what the f i l t e r t o l d us to do, we should have a . larger return than expected. Once again the study revealed that with increased charges these p r o f i t s would be reduced. Conclusion Fama and Blume state there appears to be both p o s i t i v e and negative dependence but not of the magnitude to enchance p r o f i t s , hence the random walk theory i s s t i l l strong evidenc of r e a l i t y . 22 CHAPTER 3 METHOD OF RESEARCH D a t a Used The d a t a u s e d i n t h i s s t u d y c o n s i s t e d o f t h e m o n t h l y c l o s i n g p r i c e on a l l s t o c k s l i s t e d on t h e VSEM f o r t h e p e r i o d M a r c h 1963 t o F e b r u a r y 1973. T h r o u g h o u t t h e 10 y e a r p e r i o d a t o t a l o f 425 s e c u r i t i e s were l i s t e d . T h e s e 425 s e c u r i t i e s c o n s i s t e d o f 289 s t o c k s p r e s e n t l y t r a d i n g a t t h e end o f t h e p e r i o d and 112 s e c u r i t i e s t h a t s u b s e q u e n t l y c h a n g e d names t h r o u g h a c o n s o l i d a t i o n d u r i n g t h e p e r i o d . F o r t y - f i v e c o m p a n i e s i n t h e d a t a e i t h e r went b a n k r u p t o r were d e l i s t e d o r s u s p e n d e d and by t h e end o f t h e s t u d y p e r i o d were n o t r e i n s t a t e d . S i n c e s e c u r i t y p r i c e s t e n d t o h a v e an upward d r i f t o v e r t i m e t h e f i r s t t h i n g t h a t was done t o t h e d a t a was t o d e v e l o p an I n v e s t m e n t P e r f o r m a n c e M a t r i x . T h i s was done by c o m p u t i n g t h e i n v e s t m e n t p e r f o r m a n c e r e l a t i v e , ( h e r e i n a f t e r r e f e r r e d t o as I P R ' s ) , f o r e a c h company i n t h e d a t a o v e r t h e 120 p e r i o d s c o v e r e d . An IPR i s t h e p r i c e o f a s e c u i r t y a t t h e b e g i n n i n g o f t h e month, (P ), d i v i d e d i n t o t h e p r i c e o f t h e s e c u r i t y a t t h e end o f t h e month, ( p t + 1 ) • The f o r m u l a w o u l d be: P t + 1 IPR = -P t The r a t e o f r e t u r n f o r any p e r i o d o f t i m e may be c a l c u l a t e d by t a k i n g t h e p r o d u c t o f t h e a p p r o p r i a t e IPR's minus 1.0. The r a t e s o f r e t u r n u s e d i n t h i s s t u d y were c a l c u l a t e d by t h i s method. "The u s e o f c h a n g e s i n l o g e p r i c e as t h e m e asure o f r e t u r n i s common i n t h e random w a l k l i t e r a t u r e . I t c a n be j u s t i f i e d i n s e v e r a l ways. B u t f o r c u r r e n t p u r p o s e s , i t i s s u f f i c i e n t t o n o t e t h a t f o r p r i c e c h a n g e s l e s s t h a n f i f t e e n p e r c e n t , t h e change i n l o g e p r i c e i s a p p r o x i m a t e l y t h e p e r c e n t a g e p r i c e change o r o n e - p e r i o d r e t u r n . And f o r d i f f e r e n c i n g i n t e r v a l s s h o r t e r t h a n one month, r e t u r n s i n e x c e s s o f f i f t e e n p e r c e n t a r e u n u s u a l . Thus , t e s t s c a r r i e d o u t i n p e r c e n t a g e s o r o n e - p e r i o d r e t u r n s • y i e l d e d r e s u l t s e s s e n t i a l l y i d e n t i c a l t o t h e t e s t s b a s e d on c h a n g e s i n l o g p r i c e . " (5) S i m i l a r l y , t h e c u m u l a t i v e IPR was c a l c u l a t e d f o r e a c h s e c u r i t y . The c u m u l a t i v e IPR t e l l s us what an i n v e s t o r w o u l d e a r n i f he had h e l d t h e s e c u r i t y f o r one month, o r two months, e t c . up t o 12 0 months. The f o r m u l a w o u l d be: The m o n t h l y IPR's and CIPR's were a l s o c a l c u l a t e d f o r t h e m a r k e t as a w h o l e a s s u m i n g e q u a l w e i g h t f o r e a c h r e l a t i v e p r i c e c h a n g e . e P t + i CIPR f o r i = 2 t o n P where P n g i v e n y e a r s P r i c e I o K P O b a s e y e a r P r i c e K number o f i n d e x i t e m s 24 To c l a r i f y , t h i s assumes t h a t an i n v e s t o r w o u l d p l a c e e q u a l d o l l a r s i n e a c h s e c u r i t y he p u r c h a s e s . Thus, no one s e c u r i t y b e c a u s e o f i t s a b s o l u t e d o l l a r s i z e c a n i n f l u e n c e t h e r e t u r n e a r n e d on t h e m a r k e t i n d e x . T h i s i s t o i n s u r e t h a t i f t h e s t o c k s o f l a r g e c o m p a n i e s behave d i f f e r e n t l y t h a n t h o s e o f s m a l l e r f i r m s t h e i r i n f l u e n c e on t h e i n d e x w i l l be f e l t o n l y t o t h e e x t e n t t h a t t h e y a r e a p a r t o f t h e i n d e x . The m o n t h l y IPR f o r t h e m a r k e t was b a s e d o n l y o n t h e number o f s t o c k s t r a d i n g d u r i n g t h e month. I f a p a r t i c u l a r .... s e c u r i t y had m i s s i n g d a t a , ( s t o c k d i d n o t t r a d e d u r i n g month), no m o n t h l y IPR was c a l c u l a t e d f o r i t d u r i n g t h a t month. Sim-i l a r l y , t h e IPR f o r t h e m a r k e t c o n s i s t e d o f t h e sum o f t h e IPR's f o r e a c h s e c u r i t y d i v i d e d by t h e number i f IPR's f o r t h a t month. T h i s means t h a t i f a s e c u r i t y d i d n o t t r a d e o r no p r i c e d a t a was a v a i l a b l e f o r t h a t p a r t i c u l a r month, t h e n t h e s t o c k was n o t i n c l u d e d i n t h e m a r k e t i n d e x u n t i l s u c h t i m e as i t s t a r t e d t r a d i n g a g a i n . S e r i a l C o r r e l a t i o n Once t h e d a t a had b e e n c o n v e r t e d i n t o IPR's t h e n e x t s t e p was t o compute t h e 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 f o r e a c h s e c u r i t y f o r a l a g o f 1 month, 2 months, and.up t o 6 months i n c l u s i v e . The d e f i n i t i o n o f t h e 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 ( P u ) i s g i v e n b e l o w . pk Cov(X t,X t + k) (sx t) ( s x t + k ) where X t = IPRfc X t + k = I P \ + k for k = 1, 2, 3, 4, 5, 6. S = standard deviation The actual computation of the c o e f f i c i e n t s were c a r r i e d out on the computer using the following formula: n £ X Y - S X S Y P, k \l[(nSX2) (SX) 2] I ( n £ Y 2 ) - (27Y)2] where n = number of observations X = IPR t Y = I P R t + k The 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 way two variables covary. S e r i a l c o r r e l a t i o n measures the tendency of a time series of data to move i n cycles or trends. Hence high c o e f f i c i e n t s should indicate that the price changes imply some form of dependency. Conversly, a c o e f f i c i e n t approximating zero would indicate l i t t l e dependency in price changes. Runs Tests In the event that security prices i n the data do have some form of dependency which the s e r i a l correlations did not detect, runs tests were i n s t i t u t e d . Security price changes 26 m i g h t be random most o f t h e t i m e t h u s y i e l d i n g low c o r r e l a t i o n c o e f f i c i e n t s , however, t h e r e may be o c c a s i o n s where t h e r e i s a s i g n i f i c a n t t r e n d f a c t o r . Runs t e s t s s h o u l d d e t e r m i n e i f t h e r e a r e any. D e f i n i t i o n o f a Run A r u n c a n be d e f i n e d as a s e q u e n c e o f p r i c e c h a n g e s i n t h e same d i r e c t i o n o r o f t h e same s i g n . A r u n i s d e t e r m i n e d whenever t h e s i g n o f t h e n e x t p r i c e change i s d i f f e r e n t . Thus a r u n c o u l d c o n s i s t o f o n l y one p r i c e change o r a l a r g e s e q u e n c e o f p r i c e c h a n g e s . F o r example, i f t h e f o l l o w i n g p r i c e s e q u e n c e was o b s e r v e d ; 15, 20, 20, 25, 18, 15, 16, and 15, t h e p r i c e c h a n g e s w o u l d be +5, 0, +5, -7, -3, +1, - 1 , g i v i n g us 6 r u n s . I t i s p o s s i b l e t o compare t h e number o f r u n s a c t u a l l y o b t a i n e d w i t h what w o u l d be e x p e c t e d i f t h e p r i c e c h a n g e s were random. T h i s was done w i t h t h e u s e o f t h e f o l l o w i n g f o r m u l a ( 6 ) . 3 M = [N(N+1) - _ £ ^ ± 2 ] /N i = l where M = t o t a l e x p e c t e d number o f r u n s N = t o t a l number o f p r i c e c h a n g e s N^= t h e number o f p r i c e c h a n g e s o f e a c h s i g n . Runs were c a l c u l a t e d f o r a l l o f t h e s t o c k s i n t h e d a t a t o s e e i f t h e y were c o n s i s t e n t w i t h t h e a s s u m p t i o n o f i n d e p e n d e n c e . Testing Independence With F i l t e r Rules The pure form of the random walk theory states that ... security price changes are independent of each other. The e f f i c i e n t market hypothesis i s concerned more with the assumption that superior p r o f i t s cannot be earned on the average by analyzing e x i s t i n g information. This means that c o r r e l a t i o n tests and runs tests might indicate a degree of dependency but i s the dependency i n price changes s i g n i f -icant enough to earn higher p r o f i t s than normal. A random walk implies e f f i c i e n c y but an e f f i c i e n t market i s not neces-s a r i l y random. One way to t e s t i f above average p r o f i t s can be earned i s to employ a mechanical trading rule that assumes the existence of trends. D e f i n i t i o n of F i l t e r Rule If the price of a security r i s e s at least x percent, buy and hold the security u n t i l i t ' s price drops at l e a s t x percent from a subsequent high; when the price decreases x percent or more, liquidate any long p o s i t i o n and assume a short p o s i t i o n u n t i l the price r i s e s at l e a s t x percent. The f i l t e r rule assumes that once a security's price moves i n a p a r t i c u l a r d i r e c t i o n by at least x percent the p r o b a b i l i t y exists that the trend i n that d i r e c t i o n w i l l continue. The f i l t e r rule was applied to the data for f i l t e r s rangi i n size from: 28 x equal to: .005 .01 .02 .05 .10 .20 .25 .50 An example of how t h i s technique was applied i s i l l u s t r a t e d below. Transaction costs and dividends were excluded. Most mining companies do not give dividends so the r e s u l t s w i l l not be influenced to any great degree, however, the omission of transaction costs could have a s i g n i f i c a n t influence on the r e s u l t s , p a r t i c u l a r l y for the small f i l t e r s , because of the frequency of transactions. Hence the omission of transaction costs w i l l bias the r e s u l t s upwards i n favor of the f i l t e r rule. t Action Signal* Price P r o f i t / (Loss) Return 1 1.00 2 1.05 3 Buy 1.10 4 1.20 5 1.30 1.80 - 1.10 6 1.50 = .70 1.30 = 118? 7 2.00 " 1.10 8 S e l l & go short 1.80 9 1.50 10 1.25 1.80 - 1.20 11 1.00 = - 6 0 12 Buy and go long 1.20  * f i l t e r size of 10% 29 In the example the return for the f i l t e r would be 118% compared to 20% for a buy and hold p o l i c y . The f i l t e r rule 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 that the investor can buy and s e l l the security at the time and p r i c e that the f i l t e r commands. In practise t h i s i s not always true. The f i l t e r r ule i n i t s pure abstract form w i l l indicate whether price changes are independent or not. As a r e s u l t i t might possibly refute the random walk theory but not the e f f i c i e n t market hypothesis. The results however, should give some indicati o n as to the p r o f i t a b i l i t y of a trading ru l e . Measure of Risk In comparing the. rates of return earned on the TSE with those earned on the VSEM some consideration must be given to the r i s k assumed i n each case. For purposes of analysis i n th i s study the standard deviation of returns was used as a surrogate for r i s k . The following formula was used: N £ X 2 - ( X X) 2I S = -(N - 1) The c o e f f i c i e n t of v a r i a t i o n was also calculated such that: S CV = — — X The c o e f f i c i e n t of v a r i a t i o n i s necessary to determine the r e l a t i v e v a r i a t i o n i n returns between groups of data with varying means. Stat i o n a r i t y of Returns One part of the weak form hypothesis states that the returns generated from successive price changes are ident-i c a l l y d i s t r i b u t e d . " I d e n t i c a l l y d i s t r i b u t e d i s a technical s t a t i s t i c a l phrase which means the numbers a l l conform to some given pro-b a b i l i t y d i s t r i b u t i o n . Since the pro-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 of return tend to be stationary for any given security, t h i s indicates that the rates of return for those s e c u r i t i e s are i d e n t i c a l l y distributed."(8) In February of 1973 there were 289 s e c u r i t i e s trading. Only 25 of these had complete price data for the ten years under observation. This simply means that 25 companies maintained the same corporate name for the entire 10 years. As a r e s u l t they were used as a sample to te s t the assumption that h i s t o r i c a l rates of return tend to be stationary over time. The companies were f i r s t divided down into f i v e , 2 year periods and l a t e r into two, 5 year periods. For each period the mean return and standard deviation of returns were determined to see i f there had been any change i n either of these two measures. If the mean return and/or 31 t h e s t a n d a r d d e v i a t i o n c h a n g e d i t w o u l d i n d i c a t e t h a t t h e r e t u r n s a r e n o t s t a t i o n a r y and t h e r e f o r e , a r e n o t i d e n t i c a l l y d i s t r i b u t e d . The m a j o r i m p l i c a t i o n t o be drawn f r o m s t a t i o n a r y d i s t r i b u t i o n s i s t h a t we c a n more a c c u r a t e l y p r e d i c t what t h e e x p e c t e d r e t u r n and r i s k c h a r a c t e r i s t i c s o f a s e c u r i t y w i l l be. T h i s knowledge w o u l d a i d p o r t f o l i o managers i n d e v e l o p i n g p o r t f o l i o s a l o n g t h e M a r k o w i t z - S h a r p e model o f r i s k - r e t u r n s p a c e and e f f i c i e n t c o m b i n a t i o n s o f s e c u r i t i e s . C a l c u l a t i o n o f G e o m e t r i c Mean R a t e o f R e t u r n R a t h e r t h a n t a k i n g t h e a r i t h e m e t i c mean o f t h e v a r i o u s p e r i o d s , g r e a t e r a c c u r a c y i s o b t a i n e d i f t h e g e o m e t r i c mean i s u s e d . The g e o m e t r i c mean was d e r i v e d u s i n g t h e f o l l o w i n g f o r m u l a : .rvy A v e r a g e m o n t h l y r a t e = A / I P R t X I P T t + 1 . . . X I P R t + n n = number o f months i n p e r i o d I f t h e a v e r a g e a n n u a l r e t u r n f o r t h e p e r i o d was r e q u i r e d i t was c a l c u l a t e d w i t h t h e f o l l o w i n g e q u a t i o n : R t + 1 2 = (1.0 + R t ) 1 2 - 1.0 where R = m o n t h l y g e o m e t r i c mean. 32 CHAPTER FOUR FINDINGS S e r i a l Correlation 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 were generated for 4 8 s e c u r i t i e s for a period of 10 years. The c o e f f i c i e n t s were calculated for monthly changes with lags up to 6 months. The findings are detailed i n table II and summarized i n table I I I . Fama, (6) has shown that for large sample sizes., even though the c h a r a c t e r i s t i c exponent <K of the underlying stable Paretian process i s greater than 1, the c o e f f i c i e n t s generated are consistent and unbiased estimates of the true s e r i a l c o r r e l a t i o n i n the population. The number of s i g n i f i c a n t correlations at the .05 l e v e l ranged from 18.7% of the t o t a l sample for a lag of one month to 6.2% for lags of 2 and 3 months. The largest c o e f f i c i e n t was for the firm NGD for a lag of 1 month. The r e s u l t i n g s t a t i s t i c was a - .3868. The greatest degree of c o r r e l a t i o n appears for a lag of 1 month. The average (mean) c o e f f i c i e n t was .1192 compared with .0680 for a lag of 3 months. Once again except for t = 3, the majority of the c o e f f i c i e n t s had negative.signs. For a lag equal to 6, 31 of 48 co r r e l a t i o n s , or 64.5%, were negative. It was in t e r e s t i n g to note that when tests for dependence involving s e r i a l c o r r e l a t i o n were run on firms that ceased to trade during the period, the re s u l t s were quite s i m i l a r . A t o t a l of 41 firms for varying periods of time were observed 33 and as i s indicated i n table III and IV the percentage of s i g n i f i c a n t correlations was only 11.3% for t = 1,2,...6; versus 11.06% for the active firms. The sign of the c o e f f i c i e n t s tended to follow the same pattern as well. However, the average 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 was s i g n i f i c a n t l y higher for a l l values of t. This can be explained by the smaller number of observations on average with the inactive firms. Based on the results thus far attained the suggestion appears to be that there i s l i t t l e dependence between the returns generated i n one period and the returns generated i n some future period. For the active firms between .46% and 1.42% of the movement i n lagged price changes can be used to explain the v a r i a t i o n i n the current price change. In terms of deciphering p r o f i t a b l e trading rules based on h i s t o r i c a l price changes, s e r i a l c o r r e l a t i o n gives l i t t l e i n sight and would appear to add strength to the E f f i c i e n t Market Hypothesis. TABLE II Monthly S e r i a l Correlation Coefficients for Lags of 1,2, 6 Months (ten year time span) Lag Stock 1 2 3 4 5 6 BCC .1333 -.0349 .0028 -.0381 .0373 .0333 BR .0390 .0976 .0621 .0894 .0249 -.0917 BSM -.1126 -.0469 .0244 -.0570 .1641 -.0255 CGQ .0297 -.0927 -.0020 .0199 -.0569 -.0954 CMNA -.0223 .2016 -.0171 .0168 .0185 .0569 COP .0050 .0057 .1002 -.0787 -.0555 -.0737 CPG .0845 .1132 .2678* .0079 -.1113 -.0660 CRI -.2988* .1604 -.0823 -.0226 -.0556 -.1453 CSR -.0510 -.2044* .0162 -.0258 .2340* .0222 CST -.1471 .1227 -.1925* .0754 -.0663 -.0785 DVM -.0912 -.0840 .0419 .0061 -.2480* -.1339 GDC -.0868 -.0011 .0126 -.0192 -.0311 .0217 GIM .0494 -.0260 .0099 -.1638 . 0089 -.0606 GRL .1143 -.0827 -.0486 .0262 -.1209 -.2070 GRV -.2179* -.1631 -.0622 .3133* -.0709 -.1305 MM -.1047 -.0592 .0156 .0038 . 0433 .0629 MTW -.0277 -.1001 -.0245 -.2350* .0178 .0563 NCR -.0949 .0336 -.0355 .0737 -.0502 -.2506 NIN .0372 -.1354 -.0099 .0325 .0165 -.2475 NOV .3212* .2689* .1256 .1641 .0124 .0057 NPM -.1253 -.0247 .0155 -.0316 -.0413 -.1399 PB .1855* .0114 .0967 .2552* .0428 .018 3 PDL . .0033 -.0788 .1150 -.1701 .0509 .0767 PEEL -.0843 .0816 -.0965 .0761 -.0396 -.0658 PSS -.0910 .1648 .1249 .1171 -.0780 .0278 QUT. -.2534* .0414 -.0418 -.0115 .0736 -.1004 RV -.1385 -.1183 .1646 -.0121 -.0215 -.1018 SBC -.1769 -.1768 .0183 -.0610 -.2576* .2146 TABLE II (continued) Monthly S e r i a l Correlation Coefficients for Lags of 1,2, (ten year time span)  , 6 Months Lag 1 2 3 4 5 6 SCH -.0962 .1128 .1231 -.0942 .0442 -.0040 SRD -.1382 -.0548 -.0712 -.1310 -.0832 .0931 SS .2400* .0658 .0286 -.0478 -.1347 -.0685 TR -.0587 -.1266 .0553 -.1199 . 0024 .0425 TRJ -.0519 . 0520 -.0191 .0425 .0189 -.0223 TWT NEW .0210 -.0261 .0589 -.0265 -.0677 -.0767 VN -.1644 -.0028 -.0330 -.0917 .1855* -.2514* WMI .1343 -.1917 * .0531 -.0040 -.1465 .0292 * Co e f f i c i e n t i s twice i t s computed standard error Monthly S e r i a l Correlation Coefficients for Lags of 1,2, 6 Months (eight year time span); Stock 1 2 3 4 5 6 ATS -.2121* -.0720 .0429 -.0271 -.1098 .0065 CCD -.1121 -.0478 -.1137 .0585 -.1656 -.0924 CYD .2406* -.1081 -.0284 -.0290 -.0495 -.0120 DVN .0603 -.0214 .0921 -.1213 -.1143 .0555 JY .1027 -.0599 -.1146 -.0842 -.0059 -.0674 JRC .0241 -.0503 -.0477 .0327 -.0327 -.1072 LTL'A' -.1169 .0510 -.0136 .0297 -.0218 -.0088 NGD -.3868* .1609 -.2145* .0528 -.0168 -.0863 PPT .1465 .0080 -.1720 -.3051* -.0420 -.2115* RHM .1085 .0656 .0403 -.1861 -.2078 -.2459* SLO .1040 -.0057 -.1070 .1809 .199 -.0562 TMX .0754 .0101 -.0280 -.2784* .0532 .0551 * C o e f f i c i e n t i s twice i t s computed standard error TABLE III Summarization of Results of S e r i a l Correlation C o e f f i c i e n t s 1 2 3 4 5 6 no. of negative & po s i t i v e signs 26(-) 22( + ) 28(-) 20( + ) 23(-) 25( + ) 27(-) 21( + ) 29(-) 19( + ) 3K-) 17( + ) % of 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 Percentage of s i g n i f i c a n t c o r r e l a t i o n s * 18. 7 6.2 6.2 10.4 10.4 14.5 for inactive firms 17.0 4.8 7.3 7.3 14.6 17.0 * * Average c o e f f i c i e n t inactive firms .1192 .2062 .0838 .1579 .0680 .1622 .0865 .1846 .0744 .1775 .0875 .1934 <t _• . . • r™^  : ^ 5 • —• *approximately twice the standard error **absolute value TABLE IV Monthly S e r i a l Correlation Coefficients for Lags of 1,2, 6 Months Inactive Firms # of Stock Observations ^ ^ ^ ^ ^ ^ Lag 1 2 3 4 5 6 AET 91 -.0078 -.0062 -.0041 -.0059 -.0191 -.0052 AKN 72 -.0486 •.0196 .1174 -.0917 -.0822 .0249 BAP 21 .1739 .1848 -.0426 -.2237 -.1031 -.2427 BRX 27 .0380 -.0525 -.1031 -.0428 -.1963 -.3803 BTL 29 -.3772* -.1130 .1600 -.5188* .4586* -.0640 CDT 41 -.3014 .0760 .1878 -.4110* .1292 -.1975 CHH 65 .0909 .0846 -.0736 .0320 -.0028 .0416 CMAN 58 -.0885 -.1980 .0464 -.0444 -.0017 -.0017 CTH 114 -.1968* .0225 -.0242 -.0793 .0784 -.0597 CVM 3 .9810* 1.0 0 0 0 0 DIN 13 -.1717 .0520 .6500* -.1743 -.2594 .0700 EYB 33 -.0498 -.2437 .2791 -.2041 -.1385 -.0941 FMI 73 -.0063 .0052 -.1053 .0884 -.1541 .0389 GBX 15 -.3480 .0520 .2574 / -.3288 .2878 -.3925 GDR 27 -.3711 .1985 -.1361 -.2588 .4909* -.4568* GLS 28 -.0491 -.0499 -.0519 -.0541 -.0565 • .4349* GLW 26 .1499 -.2683 -.4412* -.2803 .0085 .5155* GPU 41 .017.7 .0071 .0073 .0075 -.1828 .0047 IBL 15 -.0908 -.2339 .0602 .1627 -.0540 -.5089 IMR 22 -.1834 -.1967 .2807 .1607 .0151 -.4062 JAY 79 -.3687* .0078 -.0796 .1245 -.2070 -.0576 KAM 107 -.0469 -.0312 .0513 .0480 .0038 -.0123 KONEW 21 .0434 -.3274 .1478 -.0194 .2494 .0447 KOP 110 .2386* .0213 -.0371 -.1575 -.1149 -.0595 LBM 15 .1610 .0652 .3428 .1289 -.5293* -.5825 MGC 92 .0903 .2025* -.0583 -.0945 -.1400 -.1713 MRX 31 -.2565 .0599 -.1240 .1976 -.4075* .1595 NAI 25 -.2669 -.0190 -.2022 .2473 -.1994 -.4024* NHL 16 -.3407 -.1693 .2117 -.4589 .5305* -.0095 NKR 8 -.1660 -.6297 -.3189 .8536* -.2326 -.7495* TABLE IV (Continued) Monthly S e r i a l Correlation Coefficients for Lags of 1,2, 6 Months Inactive Firms # O f LAG Stock Observations 1 2 3 4 5 5 NLC 21 .1697 -.0902 -.2043 -.3369 -.0713 -.0057 NRX 23 -.1894 -.1490 .3671 -.1437 -.0143 .1941 PRM 24 -.2174 -.0093 .0975 -.1985 .1544 -.0540 RXM 30 .4108* .134 9 .1424 .0021 -.0783 . 0336 SEM 17 .0812 -.3837. -.2049 -.15.7.0 .2283 -.0479 SML" 33 -.3206 .0187 -.3443* .2111 -.0285 -.0635 SSD 10 .1111 .1125 .1125 .1429 .1667 .2000 SUH 33 -.2606 .1814 .2131 -.0961 -.0595 -.0043 VNS 48 .3339* .0801 .0655 .1308 .0693 .0329 WLM 12 -.4058 .5858* .1228 -.4397 .8082* -.5857* WTM 25 .2338 .1319 -.0146 -.0291 -.0883 .3375 * C o e f f i c i e n t i s twice i t s computed standard error 39 Runs Tests Runs tests were conducted on the sample stocks using the following formula: ^ M = [N(N+l) - ^ n2/N] i = l 1 where N i s the t o t a l number of price changes, and the n^ are the numbers of price changes of each sign. Table V summarizes the results of the Runs Test. Of a l l the firms tested the percentage deviation between expected and actual number of runs averaged 8.6 percent, with only 6 firms out of 4 8 showing a percentage deviation greater than 15 percent. Although the calculations were not applied to a l l the firms i n the sample, using a Bernoulli process with P( + )# P ( - ) , and P(0) on a few of the firms indicated that the number of expected p o s i t i v e , negative and no change runs corresponded c l o s e l y with the actual d i s t r i b u t i o n of runs. Fama (6) suggested that the percentage difference between actual and expected number of runs would be a good measure to determine the amount of dependence i n the observed data, hence the standardized or Z-value was. not calculated. Twenty-nine out of forty-eight s e c u r i t i e s yielded runs which were below what would have been expected, suggesting perhaps a small trend factor. Whether one could suggest that t h i s supports the results of the 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 however i s inconclusive. There appeared to be some negative c o r r e l a t i o n or downtrend in terms of the number of companies exhibiting negative c o e f f i c i e n t s . 40 It i s i n t e r e s t i n g to note that those firms that ceased trading during the period did not behave i n a s i m i l a r fashion. Of the 4 2 inactive firms only 14 had fewer runs than was expected. The d i s t r i b u t i o n of runs for both active and inactive firms were si m i l a r , with p o s i t i v e runs occuring about as frequently as negative runs. The absolute percentage difference between expected and actual number of runs was s i g n i f i c a n t l y higher. For the 42 firms tested, the spread approximated 16.02 percent for the inactive firms versus 8.6 percent for the active companies. Upon observation i t appeared that the inactive firms followed a more c y c l i c a l pattern. P o s i t i v e changes were more apt to be followed by negative changes. This i s confirmed to some degree by the greater number of negative c o r r e l a t i o n c o e f f i c i e n t s for a lag of t = 1. Once again the evidence suggests that the amount of 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 T o t a l A c t u a l and E x p e c t e d Numbers o f Runs f o r One-Month P e r i o d M o n t h l y i n f l e c t i o n s Runs S t o c k E x p e c t e d A c t u a l % D i f f . - 0 + - 0 + BCC 66.4622 66.0 . 007 51 7 61 29 7 30 BR 78.042 46.0 .696 42 50 27 16 14 16 BSM 76.9328 81.0 - .050 56 30 33 34 22 25 CGQ 73.0336 63.0 .159 58 17 44 28 8 27 CMNA 78.9496 71.0 .112 33 50 36 21 23 27 COP 72.78 71.0 .025 59 17 43 31 12 28 CPG 67. 87 65.0 .044 61 9 49 29 7 29 CRI 79.16 64.0 .237 49 37 33 26 15 23 CSR 69.33 58.0 .196 28 69 22 21 19 18 CST 73.58 81.0 - .092 55 17 47 35 13 33 DVM 66.61 70.0 - .048 60 7 52 30 7 33 GDC 71. 35 70.0 .019 52 13 54 30 9 31 GIM 62.56 59.0 .060 65 3 51 28 3 28 GRL 74.74 75.0 - .003 56 20 43 31 19 25 GRV 80.26 77.0 . 042 42 39 38 28 21 28 MM 73.86 78.0 - .053 51 18 49 27 17 34 MTW 73.87 73.0 . 012 58 19 42 29 16 28 NCR 72.24 75.0 - .037 57 15 47 33 12 30 NIN 76 . 05 69.0 .102 53 22 44 29 12 28 NOV 67.12 65.0 .033 64 9 46 29 9 27 NPM 69.70 75.0 - .071 58 11 50 32 10 33 PB 77.62 72.0 .078 47 25 47 29 14 29 PDL 76. 56 73.0 .049 44 23 52 27 17 29 PEEL 73.47 82.0 - .104 58 18 43 36 17 29 PSS 78.88 70.0 .127 50 .32 37 29 16 .2 5 QUT 71.37 83.0 - .140 53 13 53 32 12 39 RV 78.36 75.0 .045 46 36 35 28 21 26 SBC 72.33 76.0 - .048 59 16 44 32 16 28 SCH 71.75 71.0. .011 61 16 42 31 11 29 SRD 75.12 78.0 - .037 56 21 42 35 15 28 SS 65.10 68.0 - .043 64 6 49 30 6 32 TR 75.82 67.0 .132 40 26 50 28 10 29 TRJ 72.40 73.0 - .008 56 15 48 30 11 32 TWTNEW 62.03 57.0 .088 67 3 49 27 3 27 VN 72.32 71.0 .019 59 16 44 30 13 28 WMI 68.41 66.0 .037 53 9 57 28 8 30 ATS 54.71 59.0 - .073 52 6 40 27 6 26 CCD 62.15 56.0 .109 46 20 31 23 9 24 CYD 59.50 64.0 ' - .070 56 12 34 29 10 25 DVN 62.22 61.0 .020 55 11 40 27 10 24 JY 63.62 69.0 - .078 53 14 38 32 10 27 TABLE V ( c o n t i n u e d ) T o t a l A c t u a l and E x p e c t e d Numbers o f Runs f o r One-Month P e r i o d M o n t h l y I n f l e c t i o n s Runs S t o c k E x p e c t e d A c t u a l % D i f f . - 0 + - 0 + JRC 64.91 67.0 -.031 61 12 39 29 10 28 L T L ' A 1 66.47 65.0 .023 29 26 47 25 12 28 NGD 67.68 69.0 -.019 43 32 27 27 17 25 PPT 62. 38 60.0 -.039 40 25 29 23 16 21 RHN 57.10 49.0 .165 47 10 39 21 8 20 SLO 55.28 46.0 .202 43 10 39 20 9 17 TMX 64. 36 52.0 .238 44 27 27 22 11 19 43 TABLE V I T o t a l A c t u a l and E x p e c t e d Numbers o f Runs f o r One-Month P e r i o d s I n a c t i v e F i r m s S t o c k 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 . E x p e c t e d A c t u a l % D i f f e r 22.45 21 .069 43. 84 44 .003 12.36 13 .049 13.85 15 .076 12.05 14 .140 24.28 27 .100 33.19 35 ..052 19.85 13 .527 68.86 73 .057 3.50 4 .125 3. 86 4 .036 16.07 18 .107 40.97 42 .025 4.42 7 . 367 16.50 21 .214 6.36 5 .273 11.90 12 .008 6.62 5 .324 9.13 9 .014 7.43 9 .175 46.92 59 .205 64.43 59 .092 13. 82 16 .136 58.52 29 1.018 6.45 6 .076 47.95 53 .095 19.93 24 .169 17. 85 18 .009 10.65 12 .113 5.00 6 .167 12. 33 12 .028 9. 80 11 .109 14 .28 17 .160 18.48 17 . 087 12. 22 8 .528 13.96 16 .128 4.40 4 .100 20.55 20 .028 5.80 8 .275 17.231 14 .231 2.71 3 .095 19.76 23 .141 44 F i l t e r Trading Rule A f i l t e r rule i s a mechanical trading rule, where by i t i s believed that stock prices, or more s p e c i f i c a l l y changes in stock prices follow certain d i s c e r n i b l e patterns. Once a stock price i s i n motion i t w i l l continue to move i n the same di r e c t i o n long enough and consistently enough to generate p r o f i t s which hopefully are greater than a simple buy and hold p o l i c y . As mentioned i n Chapter 2, Alexander had done considerable t e s t i n g of the f i l t e r r u l e , and a f t e r correcting for biases i n previous studies, concluded that a f t e r transaction and dividend costs, s u f f i c i e n t p r o f i t s would not be generated to beat a buy and hold p o r t f o l i o . Table VII summarizes the r e s u l t s obtained when a f i l t e r r u l e , with f i l t e r sizes ranging from .5% to 50%, was . applied to the monthly price changes for f o r t y - f i v e s e c u r i t i e s . In a l l cases the f i l t e r rule generated, on the average, negative returns ranging from a minus 121.0% for a f i l t e r size of two percent, to a minus 4.1% for a f i l t e r s ize of 20%. The reader i s referred to Table VIII where the t o t a l rate of return for each security i s tabulated and compared with what the p a r t i c u l a r stock would have earned i f i t had been purchased at the beginning of the period and held for the duration. The bottom of the table displays the mean return for a l l of the s e c u r i t i e s i n the sample. This was the average return before transaction costs were applied as well as any dividend adjustments. There were s l i g h t l y more negative returns per f i l t e r than p o s i t i v e . The median number of p o s i t i v e returns 45 was 20 or approximately 44%. This corresponded very c l o s e l y to the percentage of p o s i t i v e returns for a l l 415 firms i n the data. TABLE V I I S u m m a r i z a t i o n o f F i n d i n g s o f F i l t e r R u l e T e s t s .005 .01 .02 .05 .10 .20 .25 .50 B&H* No. o f p o s i t i v e r e t u r n s ( t o t a l o f 45) 21 20 20 18 22 20 13 16 17 No. o f p i s i t i v e r e t u r n s on s h o r t p o s i t i o n 23 23 23 20 23 23 13 12 No. o f p o s i t i v e r e t u r n s on l o n g p o s i t i o n s 18 18 16 17 21 18 11 13 mean p e r c e n t r e t u r n p e r f i l t e r ( l o s s ) (109.0). (112.6) (121.0) (90.3) (33.8) (4.1) (83.0) (82.7) 29.9 mean p e r c e n t r e t u r n on s h o r t p o s i t i o n s ( l o s s ) (84.9) (61.4) (62.1) (50.0) (22.7) (10.9) (43.6) (34.1) mean p e r c e n t r e t u r n on l o n g p o s i t i o n s ( l o s s ) (24.0) (51.2) (58.9) (40.3) (11.1) 6.8 (39.4) (48.6) no. o f p o s i t i v e r e t u r n s f o r a l l f i r m s (415) 185 182 184 175 171 174 155 145 a v e r . no. o f t r a n s a c t i o n s p e r f i l t e r 96 96 96 82 62 37 30 17 * Buy and H o l d P o r t f o l i o In comparing the short and long positions the data indicates that the long positions were more p r o f i t a b l e , i n terms of o v e r - a l l mean rate of return and number of p o s i t i v e returns per f i l t e r . This can be v e r i f i e d by examination of Table IX which compares the returns generated for both the short and long positions per stock as well as the o v e r - a l l mean return for each f i l t e r size for a l l s e c u r i t i e s combined. However, the number of po s i t i v e returns for both positions were r e l a t i v e l y close to one another. For a f i l t e r size of 20%, which appeared to be the most successful f i l t e r , the mean rate of return was a p o s i t i v e 6.8% for 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 rate of return of over 29 percent. It i s s i g n i f i c a n t to note that the number of p o s i t i v e returns for a l l 415 s e c u r i t i e s i s close to 50.percent for the t o t a l for a l l f i l t e r s i z e s . Indicating that the l i k e l i h o o d of any p a r t i c u l a r firm earning a po s i t i v e return i s not s i g n i f i c a n t l y greater than the p o s s i b i l i t y of earning a negative return. Alexander, as well as Fama and Blume (7), found there was evidence of persistence or po s i t i v e dependence i n very short-term price movements. By short-term they meant d a i l y or even i n t e r - d a i l y price movements. Since the data i n t h i s paper consisted of monthly price movements, t h i s might explain why the results 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. It also casts serious doubts as to the v a l i d i t y of using monthly price data. In order for the f i l t e r to be e f f e c t i v e , i t must catch a l l movements i n the pric e . Monthly price changes TABLE VIII F i l t e r Trading Rules as Compared to a Buy and Hold Policy F i l t e r Size Stock .005 .01 .02 .05 .10 .20 .25 . 50 B&H BCC 1.410 -.130 .346 -2.4 60 1.635 -2.656 -3.044 3.667 6.226 BR 2,556 2.457 2. 605 1.790 1.741 1.211 1.000 .452 .308 BSM 1.808 1.808 1. 808 -1.038 -.885 -1.115 -.808 1.556 .103 CGQ 1.212 1.212 1.187 2.612 1.400 -.900 .414 -1.067 1.357 CMNA COP 2.048 2.048 1.290 1.513 -1.076 .555 1.173 .922 .143 CPG . 390 .390 . 390 -.878 4.488 9.585 10.634 2. 604 . 607 CRI .247 .166 -.014 .096 .241 .667 . 809 0.000 .413 CSR -.428 .682 . 830 1.830 1.317 1.510 1.208 .733 1. 214 CST -3.556 -3.556 -3.556 -2.889 -2.667 -8.333 -7.333 -.571 1.8571 DVM . 849 .849 1.068 1.068 .808 .298 -.440 -.355 .560 GDC -4.730 -4.541 -4.541 -3.703 -5.373 -2.795 -2.205 -3.282 .895 GIM 1.360 1.067 .348 .101 1.258 1. 653 .203 2.441 5.263 GRL 3. 947 3.947 3.947 3.947 2.526 -.174 -1.333 1.200 .471 MM -1.400 -1.400 -1.800 -.400 -4.818 2.067 .600 4.667 1.500 MTW 1. 953 1.953 1.953 1.739 2.096 1.662 1.690 1. 592 .096 NCR .655 .655 .655 -.379 .793 -1.483 -3.621 -.379 1.125 NIN 1. 452 1. 452 1.452 1.167 1.024 1.929 .905 -.810 .560 NOV 5.660 5.660 5.132 9.434 8.604 12.151 11.660 5.509 3". 647 NPM -1.481 -1.481 -1.481 -1.037 -3.630 -1.704 -2.963 1.333 3.474 PDL .871 . 337 .124 .374 1.162 2.060 1.735 -.091 2.055 PEEL -1.467 -1.467 -1.467 -1.462 1. 333 1.926 . 741 -.687 .828 PSS 2.124 1.992 3.642 4. 358 5. 992 5.710 2. 617 1.963 . 298 QUT -8.056 -8.056 -7.278 -5.056 -1.944 -.050 -2.550 1.545 1.438 RV -5.960 -5.960 -5.960 -3.760 -.010 -1.120 3.980 .900 .600 SBC .686 .686. .514 1.486 .371 -1.175 -2.100 -1.980 .548 SCH -2.756 -2.756 -2.000 -5.378 -5.810 .222 -.130 -.444 .148 SRD -10.400 -10.400 -10.400 -12.000 -9.000 -11.400 -7.200 -3.500 1.250 SS -.303 .667 .545 . 848 3.636 .924 -7.030 1.750 2.759 TABLE V I I I ( C o n t i n u e d ) F i l t e r T r a d i n g R u l e s as Compared t o a Buy and H o l d P o l i c y F i l t e r S i z e S t o c k .005 .01 .02 .05 .10 .20 .25 .50 B&H TR .533 .533 .533 .267 .133 -1.867 -.400 1.156 2.000 TRJ -14.167 -14.167 -16.611 -3.944 9.056 17.500 12.389 -.929 2. 571 TWTNEW 5.869 5.869 3.174 4.043 3.522 2.959 -.739 -5.250 1.438 VN 1.500 1.500 1.500 1.500 .800 2.000 .800 -3.200 .909 WMI 2. 362 2.499 2.3.52 2.423 1.370 .220 .602 .291 .791 ATS -1.659 -1.659 -1.659 -1.098 -.902 -.805 -2.317 -.707 .268 CCD .441 .441 .441 .147 .088 . 353 .324 .029 .206 CYD 4.045 4.045 3.985 3.258 5.470 4.076 -.409 1.637 .095 DVN 2.233 2.233 2.033 .267 2.433 .800 . 800 1.371' .964 JY 1.525 1.525 1.525 1.875 . 900 .600 .075 — 1 . 4 5 0 .225 JRC -.565 -.565 -.565 .913 2.696 2.575 . 875 .711 .261 NGD -4.250 -4.250 -4.250 -4.450 -4.350 -1.364 -.879 -1.061 .2812 PPT 1.305 1.416 1.093 .960 .952 1.527 1.752 .70 8 .522 RHM 4.111 4.111 3.381 3.698 2.032 1.190 1.127 -2.349 .667 SLO 4.246 4.246 4.277 4.031 3.431 3.754 2.585 3.292 3.385 TMX 2.192 2.356 2.740 2.795 2.000 -.712 -2.521 -.110 .493 GRV -2.750 -2.750 -2.750 -1.812 -2.938 -2.529 -5.059 -4.250 .5185 A v e r a g e -109.0% -112.6% -121.0% -90.3% — 33.8 % -4 . 1% -83.0% -82.7% 29.9% bury from view a l l the d a i l y price changes. Hence we are ignoring the f i l t e r rule during 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 price changes that would have activated the f i l t e r well before the end of the month. However, since the entire study has u t i l i z e d monthly data, there appears to be a consistent pattern displayed i n a l l tes t s . Namely, security price changes, when viewed from an economic perspective, appear to move i n a random manner. 51 TABLE IX R e t u r n s G e n e r a t e d From S h o r t and L o n g P o s i t i o n s F i l t e r S i z e S t o c k 005 .01 .02 .05 S h o r t Long S h o r t Long S h o r t L o n g S h o r t Long BCC -191. 4 232. 4 -268. 4 144. 5 -244. 6 179. 2 -384. 9 38. 8 BR 104. 9 50. 7 100. 0 45. 6 107. 4 53. 0 66 . 6 12. 3 BSM 82. 7 -1. 9 82. 6 - 1 . 9 82. 6 - 1 . 9 -59. 6 -144 . 2 CGQ 1. 3 20. 0 1. 2 20. 0 0. 0 18. 7 71. 2 90. 0 COP 80. 0 24. 8 80. 0 24. 8 42. 0 -13. 6 55. 0 -3. 8 CPG -1. 2 59. 8 - 1 . 2 59. 8 -1. 2 -59. 8 -64. 6 -123. 1 CRI -8. 5 -66. 9 -12. 5 -70. 9 -21. 5 -79. 8 -16. 0 -74. 4 CSR -78. 9 -63. 9 -91. 5 -76. 6 -15. 9 -1. 0 34. 0 48. 9 CST -250. 0 -205. 5 -250. 0 -205. 5 -250. 0 -205. 5 -216. 6 -172. 2 DVM 17. 1 -32. 2 17. 1 -32. 2 28. 0 -21. 2 28. 0 -21. 2 GDC -282. 4 -290 . 5 -271. 6 -279. 7 -272. 9 -281. 0 -231. 0 -239. 1 GIM -226. 9 262. 9 -241. 5 248. 3 -277. 5 212. 3 -289. 8 200. 0 GRL 176. 3 118. 4 176. 3 118. 4 176. 3 118. 4 176. 3 118. 4 GRV 159. 3 -215. 6 -159. 3 -215. 6 -159. 3 -215. 6 -112. 5 -168. 7 MM -145. 0 105. 0 -145. 0 -105. 0 -165. 0 115. 0 -95. 0 -45. 0 MTW 92. 9 2. 3 92. 9 2. 3 92. 9 2. 3 82. 6 -8. 6 NCR 17. 2 -51. 7 17. 2 -51. 7 17. 2 -51. 7 -34. 4 -103. 4 NIN 54. 7 -9. 5 54. 7 09. 5 54. 7 -9. 5 40. 4 -23. 8 NOV 166. 0 300. 0 166. 0 300. 0 139. 6 273. 5 354. 7 488. 6 NPM -196. 3 -51. 8 -196. 3 -51. 8 -196. 3 -51. 8 -174. 0 -29. 6 PDL -53. 8 40. 9 -80. 5 14. 2 -91. 1 3. 6 -78. 7 16. 1 PEEL -113. 3 -133. 3 -113. 3 -133. 3 -113. 3 -133. 3 -119. 2 -126. 9 PSS 91. 4 20. 9 86. 6 12. 5 169. 1 95. 0 205. 0 130. 8 QUT -466. 6 -438. 8 -466. 6 -438. 8 -427. 7 -400. 0 -316. 6 -288. 8 RV -328. 0 -368. 0 -328. 0 -368. 0 -328. 0 -368. 0 -218. 0 -258. 0 SBC 10. 0 -41. 4 10. 0. -41. 4 1. 4 -50. 0 50. 0 - 1 . 4 SCH -160. 0 -215. 5 -160. 0 -215. 5 -122. 2 -177. 7 -286. 6 -351. 0 SRD -1700 i . -1700 i . -570. 0 -570. 0 -570. 0 -570. 0 -650. 0 -650. 0 SS -136. 3 6. 0 087. 8 54 . 5 93. 9 48. 4 -78. 7 63. 6 TR -40. 0 -6. 6 -40. 0 -6. 6 -40. 0 -6. 6 -53. 3 -20. 0 TRJ -827. 7 -688. 0 -827. 7 -688. 0 -983. 3 -811. 0 -316. 6 -177. 7 TWTNEW 243. 4 243. 4 243. 4 243. 4 108. 6 108. 6 152. 1 152. 1 VN 50. 0 0. 0 50. 0 0. 0 50. 0 0. 0 -100. 0 -150. 0 WMI 83. 0 53. 4 89. 8 60. 0 82. 5 48. 3 86. 0 51. 8 ATS -96. 3 -169. 5 -96. 3 -169. 5 -96. 3 -169. 5 -68. 2 -141. 4 CCD 11. 7 -67. 6 11. 7 -67. 6 11. 7 -67. 6 -2. 9 -82. 3 CYD 193. 9 110. 6 193. 9 110. 6 190. 9 107. 5 154. 5 71. 2 DVN 66. 6 56. 6 66. 6 56. 6 56. 6 46. 6 -3. 3 -13. 3 JY 65. 0 -13. 7 65. 0 -13. 7 65. 0 -13. 7 82. 5 3. 7 JRC -54. 3 -100. 0 -54. 3 -100. 0 -54. 3 -100. 0 19. 5 -28. 2 NGD -235. 0 -290. 0 -235. 0 -290. 0 -235. 0 -290. 0 -245. 0 -300 . 0 PPT 39. 1 -8. 6 44. 6 -3. 0 28. 5 -19. 2 21. 9 25. 8 RHM 172. 2 138. 8 171. 4 138. 8 135. 7 91. 2 151. .5 107. 1 SLO 20. ,0 304. 6 20. 0 304. 6 21. 5 306. 1 16. 9 286. 1 TMX 84. 9 34. .2 93. 1 42. 4 112. .3 61. 6 115. 0 64. . 3 A v e r a g e -84. ,9 -24. ,0 -61. ,3 -51. 2 -62. 1 -58. 9 -50. 0 -40. ,3 52 TABLE IX R e t u r n s G e n e r a t e d From S h o r t and L o n g P o s i t i o n s F i l t e r S i z e S t o c k .10 .20 .25 .50 S h o r t L o n g S h o r t Long S h o r t L o n g S h o r t L o n g BCC - 1 8 0 . 1 2 4 3 . 6 - 3 3 0 . 0 - 3 5 . 5 - 3 3 0 . 0 - 7 4 . 4 0 . 0 2 6 6 . 7 BR 0 . 0 0 . 0 4 1 . 1 - 1 7 . 8 0 . 0 0 . 0 5. 2 - 6 0 . 0 BSM - 5 1 . 9 - 1 3 6 . 5 - 6 5 . 3 - 1 4 6 . 1 - 5 0 . 0 - 1 3 0 . 7 69 . 4 - 1 3 . 8 CGQ 1. 2 38 . 7 - 1 1 2 . 8 - 7 7 . 1 - 4 7 . 1 - 1 1 . 4 - 1 0 6 . 1 - 7 2 . 7 COP - 6 3 . 9 - 1 4 3 . 6 1 7 . 4 - 6 1 . 9 3 6 . 1 - 1 8 . 7 2 6 5 . 0 - 3 3 5 . 0 CPG 2 0 3 . 6 1 4 5 . 1 4 5 0 . 0 4 0 8 . 5 5 0 3 . 6 4 5 9 . 7 1 1 6 . 0 4 4 . 3 CRI - 1 3 . 4 - 6 2 . 4 - 3 . 5 - 2 9 . 8 0 . 0 - 1 9 . 1 0 . 0 0 . 0 CSR 4 . 5 2 7 . 2 2 0 . 4 3 0 . 6 0 . 0 2 0 . 7 0. 0 - 2 6 . 6 CST - 2 0 5 . 5 - 1 6 1 . 1 - 4 8 8 . 8 - 4 4 4 . 4 - 4 3 8 . 8 - 3 9 4 . 4 - 7 5 . 0 - 8 2 . 1 DVM 1 5 . 0 i 34 . 2 - 7 . 1 - 6 3 . 1 - 4 4 . 0 - 1 0 0 . 0 - 3 7 . 6 - 9 7 . 8 GDC - 3 0 9 . 6 - 3 2 7 . 7 - 1 8 0 . 0 - 1 9 8 . 7 - 1 4 8 . 8 - 1 7 1 . 5 - 2 2 0 . 9 2 0 7 . 2 GIM - 2 1 7 . 9 2 4 3 . 8 - 1 1 8 . 6 1 8 3 . 8 - 1 5 9 . 3 7 9 . 6 - 4 7 . 4 - 2 7 . 1 GRL 1 0 5 . 2 4 7 . 3 - 4 3 . 4 - 7 3 . 9 - 1 0 0 . 0 - 1 4 5 . 8 3 3 . 3 - 1 3 . 3 GRV - 1 6 8 . 7 - 2 2 5 . 0 - 1 4 7 . 0 - 2 0 5 . 8 - 2 7 3 . 5 - 3 3 2 . 3 - 2 3 1 . 2 - 2 9 3 . 7 MM - 3 0 9 . 1 - 2 7 2 . 7 5 3 . 3 5 3 . 3 - 2 0 . 0 - 2 0 . 0 1 9 3 . 3 1 7 3 . 3 MTW 1 0 0 . 0 9 . 2 7 5 . 3 - 9 . 2 7 5 . 8 - 6 . 8 7 3 . 0 - 1 7 . 7 NCR 2 4 . 1 - 4 4 . 8 - 8 9 . 6 - 1 5 1 . 7 - 1 9 6 . 5 - 2 5 8 . 6 - 3 4 . 4 - 1 0 0 . 0 NIN 3 3 . 3 - 3 0 . 9 7 8 . 5 1 4 . 2 2 8 . 5 - 3 8 . 1 - 5 7 . 1 1 1 1 . 9 NOV 3 1 3 . 2 4 4 7 . 1 4 9 0 . 5 6 2 4 . 5 4 6 4 . 1 6 0 0 . 0 1 5 8 . 4 2 9 2 . 4 NPM - 3 0 3 . 7 - 1 5 9 . 2 - 2 0 7 . 4 - 6 2 . 9 - 2 7 0 . 3 - 1 2 5 . 9 - 7 0 . 8 104 . 1 PDL - 4 3 . 6 5 9 . 9 9 1 . 1 14 . 9 1 2 . 0 6 1 . 0 - 5 4 . 5 - 5 4 . 5 PEEL 1 6 . 6 1 6 . 6 5 1 . 8 4 0 . 7 - 7 . 4 - 1 8 . 5 - 7 1 . 8 - 9 6 . 8 PSS 2 8 6 . 6 2 1 2 . 5 2 7 2 . 8 1 9 8 . 1 - 3 2 . 7 1 0 4 . 3 4 . 6 9 1 . 5 QUT - 1 6 1 . 1 - 1 3 3 . 3 - 6 0 . 0 - 4 5 . 0 - 1 8 5 . 0 - 1 6 0 . 0 0 . 0 5 4 . 0 RV - 3 1 . 0 - 7 0 . 0 - 8 6 . 0 - 1 2 6 . 0 1 6 9 . 0 1 3 9 . 0 - 7 5 . 0 . 9 0 . 0 SBC - 5 . 7 - 5 7 . 1 - 8 0 . 0 - 1 3 7 . 5 - 1 2 6 . 2 - 1 8 3 . 7 - 1 6 . 3 - 1 8 1 . 6 SCH - 3 0 9 . 5 - 3 7 1 . 4 - 3 . 7 - 7 4 . 0 - 1 8 . 5 - 9 4 . 4 - 3 1 . 4 - 1 1 2 . 9 SRD - 5 0 0 . 0 - 5 0 0 . 0 - 6 2 0 . 0 - 6 0 0 . 0 - 3 6 0 . 0 - 3 6 0 . 0 - 2 2 5 . 0 - 2 2 5 . 0 SS 6 0 . 6 2 0 3 . 0 - 3 9 0 . 0 2 2 3 . 3 - 4 7 2 . 7 - 3 3 0 . 3 - 5 8 . 3 1 3 3 . 3 TR - 6 0 . 0 - 2 6 . 6 - 1 6 0 . 0 - 1 2 6 . 6 - 8 6 . 6 - 5 3 . 3 0 . 0 1 5 . 6 TRJ 3 3 3 . 3 4 7 2 . 2 7 5 5 . 5 8 9 4 . 4 500 . 0 6 3 8 . 8 - 1 2 1 . 4 - 7 1 . 4 TWTNEW 1 2 6 . 1 1 3 4 . 7 9 7 . 8 9 7 . 8 - 8 6 . 9 - 8 6 . 9 - 3 5 8 . 3 - 2 6 6 . 6 VN 1 5 . 0 - 3 5 . 0 7 5 . 0 2 5 . 0 1 5 . 0 - 3 5 . 0 - 1 8 5 . 0 - 2 3 5 . 0 WMI 3 3 . 4 3. 5 - 2 2 . 7 - 5 5 . 3 - 3 . 6 - 3 6 . 2 - 1 2 . 8 - 3 9 . 6 ATS - 5 8 . 5 - 1 3 1 . 7 - 5 3 . 6 - 1 2 1 . 9 - 1 2 9 . 3 - 1 9 7 . 6 - 5 1 . 2 - 1 1 9 . 5 CCD - 5 . 8 - 8 5 . 2 7. 3 - 7 2 . 1 5. 9 - 7 3 . 5 - - 8 . 8 - 7 9 . 4 CYD 2 6 5 . 1 1 8 1 . 8 1 9 5 . 4 1 1 2 . 1 - 2 8 . 7 - 1 1 2 . 1 7 5 . 0 ^ 5 . 0 DVN - 3 1 . 6 - 4 1 . 6 7 6 . 6 3 3 . 3 - 5 . 0 - 1 5 . 0 4 6 . 7 - 9 . 7 JY 3 3 . 7 - 4 5 . 0 1 8 . 7 - 6 0 . 0 - 7 . 5 8 5 . 0 - 9 5 . 0 - 1 5 0 . 0 JRC 1 0 8 . 6 6 0 . 8 1 0 5 . 0 5 2 . 5 2 0 . 0 - 3 2 . 5 2 8 . 0 - 5 7 . 0 NGD - 2 4 0 . 0 - 2 9 5 . 0 - 8 1 . 8 - 1 5 4 . 5 - 5 7 . 6 - 1 3 0 . 3 - 6 6 . 6 - 1 3 9 . 3 PPT 2 1 . 4 - 2 6 . 3 5 0 . 2 0. 2 6 1 . ,5 1 1 . 5 0 . 0 - 2 9 . 2 RHM 6 8 . 2 2 3 . 8 2 6 . 2 - 6 . 4 2 3 . ,0 - 9 . 5 - 1 5 7 . 1 - 1 7 7 . 7 SLO 2. 3 2 4 0 . ,1 1 8 . 5 2 7 . 7 - 4 0 . ,0 1 6 . 9 - 4 . .6 2 3 3 . .8 TMX 7 5 . ,3 24 . 6 - 6 0 . 3 - 1 0 9 . ,5 - 1 5 0 . , 6 - 2 0 1 . 4 - 3 0 . ,1 - 8 0 . ,8 A v e r a g e - 2 2 . ,7 - 1 1 . ,1 - 1 0 . ,9 6. 9 - 4 3 . ,6 - 3 9 . 4 - 3 4 . ,1 - 4 8 . ,6 5 3 S t a t i o n a r i t y o f R e t u r n s I n k e e p i n g w i t h t h e d e f i n i t i o n o f a random w a l k , t h e t h e o r y s t a t e s t h a t t h e r e t u r n s must be i d e n t i c a l l y d i s t r i b u t e d . I n i t i a l l y , i t was f e l t by r e s e a r c h e r s t h a t t h e r e t u r n s f r o m s e c u r i t i e s c o n f o r m e d t o a n o r m a l d i s t r i b u t i o n w h i c h c o u l d be c o m p l e t e l y d e s c r i b e d by two moments; t h e mean and v a r i a n c e , and f u r t h e r d i s t r i b u t i o n s had f i n i t e v a r i a n c e . R e c e n t s t u d i e s by Fama (6) and M a n d e b r o t (14) s u g g e s t e d t h a t r e t u r n s ..conformed . t o a s t a t i o n a r y s y m e t r i c d i s t r i b u t i o n w i t h i n f i n i t e v a r i a n c e . Thus t h e s t a n d a r d d e v i a t i o n l o s e s i t s e f f e c t i v e n e s s a s an a c c u r a t e measure o f r i s k . As sample s i z e s a r e i n c r e a s e d t o a p p r o x i m a t e t h e t r u e p o p u l a t i o n , t h e s t a n d a r d d e v i a t i o n w i l l i n c r e a s e e r r a t i c a l l y . A good s u b s t i t u t e f o r t h e s t a n d a r d d e v i a t i o n i s t h e mean a b s o l u t e d e v i a t i o n , (MAD). T h e r e f o r e , i n d e s c r i b i n g t h e d i s -t r i b u t i o n o f r e t u r n s f o r t h e sample s t o c k s , t h e MAD was u s e d a c c o r d i n g t o t h e f o l l o w i n g f o r m u l a : MAD = - 2 i = l where r^_ = r a t e o f r e t u r n r = mean r a t e o f r e t u r n The d a t a was d i v i d e d i n t o two t i m e p e r i o d s o f f i v e y e a r s e a c h . F o r e a c h p e r i o d t h e mean and MAD were c a l c u l a t e d . T a b l e X d e s c r i b e s t h e r e s u l t s . The mean and MAD were c a l c u l a t e d f o r t h e two t i m e p e r i o d s t o d e t e r m i n e w h e t h e r o r n o t t h e d i s t r i b u t i o n o f r e t u r n s were s t a t i o n a r y o v e r t i m e . As T a b l e X i n d i c a t e s , o u t o f t h i r t y f i r m s TABLE X C o m p a r i s o n o f S h i f t Between Mean M o n t h l y R a t e o f R e t u r n and MAD f o r P e r i o d Mar. 1963 t o F e b . 1968 & Mar. 1968 t o F e b . 1973 F i r m Mean MAD Mean MAD C V ( 1 ) * CV ( 2 ) * BCC 1. 0215 . 0660 1 .0056 .0882 .2.069 15. 75 BSM 1. 0060 .1457 .9746 .1236 24.283 4. 866 CGQ • 9997 .1188 1 .0352 .1411 396.0 4. 008 COP 1. 0041 .0714 .9795 .0976 17.415 4. 761 CPG 1. 0271 .1718 1 .0204 .1941 .6.339 9. 514 CRI . 9926 .0535 .9963 .0312 7.229 8. 432 CST 1. 0570 .2212 1 .0400 .2531 3.881 6. 328 DVM 1. 0054 .1069 1 .0051 .1232 19.796 24. 157 GDC 1. 0137 .1763 1 .1478 . 3449 5.569 2. 334 GIM 1. 0132 .0831 1 .0275 .0968 6.295 . 3. 520 GRL 1. 0181 .1497 1 .0053 . 1424 8.270 26. 86 8 GRV 1. 0356 .1709 1 .0326 .1751 4 . 800 5. 371 MM 1. 0355 .1380 1 .0102 .1790 3. 887 17. 548 MTW . 9817 .1282 1 . 0175 .1741 7.005 9. 949 NCR 1. 0618 . 2006 1 .0029 .1492 3.246 51. 448 NIN 1. 0197 .1384 .9959 .0993 7.025 24. 219 NOV 1. 0007 .1284 1 .0740 .2283 183.4 3. 085 NPM 1. 0331 .1635 1 .0318 .1595 4.939 5. 0157 PB 1. 0152 .0871 1 .0322 .1272 5.730 3. 950 PDL 1. 0046 . 0578 1 .0198 . 0727 12.560 3. 670 PEEL 1. 0101 .1262 1 .0077 .1661 12.495 21. 571 PSS 1. 0212 .1159 .9800 .0883 5.467 4. 415 QUT 1. 0272 .1328 1 .0025 .1068 4.882 42. 720 RV 1. 0142 .0679 1 .0135 .1669 4.782 12. 363 SBC 1. 0006 .0786 1 .0413 .2206 131.0 5. 3414 SCH 1. 0187 .1473 .9799 .116 3 7.877 5. 786 SRD 1. 0654 .2263 1 .0096 .1663 3.460 17. 322 SS 1. 0243 .1240 1 . 0175 .1197 5.103 6. 840 TRJ 1. 0605 .2216 1 .0193 .1599 3.663 . 8. 285 TWTNEW 1. 0410 .1593 1 .0087 .1548 3.885 17. 793 * c o e f f i c i e n t o f v a r i a t i o n 55 tested only seven appeared to display any s t a b i l i t y with respect to t h e i r mean return. Eight firms showed an increase i n the mean return while f i f t e e n firms showed a noticable drop i n average return. S i m i l a r l y , there were no instances where the computed c o e f f i c i e n t s of v a r i a t i o n (CV) remained the same. From th i s i t was concluded that there was no relat i o n s h i p between the mean and MAD for a l l the firms tested, i n d i c a t i n g not only are the d i s t r i b u t i o n of returns non-stationary but t h e i r shape changes as well. Thus i t would appear upon th i s cursury examination that the security price changes do not completely conform to a random walk. However, as was stated e a r l i e r , an e f f i c i e n t market does not require a random walk but a random walk would be a good indicator of e f f i c i e n c y . Had the d i s t r i b u t i o n of returns as tested, proved to be stationary, then we would have been able to make p r o b a b i l i t y statements about the percentage price changes to be expected i n the future, and the h i s t o r i c a l mean return and standard deviation would have provided us with a good estimate of the future expected r i s k and return. As Fama states: "The random walk model does not say, however, that past information i s of no value i n assessing d i s -t r i b u t i o n s of future returns. Indeed since return d i s t r i b u t i o n s are assumed to be stationary through time, past returns are the best source of such information. The random walk model does say, however, that the sequence, (or the order), of the past returns i s of no consequence i n assessing d i s t r i b u t i o n s of future returns." (5) 56 The s h i f t i n mean r e t u r n s f o r t h e sample f i r m s m i g h t be e x p l a i n e d i n t h a t t h e d a t a d i d n o t a p p e a r t o c o v e r one c o m p l e t e b u s i n e s s c y c l e . The c u m u l a t i v e m o n t h l y i n d e x f o r t h e e n t i r e VSEM shows an IPR o f .8930 f o r t h e l a s t month o f t h e s t u d y . T h i s d e c l i n e i n t h e m a r k e t was p a r t i c u l a r l y e v i d e n t f o r t h e l a s t y e a r o f t h e s t u d y . T h i s s t u d y d i d n o t a s c e r t a i n w h e t h e r o r n o t s e c u r i t y r e t u r n s c o n f o r m e d t o a n o r m a l d i s t r i b u t i o n w h i c h c a n be c o m p l e t e l y d e s c r i b e d by i t s mean and s t a n d a r d d e v i a t i o n . I t was f e l t by t h e w r i t e r t h a t t h i s was b e y o n d t h e s c o p e o f t h e p r e s e n t s t u d y . However, a t e s t was c o n d u c t e d t o s e e w h e t h e r o r n o t t h e m o n t h l y r e t u r n s f o r t h e VSEM c o n f o r m e d t o a n o r m a l d i s t r i b u t i o n . The h i g h e s t and l o w e s t m o n t h l y IPR's f o r t h e p e r i o d were r e s p e c t i v e l y , 1.3222 and .8310. The r a n g e o f IPR's i n b e t w e e n were s u b s e q u e n t l y g r o u p e d i n t o s e v e n c l a s s i n t e r v a l s o f e q u a l s i z e . The r e s u l t s o f t h i s g r o u p i n g a r e d e t a i l e d b e l o w i n T a b l e XI. TABLE XI F i t t i n g a Normal C u r v e t o O b s e r v e d D a t a C l a s s L i m i t s N o r m a l C u r v e F r e q u e n c i e s O b s e r v e d F r e q u e n c i e s .8310-.90117 .90117-.9713 .9713-1.0415 1.0415-1.1116 1.1116-1.1818 1.1818-1.2519 1.2519-1.3222 9 25 37 30 14 3 1 8 29 43 28 5 2 4 The n o r m a l c u r i v e f r e q u e n c i e s were o b t a i n e d by c o m p u t i n g t h e r e s p e c t i v e z - v a l u e s f o r t h e c l a s s b o u n d a r i e s . To c o n f i r m w h e t h e r t h e n o r m a l c u r v e p r o v i d e s a r e a s o n a b l y good f i t t o t h e 57 o r i g i n a l d i s t r i b u t i o n the chi - square test-of goodness of f i t was used i n accordance with the following formula, at a l e v e l of significance of .05: i= l e. 1 where n = actual frequencies e = expected frequencies 2 A value of X =4.17 was obtained i n d i c a t i n g that the observed d i s t r i b u t i o n constitutes a sample from a population having a normal d i s t r i b u t i o n . R i s k a n d R e t u r n o f V S E M V e r s u s R i s k a n d R e t u r n T S E M 58 T h e p r e v i o u s s e c t i o n s h a v e d e a l t p r i m a r i l y w i t h t h e p r o b l e m o f d e t e r m i n i n g w h e t h e r o r n o t s e c u r i t y p r i c e c h a n g e s m o v e i n d e p e n d e n t l y o f o n e a n o t h e r . I f i t i s g e n e r a l l y r e c o g n i z e d t h a t t h e s e p r i c e m o v e m e n t s c o n t a i n n o i n f o r m a t i o n w h i c h c a n b e u s e d t o e a r n a t r a d i n g p r o f i t a b o v e w h a t c o u l d b e a t t a i n e d w i t h a n a i v e b u y a n d h o l d p o l i c y , w e h a v e r e a c h e d t h e f i r s t l e v e l i n o u r d e f i n i t i o n o f a n E f f i c i e n t M a r k e t . T h i s d e f i n i t i o n i s p r e d -i c a t e d o n t h e a s s u m p t i o n t h e r e i s c o m p l e t e d i s s e m i n a t i o n o f i n f o r m a t i o n , p r i c e s f l u c t u a t e f r e e l y , a n d t h e r e a r e a g r e a t m a n y i n v e s t o r s a c t i n g r a t i o n a l l y i n t h e i n t e r p r e t a t i o n o f a n y n e w s t h e y r e c e i v e . I f i n d i v i d u a l s e c u r i t y p r i c e s b e h a v e i n a n i n d e p e n d e n t m a n n e r t h e n t h e s u m o f t h e i r m o v e m e n t s a c r o s s s e c u r i t i e s w i l l e q u a l a m a r k e t p r o t f o l i o i n w h i c h t h e m o n t h l y r e t u r n s w o u l d b e n o r m a l l y d i s t r i b u t e d . B a s e d o n t h i s o b s e r v a t i o n t h e s t a n d a r d d e v i a t i o n o f r e t u r n s w a s u s e d a s t h e m e a s u r e o f v a r i a b i l i t y o f r e t u r n s , h e n c e , a g o o d m e a s u r e o f r i s k . T h e r e f o r e , t h e a v e r a g e m o n t h l y r a t e o f r e t u r n f o r t h e V S E M a n d s t a n d a r d d e v i a t i o n w e r e c o m p a r e d w i t h t h e a v e r a g e m o n t h l y r a t e o f r e t u r n f o r t h e T S E M a n d i t s s t a n d a r d d e v i a t i o n . T a b l e X I I d i s p l a y s t h e a c t u a l m o n t h l y r e t u r n s ( I P R ) f o r t h e p e r i o d a s w e l l a s t h e n u m b e r o f f i r m s i n c l u d e d i n t h e i n d e x f o r e a c h m o n t h . T a b l e X I I I i n d i c a t e s t h e r e l a t i o n s h i p b e t w e e n r i s k a n d r e w a r d f o r b o t h t h e V S E M a n d T S E M . 59 CHAPTER F I V E INTERPRETATION OF NUMERICAL RESULTS G e n e r a l S t a t e m e n t o f F i n d i n g s The f i n d i n g s o f t h i s s t u d y i n d i c a t e t h e p r i c e movements o f t h e L i s t e d V a n c o u v e r M i n i n g S t o c k s c o n f o r m t o t h e w e a k l y ^ e f f i c i e n t m a r k e t h y p o t h e s i s , w h i c h s a y s t h a t h i s t o r i c a l p r i c e d a t a f o r s e c u r i t i e s c o n t a i n no i n f o r m a t i o n w h i c h c a n be u s e d t o e a r n a t r a d i n g p r o f i t above what c o u l d be a t t a i n e d w i t h a n a i v e buy-a n d - h o l d i n v e s t m e n t s t r a t e g y . C o r r e l a t i o n o f P r i c e Changes As was e x p e c t e d , t h e s t u d y shows t h e r e were few s i g n i f i c a n t c o r r e l a t i o n s between l a g g e d p r i c e c h a n g e s . E x c e p t f o r a l a g o f 3 months, t h e m a j o r i t y o f t h e s i g n s o f t h e c o e f f i c i e n t s were n e g a t i v e i n d i c a t i n g p e r h a p s t h e r e were a l t e r n a t i n g p a t t e r n s b e i n g g e n e r a t e d i n t h e r e t u r n s . L a r g e r e t u r n s f o l l o w e d by s m a l l e r r e t u r n s e t c . The m a g n i t u d e o f t h i s d e p e n d e n c y a p p e a r e d t o be q u i t e low as e v i d e n c e d by t h e low c o e f f i c i e n t s . The r u n s t e s t s a l s o v e r i f y t h i s f a c t . Had t h i s a l t e r n a t i n g p a t t e r n b e e n s i g n i f i c a n t , t h e r u n s t e s t s w o u l d have i n d i c a t e d more r u n s t h e n e x p e c t e d . F u r t h e r m o r e , t h e f i l t e r r u l e s s h o u l d h a v e p i c k e d o u t t h i s t y p e o f c o n s i s t e n t p a t t e r n . What was u n e x p e c t e d was t h e i n f o r m a t i o n d e r i v e d f r o m t h o s e f i r m s t h a t went b a n k r u p t o r were d e l i s t e d d u r i n g t h e p e r i o d . One w o u l d have e x p e c t e d t h e r e w o u l d have b e e n some t r e n d i n t h e p r i c e c h a n g e s . Y e t t h e 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 f o r a l l l a g g e d p e r i o d s a v e r a g e d o n l y 11.3% w h i c h was e q u i v a l e n t t o t h e 60 a c t i v e f i r m s . An a t t e m p t t o e x p l a i n t h i s m i g h t be p o s s i b l e w i t h t h e use o f C o o t n e r ' s model ( 3 ) . He s u g g e s t s s e c u r i t y p r i c e s c a n be v i e w e d as a s e r i e s o f c o n s t r a i n e d random f l u c t -u a t i o n s a r o u n d t h e t r u e i n t r i n s i c v a l u e . T h r o u g h t h e a c t i o n o f e x p e r i e n c e d ( i n f o r m e d ) i n v e s t o r s r e f l e c t i n g b a r r i e r s a r e e s t a b l i s h e d above and b e l o w t h e i n t r i n s i c v a l u e o f t h e s e c u r i t y . I n between t h e s e two b a r r i e r s t h e n a i v e i n v e s t o r o p e r a t e s . Thus, as t h e i n t r i n s i c v a l u e o f t h o s e f i r m s n e a r i n g b a n k r u p t c y d e c l i n e s , t h e l e v e l s o f t h e r e f l e c t i n g b a r r i e r s d e c l i n e as w e l l . However, t h e s e c u r i t y p r i c e s t i l l moves r a n d o m l y w i t h i n t h e s e two c o n s t r a i n t s . The a v e r a g e a b s o l u t e v a l u e o f t h e • c o e f f i c i e n t s was a p p r o x i m a t e l y t w i c e as l a r g e f o r t h e i n a c t i v e f i r m s , y e t t h e y c o u l d s t i l l o n l y a c c o u n t f o r , o r e x p l a i n , a p p r o x i m a t e l y 3.7% o f t h e p r i c e movement. Runs T e s t s From b o t h a s t a t i s t i c a l and i n v e s t m e n t p e r f o r m a n c e s t a n d -p o i n t , i t w o u l d a p p e a r t h e r e i s l i t t l e d e p e n d e n c e i n p r i c e c h a n g e s t h a t w o u l d i m p l y s u p e r i o r p e r f o r m a n c e c o u l d be had by s t u d y i n g p r e v i o u s m o n t h l y p r i c e d a t a . The m a r k e t m a k i n g p r o c e s s i n d i c a t e s t h e r e i s no g r o u p c o n s e n s u s r e g a r d i n g t h e t r e n d i n s e c u r i t y p r i c e s and p r i c e s a r e b a s e d on i n f o r m a t i o n o t h e r t h a n h i s t o r i c a l p r i c e movements. C o m p a r i n g t h e number o f p o s i t i v e r u n s w i t h n e g a t i v e r u n s s u g g e s t e d no m a j o r o r s i g n i f i c a n t d e p a r t u r e . The a v e r a g e number o f p o s i t i v e and n e g a t i v e r u n s f o r t h e sample were 2 7.18 and 2 8.18 r e s p e c t i v e l y . 61 The i m p l i c a t i o n t o be drawn f r o m t h e r e s u l t s o f t h e c o r r e l a t i o n c o e f f i c i e n t s and r u n s t e s t s i s a l t h o u g h t h e y d e p a r t s l i g h t l y f r o m a p u r e random s e r i e s t h e i r s i m i l a r i t y s u g g e s t s no s i g n i f i c a n t d e p a r t u r e . F i l t e r T e s t s T e c h n i c i a n s a r g u e d t h a t r u n s t e s t s and s e r i a l c o r r e l a t i o n t e c h n i q u e s were i n s e n s i t i v e t o p o s s i b l e c o m p l i c a t e d d e p e n d e n c i e s i n s u c c e s s i v e p r i c e c h a n g e s . However, t h e r e s u l t s o f t h e t r a d i n g r u l e s were e v e n more s t a r t l i n g . A l e x a n d e r , had a r g u e d t r a n s a c t i o n c o s t s and d i v i d e n d s were n o t r e l e v a n t when c o n s i d e r i n g t h e movement o f s e c u r i t y p r i c e s . From an i n v e s t o r p o i n t o f v i e w t h i s i s o b v i o u s l y n o t t h e c a s e . Hence, i f t r a n s a c t i o n c o s t s were i n c l u d e d t h e l o s s e s t o a l l f i l t e r s i z e s w o u l d have i n c r e a s e d . E v e n f r o m a p u r e l y t h e o r e t i c a l o r s t a t i s t i c a l v i e w p o i n t , f i l t e r r e t u r n s , w i t h o u t i n c l u d i n g t r a n s a c t i o n c o s t s and d i v i d e n d s , i n d i c a t e d t h a t t h e r e was no d i s c e r n i b l e p a t t e r n i n p r i c e c h a n g e s . F o r any p a r t i c u l a r f i r m t h e r e was a b o u t an e v e n c h a n c e o f e a r n i n g a p o s i t i v e r e t u r n o r n e g a t i v e r e t u r n f o r any f i l t e r s i z e . S t a t i o n a r i t y o f R e t u r n s I t was p o i n t e d o u t i n t h e p r e v i o u s c h a p t e r t h a t t h e r e a p p e a r e d t o be l i t t l e r e l a t i o n s h i p between t h e mean r e t u r n and MAD f o r e a c h i n d i v i d u a l s e c u r i t y . The d i s t r i b u t i o n o f r e t u r n s d i d n o t a p p e a r t o be s t a t i o n a r y as e v i d e n c e d by t h e a v e r a g e d e c l i n e i n r e t u r n s , and t h e shape o f t h e d i s t r i b u t i o n c h a n g e s as w e l l . 62 Upon e x a m i n a t i o n o f t h e m a r k e t f o r t h e p e r i o d , t h e d e c l i n e i n t h e mean r e t u r n c a n be e x p l a i n e d . From t h e p e r i o d 1963 t o 19 67 t h e m a r k e t , as measured by t h e Base M e t a l I n d e x for. t h e TSE showed s t e a d y imporvement. The i n t e r v a l f r o m 1968 t o 1973 showed a r a t h e r s l u g g i s h p e r f o r m a n c e by c o m p a r i s o n . The c u m u l a t i v e m a r k e t i n d e x f o r t h e t o t a l m i n i n g s t o c k s o f t h e VSE a l s o b e a r s t h i s f a c t o u t . The q u e s t i o n t h a t needs a n s w e r i n g i s why d i d t h e 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 c h ange so r a d i c a l l y f o r many o f t h e s e c u r i t i e s ? I t w o u l d a p p e a r f r o m o b s e r v a t i o n t h a t t h e m a j o r i t y o f f i r m s u n d e r s t u d y c o u l d be c l a s s i f i e d a s s p e c u l a t i v e s t o c k s . T h a t i s , many o f t h e s e c u r i t i e s were t r a d i n g a t a p r i c e r a n g e w e l l b e l o w a d o l l a r . S u b s e q u e n t l y many f o t h e s e f i r m s e s t a b l i s h e d t h e m s e l v e s r e s u l t i n g i n i n c r e a s e s i n t h e p r i c e p e r s h a r e . Hence t h e t r a n s i t i o n was f r o m s p e c u l a t i v e t o s t a b l e s t o c k , r e s u l t i n g i n a change i n t h e r i s k c h a r a c t e r i s t i c s o f t h e s e c u r i t y . Many penny s t o c k s a r e i n f l u e n c e d by ' p r o m o t e r s ' t r y i n g t o make a m a r k e t i n a p a r t i c u l a r s e c u r i t y , h e n c e t h e y a r e o r c a n be s u b j e c t t o s i g n i f i c a n t p r i c e c h a n g e s . B e c a u s e o f t h e s p e c u l a t i v e n a t u r e o f m i n i n g s t o c k s , i . e . , t h e a n t i c i p a t i o n o f a l l o r n o t h i n g t y p e v e n t u r e s , s u g g e s t s t h a t t h e t r a d i t i o n a l a p p r o a c h t o v a l u a t i o n does n o t h o l d . T r a d e - o f f s between r i s k and r e w a r d 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 e x i s t and t h a t t h e s p i n o f a r o u l e t t e w h e e l m i g h t be more a p p r o p r i a t e i n a s s i g n i n g p r o b a b i l i t i e s . The i m p o r t a n t t h i n g i s t h e s e s e c u r i t i e s t e n d t o be e i t h e r boom o r b u s t v e n t u r e s . Once 63 the boom, (or bust), 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 security being studied i n period 1 with i t s average return and MAD might be e n t i r e l y d i f f e r e n t in period 2 with a new risk/reward r e l a t i o n s h i p . The results would indicate that p r o b a b i l i t y statements about future expected returns and v a r i a b i l i t y of returns cannot be made, but, they do not indicate that the returns as they are being generated are not s u f f i c i e n t l y non-random as to comply with the e f f i c i e n t market hypothesis. TABLE X I I M o n t h l y R a t e s o f R e t u r n f o r M a r k e t M a r c h 1963 t o F e b r u a r y 1973 Y e a r 1 Months 5 6 8 10 11 12 10 0.0 1.142 1.102 .943 0 68 71 73 1.062 1.322 1.065 1.039 86 86 87 88 .9924 1.035 .996 .860 98 100 103 104 .955 1.108 .8839 .945 119 127 140 143 .946 1.025 .956 .989 153 152 152 152 .980 1.016 1.096 1.093 167 169 170 171 .951 1.089 1.043 .831 190 192 196 200 .946 .884 .889 1.006 210 214 216 217 1.021 1.077 .927 .919 231 235 , 236 241 .985 1.188 .879 1.005 239 243 252 263 .959 .976 .979 77 78 80 1.058 1.044 1.074 87 88 91 .997 1.019 .943 106 107 108 .990 .942 .922 145 148 150 1.063 1.055 .994 153 153 157 1.001 1.048 1.084 176 178 182 .919 1.011 .953 201 204 206 .977 1.026 .998 223 228 231 .957 .932 .968 244 245 246 .939 1.002 .984 273 274 277 .999 .970 1.009 1.169 1.019 81 82 83 84 86 1.048 1.053 1.003 1.104 .970 91 93 93 98 98 1.054 1.263 1.016 1.107 .973 111 112 116 117 120 .990 .966 1.018 1.145 1.088 150 152 155 155 156 .968 .989 1.040 1.111 .976 158 161 165 167 171 1.101 1.093 1.032 1.252 1.117 181 185 191 195 196 .961 1.054 .968 1.033 .946 206- 209 213 219 221 1.001 .993 .964 1.091 1.020 231 233 237 236 238 .877 .955 1.136 1.312 1.038 251 253 254 254 258 .868 1.025 .942 1.222 1.060 278 281 286 288 289 65 TABLE X I I I C o m p a r i s o n o f R i s k and R e t u r n f o r VSEM and TSEM Mean R e t u r n S t d . D e v i a t i o n C.V.* TSEM . 9 % 4 . 7 % 5 . 8 7 5 VSEM 1.7% 8.6% 6.014 * c o e f f i c i e n t o f v a r i a t i o n I n t e r m s o f t h e r e t u r n s g e n e r a t e d , t h e VSEM o u t p e r f o r m e d t h e TSEM. Y e t w i t h r e s p e c t t o a b s o l u t e r i s k i n e s s t h e VSEM d i s p l a y e d g r e a t e r v a r i a b i l i t y o f r e t u r n s . The r e l a t i v e v a r i a t i o n o f r e t u r n s was a l s o much g r e a t e r a s e v i d e n c e d by t h e l a r g e r c o e f f i c i e n t o f v a r i a t i o n . C a p i t a l M a r k e t t h e o r y s t a t e s t h a t i n e q u i l i b r i u m i n v e s t o r s w i l l p l a c e t h e i r money i n t h e m a r k e t p o r t f o l i o w h i c h i s deemed t o be an e f f i c i e n t p o r t f o l i o . I n o t h e r words t h e y w i l l a t t e m p t t o m a x i m i z e t h e i r r e t u r n f o r a g i v e n l e v e l o f r i s k o r m i n i m i z e t h e i r r i s k f o r a g i v e n l e v e l o f r e t u r n . I f we assume t h a t i n e q u i l i b r i u m a l l i n v e s t o r s c a n b o r r o w o r l e n d a t t h e p u r e r a t e o f i n t e r e s t ( p ) , t h e n t h e r e l a t i o n s h i p b e t w e e n t h e two m a r k e t p o r t f o l i o s c a n ch a n g e . The a c t u a l p u r e i n t e r e s t r a t e was s e t e q u a l t o t h e r a t e o f a t e n y e a r government bond d u r i n g t h e t i m e p e r i o d u n d e r c o n s i d e r a t i o n . S u b s t i t u t i n g i n t o t h e f o l l o w i n g f o l m u l a i t i s p o s s i b l e t o d e t e r m i n e t h e r e q a r d - t o - v a r i a b i l i t y r a t i o s f o r b o t h m a r k e t s . 66 A " P P L (f P where A. P = a v e r a g e r a t e o f r e t u r n f o r m a r k e t P = a c t u a l p u r e i n t e r e s t r a t e (f p = v a r i a b i l i t y o f m a r k e t The r e s u l t i s a c o e f f i c i e n t o f .1064 f o r t h e TSEM and .1314 f o r t h e VSEM. By c o m b i n i n g b o t h b o r r o w i n g and l e n d i n g i t i s a p p a r e n t t h a t t h e VSEM becomes t h e d o m i n a n t p o r t f o l i o and i s s u p e r i o r t o t h e TSEM p o r t f o l i o . T a b l e XIV p r e s e n t s d a t a on t h e c u m u l a t i v e m o n t h l y r e t u r n s f o r t h e m a r k e t p o r t f o l i o . The f i r s t row o f numbers r e p r e s e n t s t h e IPR f o r e a c h p e r i o d w h i l e t h e s e c o n d row c o n t a i n s t h e number o f f i r m s u s e d i n t h e m a r k e t . G e n e r a l l y t h e number o f s e c u r i t i e s i n t h e p o r t f o l i o i n c r e a s e d a t c o n s t a n t r a t e f r o m 6 8 t o 333. I n o r d e r t o c l a r i f y T a b l e XIV t h e r e a d e r s h o u l d compare i t t o T a b l e X I I , t h e m o n t h l y r e t u r n s . B o t h i n d i c e s b e g i n w i t h 68 s e c u r i t i e s , however, T a b l e X I I c o n c l u d e s w i t h 289 f i r m s . T h i s c a n be e x p l a i n e d by t h e f a c t t h a t i n t h e c u m u l a t i v e i n d e x f i r m s t h a t went b a n k r u p t o r were d e l i s t e d were n o t removed f r o m t h e i n d e x . I t was m a n d a t o r y t o i n c l u d e t h e s e i n a c t i v e f i r m s so t h a t t h e i r i m p a c t w o u l d be f e l t t h r o u g h o u t t h e e n t i r e p e r i o d . T h i s was done w i t h t h e v i e w i n mind t h a t an i n v e s t o r , p u r c h a s i n g t h i s m a r k e t p o r t f o l i o w o u l d i n c u r s u c h l o s s e s u n t i l t h e end o f t h e p e r i o d . I f t h e f i r m s h a d b e en removed, t h e i r i m p a c t on t h e m a r k e t w o u l d o n l y have o c c u r e d a t t h e t i m e o f t h e i r d e l i s t i n g . 67 Subsequently i n the following month the market index would show a s i g n i f i c a n t improvement. This, i t was f e l t , would be u n r e a l i s t i c . Year TABLE XIV Cumulative Monthly Rates of Return for Market March 1963 to February 1973  Months 6 8 10 11 12 10 0.0 0 1.456 90 1.163 272 1.022 281 1.142 68 1. 337 92 1.240 71 1. 368 93 1.156 1.092 1.043 73 78 79 1.014 82 997 84 944 85 934 87 1.075 88 1.387 1.493 1.471 1.498 95 96 98 104 1.584 1.588 1.523 1.272 1.268 1.264 1.167 114 118 124 125 127 131 132 1.014 1.035 1.006 1.006 1.068 1.119 1.097 186 185 185 186 187 187 191 1.192 1.199 1.290 1.339 1.290 1.323 1.418 202 204 205 206 211 213 217 2.058 2.213 2.236 1.905 1.735 1.781 1.716 226 228 233 237 - 239 242 244 1.286 1.165 1.019 1.037 1.008 1.039 1.052 249 253 255 256 262 267 270 1.195 276 1.067 285 1.066 277 . 913 294 1.035 282 .990 305 .957 285 .953 315 992 286 948 317 947 287 904 320 . 816 292 .781 322 .791 294 .778 325 889 295 768 330 1.140 295 . 866 332 1.080 90 1.547 1.609 1.626 1.721 1.612 104 106 106 112 113 1.190 1.447 1.419 1.521 1.450 136 . 138 143 146 149 1.344 1.461 1.208 1.123 1.106 1.051 .981 .944 .876 .898 1.010 1.090 150 158 171 174 176 179 181 181 185 188 188 189 1.054 1.043 1.116 1.212 1.185 192 195 199 201 205 1.504 1.634 1.678 1.018 1.243 216 221 227 231 232 1.696 1.773 1.707 1.679 1.610 244 237 251 258 260 1.013 1.052 1.006 1.062 1.159 270 272 277 277 279 1.087 29 9 .893 333 69 Relationship Between the VSEM and TSEM The cursory examination given i n the previous chapter would indicate that the f o l k l o r e surrounding the VSEM i s simply f o l k l o r e . Contrary to what was expected the r e l a t i v e r i skiness of the two markets were quite s i m i l a r . The conclusion to be drawn i s that an investor on the average i s not assuming much greater r i s k by investing i n the VSEM versus the TSEM r e l a t i v e to the returns generated. In fact i f one subscribes to Capital Market Theory, with the a b i l i t y to borrow and lend funds at the r i s k free rate, the investor could become more e f f i c i e n t by investing 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 -played between mean return and standard deviation of returns and does not consider other factors such as the breadth and depth of the two markets and how t h i s would e f f e c t marketability. IMPLICATIONS FOR INVESTMENT MANAGEMENT Hamilton and Lorie (13) state that the most general implication of the e f f i c i e n t market hypothesis i s that most security analysis i s l o g i c a l l y incomplete and valueless. This study centred only on the behavior of security p r i c e s , without reference to fundamental information. The conclusion to be drawn from the series of tests conducted i s that price 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 information to generate speculative p r o f i t s . The implication for the Chartist or Technician i s that he i s wasting his time. Patterns may be found i n price changes, they can also be found i n a randomly generated series of numbers, but they w i l l not provide 70 s u f f i c i e n t i n f o r m a t i o n f o r p r e d i c t i v e p u r p o s e s . L o r i e and H a m i l t o n ( 1 3 ) , e f f e c t i v e l y summarize t h e i m p l i c a t i o n o f t h e E f f i c i e n t M a r k e t T h e o r y : " T h e r e i s a c u r i o u s p a r a d o x . I n o r d e r f o r t h e 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 t o d i s b e l i e v e i t . T h a t i s , m a r k e t 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 nowable a b o u t t h e c ompanies whose s h a r e s a r e t r a d e d o n l y i f i n v e s t o r s s e e k t o e a r n 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, t h e e f f i c i e n c y o f t h e m a r k e t w o u l d d e m i n i s h r a p i d l y . " LIMITATIONS M o n t h l y D a t a U s i n g m o n t h l y d a t a c r e a t e d a number o f i n h e r e n t w e a k n e s s e s i n t h e r e s u l t s o f t h i s s t u d y . I n p a r t i c u l a r , f i l t e r t r a d i n g r u l e r e s u l t s a r e s u b j e c t t o s e r i o u s c r i t i c i s m . M o n t h l y d a t a e f f e c t i v e l y h i d e s a l l o f t h e d a i l y p r i c e c h a n g e s t h a t an i n v e s t o r w o u l d have a c c e s s t o . Thus s i g n a l s , t o buy o r s e l l , c o u l d have been o b s e r v e d much e a r l i e r d u r i n g t h e month e n a b l i n g t h e i n v e s t o r t o i n i t i a t e t h e f i l t e r e a r l i e r . U s i n g d a i l y p r i c e c h a n g e s f o r a l l o f t h e t e s t s w o u l d have r e f i n e d t h e d a t a and a l s o g i v e n a l a r g e r sample s i z e . Runs T e s t s T h i s s t u d y c o n c e n t r a t e d o n l y on t h e t o t a l number o f r u n s and no a t t e m p t was made t o l o o k a t t h e number o f r u n s e x p e c t e d , i f t h e s e r i e s was random, f o r b o t h p o s i t i v e and n e g a t i v e r u n s . 71 T h i s s t u d y i s f u r t h e r l i m i t e d i n t h a t t h e s e q u e n c e . o f t h e c h a n g e s were n o t l o o k e d a t . T h a t i s , were l a r g e d a i l y p r i c e c h a n g e s f o l l o w e d b y l a r g e d a i l y p r i c e c h a n g e s and i f so what was t h e s i g n o f t h e s u c c e s s o r c h a n g e . I t was f e l t , however, t h a t much o f t h i s a d d i t i o n a l r e s e a r c h was b e y o n d t h e s c o p e o f t h i s s t u d y . AVENUES OF FURTHER RESEARCH S e a s o n a l i t y The s t u d y c o n c e n t r a t e d on s h o r t - r u n p r i c e movements. The c o r r e l a t i o n t e s t s i n d i c a t e d t h a t o v e r a p e r i o d o f up t o s i x months t h e r e d i d n o t a p p e a r t o be s i g n i f i c a n t i n f o r m a t i o n i n t h e d a t a upon w h i c h t o make a t r a d i n g d e c i s i o n . P e r h a p s t h e p r i c e s s h o u l d have been l a g g e d upwards t o one c o m p l e t e y e a r . S t i l l t h e r e s u l t s w o u l d n o t i n d i c a t e w h e t h e r t h e r e were some months when s t o c k p r i c e s m i g h t behave i n some p r e d i c t a b l e f a s h i o n . T a b l e XV i n d i c a t e s t h a t f o r t h e combi n e d r e s u l t s o f a l l t h e s t o c k s i n t h e sample o v e r t h e t e n y e a r p e r i o d , t h e r e were some months when t h e m a r k e t a p p e a r e d t o have a h e a v y c o n c e n t r a t i o n o f a d v a n c e s f o l l o w e d by d e c l i n e s . TABLE XV S e a s o n a l V a r i a t i o n i n M a r k e t A d v a n c e s a n d D e c l i n e s J F M A M J J A S 0 N D A d v a n c e s 100% 60 22 90 40 40 30 70 L 20 40 50 70 D e c l i n e s 0% 40 77 10 60 60 70 30 80 60 50 30 72 The month of January had a p o s i t i v e return throughout the study, followed by A p r i l with 90% of the pr i c e changes being p o s i t i v e and August and December with 70%. These tentative r e s u l t s would indicate a si g n i f i c a n t ' seasonal factor. By the elimination of c y c l i c a l secular and i r r e g u l a r fluctuations a seasonal index could be developed to measure t h i s seasonal impact upon the returns. D i s t r i b u t i o n of Price Changes The preliminary findings of t h i s paper suggest that further research i s needed i n assessing the d i s t r i b u t i o n of price changes. The res u l t s of chapter four indicate that security returns are not stationary over time. If t h i s i s i n fact the case, i t becomes d i f f i c u l t to assess the risk/reward c h a r a c t e r i s t i c s of i n d i v i d u a l s e c u r i t i e s . However, i t could be possible to measure the relationship i n d i v i d u a l s e c u r i t i e s have to the market. We could measure t h e i r v o l a t i l i t y to the market, and describe t h e i r r i s k using the sl o p e . c o e f f i c i e n t . Mechanical Trading Rules Of the f o r t y - f i v e firms tested, t h i r t y - f o u r s e c u r i t i e s out-performed the buy-and-hold p o r t f o l i o for some f i l t e r s i z e . The obvious problem, however, was that there was no consistency i n which f i l t e r was appropriate. Only f i v e stocks consistently out performed the buy-and-hold strategy for a l l f i l t e r s i z e s . If the opposite of what the f i l t e r dictated had been followed, i t might have been possible to improve the r e s u l t s . Further study i n t h i s area might uncover some clues. Perhaps instead 73 of measuring the percentage price change, a moving average of the stock price changes could 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 M a r k e t s : 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  Review, v o l . 2, no. 2, (May 1961), pp. 7-26. 2. . " P r i c e Movements i n S p e c u l a t i v e M a r k e t s : T r e n d s o r Random Wal 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 P r i c e s . " 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 Changes," I n d u s t r i a l Management Review, v o l . 3, no. 2, pp. 24-25, S p r i n g 1962. 4. George W. D o u g l a s . " R i s k i n t h e E q u i t y M a r k e t : An E m p e r i c a l A p p r a i s a l o f M a r k e t E f f i c i e n c y . " U n p u b l i s h e d  Ph. 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. Eugene F. Fama. " E f f i c i e n t C a p i t a l M a r k e t s : 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 . 25, no. 2, (May 1 9 7 0 ) , pp. 383-417. 6. _ _ . "The B e h a v i o r o f S t o c k M a r k e t 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 . 38, ( J a n u a r y 1 9 6 5 ) , pp. 24-105. 7. and M a r s h a l l Blume. " F i l t e r R u l e s and S t o c k M a r k e t T r a d i n g P r o f i t s , " J o u r n a l o f B u s i n e s s , 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 1966), pp. 226-41. 8. J a c k C l a r k F r a n c i s . " I n v e s t m e n t s : A n a l y s i s and Management," M c G r a w - H i l l Book Company; 1972, p p . 5 3 7 . 9 . I b i d . , pp. 554 10. C. W. J . G r a n g e r and 0. M o r g e n s t e r n . " S p e c t r a l A n a l y s i s 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 . " R i s k , t h e P r i c i n g o f C a p i t a l A s s e t s , and t h e E v a l u a t i o n o f I n v e s t m e n t P o r t f o l i o s , " J o u r n a l o f B u s i n e s s , v o l . 42, no. 2, ( A p r i l 1 969), pp. 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, ( J a n u a r y 1 9 6 6 ) , pp. 139-190. 13. James H. L o r i e , Mary T. H a m i l t o n . "The S t o c k M a r k e t ,  T h e o r i e s and E v i d e n c e , " R i c h a r d D. I r w i n , I n c . , Homewood, I l l i n o i s , 1973, pp. 98. 75 14. Benoit Mandelbrot. "The Vari a t i o n of Certain Speculative Prices," Journal of Business, v o l . 36, (October, 1963), pp. 394-419. 15. Arnold B. Moore. "Some Characte r i s t i c s of Changes i n Common Stock Prices," i n Paul H. Cootner, The Random  Character of Stock Market Prices, Canbridge, Mass., The M.I.T. Press, 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 Patterns and F i n a n c i a l Analysis: Methodological Suggestions," Journal of  Finance, v o l . 15, no. 1, (March 1959), pp. 1-10. 18. William F. Sharpe. " P o r t f o l i o Theory and Capital Markets," New York, McGraw-Hill Book Co., 1970, pp. 82. 19. Ibid., pp. 83. 76 APPENDIX Firms Used In Study ATS Arlington S i l v e r Mines Ltd. BCC Bethlehem Copper Corp. Ltd. BR Bralorne Can Fer Resources Ltd. BSM Blue Star Mines Ltd. CCD Cassiar Consolidated Mines Ltd. CGQ Cariboo Gold Quartz Mining Co. Ltd. CMNA Coleman C o l l i e r i e s Ltd. 'A' COP Coast Copper Co. Ltd. CPG Copper Ridge Mines Ltd. CRI Craigment Mines Ltd. CSR Cassiar Asbestos Corp. Ltd. CST Consolidated Standard Mines Ltd. CYD Croyden Mines Ltd. DVM Dolly Varden Mines Ltd. DVN Dundee Mines Ltd. GDC Granduc Mining Co. Ltd. GIM Giant Mascot Mines Ltd. GRL General Resources Ltd. GRV Grandview Mines Ltd. JY Jersey Consolidated Mines Ltd. JRC Jericho Mines Ltd. LTL'A1 Lytton Minerals Ltd. MM Mineral Mountain Mining Co. Ltd. MTW . . . . . . Mt. Washington Copper Co. Ltd. 77 NCR New C r o n i n B a b i n e M i n e s L t d . NGD N o r g o l d M i n e s L t d . NIN New I n d i a n M i n e s L t d . NOV N o r t h w e s t V e n t u r e s L t d . NPM New P r i v a t e e r M i n e s L t d . PB Pend O r e i l l e M i n e s and M e t a l s Co. L t d . PDL P l a c e r D e v e l o p m e n t L t d . PEEL P e e l R e s o u r c e s L t d . PPT P i n e P o i n t M i n e s L t d . PSS Peso S i l v e r M i n e s L t d . QUT Q u a t s i n o C o p p e r - G o l d M i n e s L t d . RHM R o l l i n g H i l l s C o p p e r M i n e s L t d . RV Reeves M a c D o n a l d M i n e s L t d . SBC S i l b a k P r e m i e r M i n e s L t d . SCH S i l e u r i a n C h i e f t a i n M i n i n g Co. L t d . SLO S l o c a n Ottawa M i n e s L t d . SRD S i l v e r R i d g e M i n i n g Co. L t d . SS S i l v e r S t a n d a r d M i n e s L t d . TMX Texmont M i n e s L t d . TR T r a n s c o n t i n e n t a l R e s o u r c e s L t d . TRJ T r o j a n C o n s o l i d a t e d M i n e s L t d . TWT NEW . . . . T o r w e s t R e s o u r c e s (1962) L t d . VN Vananda E x p l o r a t i o n s L t d . WMI W e s t e r n M i n e s L t d . 78 PROGRAM TO RUN F I L T E R RULE M i c h i g a n T e r m i n a l S y s t e m F o r t r a n G(41336) COMMON/A1/IFELT,CRRT, MRRT, RTT, PSERCT, PFT, NUMLAG, NUMY, CONSNT, FELTER 1,XP ( 1 0 ) , I T I T L E ( 6 0 , 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 ) REAL 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), *NI(3),NR(3),RT/4/,PCRR, PMRR, PAGEL/60/,CONSNT,TY/19/,PF,PFT, *CRRT, MRRT, FELTER, FR/1/ EQUIVALENCE ( N E G , N I ( 1 ) ) , ( Z E R O , N I ( 2 ) ) , ( P O S , N I ( 3 ) ) , *(RNEG,NR(1)),(RXERO,NR(2)),(RPOS,NR(3)), * ( E X P E C T , E ( 1 ) ) , ( A C T U A L , E ( 2 ) ) , ( D T F F , 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) ,LASTFJ/'999'//BLANKS/ 1 '/ 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'/ C C PF=PFT C C READ (TU,24) NUMLAG 24 FORMAT(12) DO 983 k = l , 5 READ(TU,333) ( I T I T L E ( J , K ) , J = l , 6 0 ) WRITE(0,444) ( I T I T L E ( J , K ) , J = l , 6 0 ) 444 FORMAT(' ',30A4,/,IX,30A4) 333 FORMAT(60A4) 983 CONTINUE IFELT=9 DO 142 k-1,FELTER KK=IFELT+K WRITE(KK,338)K,XP(K) 338 FORMAT('1****FILTER RULES****',4X,'TYPE = ',12,3X, *'PRECENTAGE = ',F9.4,//, *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=1,1000 WRITE(6,243) 243 FORMAT (1X.,131 (' = ') ) LASTY=-1 IF (EOF) GOTO 9999 IF (1-1) 177,178,177 177 NUMY=NUMY+1 LASTY=YEAR(NUMY) LASTFJ=FIRM(NUMY) DO 13 K=l,12 13 Fl(K,1)=F1(K,NUMY) YEAR(1)=YEAR(NUMY) FIRM(1)=FIRM(NUMY) 17 8 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) 12 F0RMAT(12F6.3,A7,I1) GOTO 8 88 34 0 EOF=.TRUE• 8 88 CONTINUE IF (J.EQ.l) GOTO 9 31 IF (LASTFJ.NE.FIRM(J).OR.ECF) GOTO 7 C 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(1 ***',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 80 TXMAX = P(KSTART) TXMIN = P(KSTART) IXX=IZ1 LOGM=BLK DO 31 K=KSTART,IZI IF(P(K).GT.O.O) GOTO 430 IZ.Z=K LOGM=STAR PLAST=0.0 GOTO 4 73 430 K1=K+1 I F ( P ( K ) .EQ.0.0) P(K1)=P(K) IF(P(K).GT.TXMAX) TXMAX=P(K) IF( P ( K ) . L T . T X M I N ) IXMIN = P(K) 290 GOTO (291,292,293),ITYPE 291 I F (P (K)-TXMIN)/TXMIN.LT.XP (J).) GOTO 300 C C WE GET HERE I F WE HAVE BOUGHT. C 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 1 S T A R T , K , I T Y P E , I Z l XMIN = P (K) XMAX=P(K) ITYPE = 2 241 FORMAT(1X,3F10.4,A2,5F10.4,4I10) GOTO 300 292 IF(P(K).GT.SMAX) SMAX = P(K) IF ( ( S M A X - P ( K ) ) / X M A X . L T . X P ( J ) ) GOTO 300 IIS=IIS+1 C C GET HERE I F WE ARE ABOUT TO SELL, C IN THIS CASE, WE BORROW SOME STOCK AND SELL THE EQUIVALENT C AMOUNT C 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 300 293 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 #)) C 81 C GET HERE I F WE ARE ABOUT TO BUY BACK AND REPAY C THE BROKER FOR LENDING US SOME STOCK C IIB=IIB+1 BUYPR=P(K) BUY=P(K) SPROF=SPROF+BORROW-BUYPR BORROW=0.0 WRITE (6, 241) XP (J) , BUY, BUYPR,.BBLOG , XMSOS, SPROF, 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 IF(ORIG.NE.0.0) FRR=1.+PROFIT/ORIG RANGE=TXMAX=TXMIN KK=IFELT+J I F (PF.GT.PAGEL) CALL RESET(PF,KK,5) WRITE(KK,14 3) LOGM,FIRM(1),I,PROFIT,FRR,SPROF,LPROF,ORIG,PLAST, *TBOR,TXMIN,TXMAX,RANGE,IIB,IIS 14 3 F O R M A T ( I X , A 1 , A 7 , 1 ( ' , 1 3 , ' ) ' , F 8 . 3 , I X , F 9 . 3 , I X , F 9 . 3 , I X , 7 ( F 7 . 3 , I X ) , 2 1 6 ) WRITE(6,642) FIRM(l),XP(J),PROFIT,XMSOS,BORROW,BUY,TXMIN,TXMAX,P(I 1Z1),LPROF,SPROF,FRR,ORIG,TBOR 642 FORMAT(IX,A7,'PER=',F10.4, 1 PROFIT=',F10.4,'XMSOS=',F10.4,' BORROW 1=',F10.4, 1 BUY=', *F10.4,' TXMIN='F10.4,' TXMAX= 1,F10.4,/, 1 F ( I Z l ) = 1 , F 1 0 . 4 , *' LPROF=',F10.4, 1 SPROF=',F10.4, 1 RATE OF RETURN= 1,F10.4, *' ORIG = ',F10.4,' TOTAL BORROWED = ',F10.4) 32 CONTINUE 10 CONTINUE 9999 RETURN END 82 SUBROUTINE RESET(IPAGE,IUNIT,INDEX) 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) E Q U I V A L E N C E ( I T I T L E ( 1 , 1 ) , T C U M ( 1 ) ) , ( I T I T L E ( 1 , 2 ) , T M O N ( l ) ) , * ( I T I T L E ( 1 , 3 ) , T R U N T ( 1 ) ) , ( I T I T L E ( 1 , 4 ) , T S E R C ( 1 ) ) C C C THIS SUBROUTINE TRSETS THE PAGE COUNTER AND THEN SKIPS TO THE C NEXT PAGE. C C GOTO (10,10,30,30,30),INDEX 10 IPAGE = IT(INDEX) + NUMY + CONSNT GOTO 100 30 IPAGE = IT(INDEX) + 1 100 CONTINUE GOTO (11,21,31,41,51),INDEX 11 WRITE(IUNIT,TCUM) GOTO 20 0 21 WRITE(IUNIT,TMON) GOTO 200 31 WRITE(IUNIT,TRUNT) GOTO 200 41 .! WRITE(IUNIT,TSERC) NUMLAG,(K,K=l,NUMLAG) GOTO 200 51 DO 142 K=l,FELTER KK=IFELT+K WRITE(KK,338)K,XP(K) 338 FORMAT( 11****FILTER RULES**** 1 ,4X, 1 TYPE =',I2,3X, *'PERCENTAGE = ',F9.4,//, *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 83 PROGRAM TO COMPUTE: RUNS TESTS, SERIAL CORRELATION C O E F F I C I E N T S , RATE OF RETURN MATRICES FOR MONTHLY AND CUMULATIVE RETURNS. C THIS PROGRAM PERFORMS ANALYSIS ON STOCK QUOTATIONS OVER THE C PERIOD OF STUDY( ABOUT 10 years). C ALTHOUGH THE PROGRAM I S SIMPLE AND NOT TO BE TAKEN C SERIOUSLY FOR THE INVESTOR, I T DOES HOWEVER ILLUSTRATE SOME C IMPORTANT POINTS. C C C C HERE ARE THE VARIABLES USED IN THE PROGRAM C C F 1 ( i , j ) THE FIRMS STOCK QUOTES FOR YEAR J FOR MONTH I . C P(K) THE SAME AS ABOVE, BUT AS A LINEAR ARRAY. C RR(K) THE RATES OF RETURNS, PICKED UP FROM P ( T + 1 ) / p ( t ) . C DOUBRR(I,J)...the rates of returns as a two dimensional array. C F I R M ( J ) THE NAME OF THE FIRM AS READ WITH THE YEAR C Y E A R ( J ) THE YEAR OF THE QUOTATIONS. C CRET(K) THE CUMULATIVE RATES OF RETURNS C DOUBCR(I,J)...the cumulative rates of returns as a two C DIMENSIONAL ARRAY C NUMLAG EQUALS THREE, FOR TOTAL NUMBER OF LAGS CONSIDERED. C COR(K) THE CORRELATION COEFFICIENTS FOR THE K'TH LAG. C CUMSUM(K) CUMULATIVE RATE OF RETURN MATRIX (MARKET). C DCUMS(I,J)....the same except i n two dimensions. C MRRMK(K) MONTHLY RATES OF RETURNS(MARKET) . C DDMRMK(I,J)...SAME AS ABOVE, EXCEPT I N TWO DIMENSIONS C U SCC SERIAL CORRELATION C O E F F I C I E N T S . C U MRR MONTHLY RATES OF RETURNS C U CRR CUMULATIVE RATES OF RETURNS. C U CRRM CUMULATIVE RATES OF RETURNS ON THE MARKET. C U MRRM MONTHLY RATES OF RETURNS ON THE MARKET. C U RT RUN TESTS. C U FR F E L T E R OUTPUT UNIT. C U CWB COMPANY WENT BROKE. C U TU THE UNIT FROM WHICH THE T I T L E S ARE READ. C U DEL THE COMPANIES DELETED DUE TO BAD DATA. C U SUMMRY A SUMMARY UNIT. C U DEBUG A DEBUGGING UNIT. C LP PCRR LINE/PAGE COUNTER FOR CUMULATIVE RATES OF RETURNS. C LP PMRR LINE/PAGE COUNTER FOR MONTHLY RATES OF RETURNS. C LP PRTC LINE/PAGE COUNTER FOR RUN TESTS. C LP PSERC LINE/PAGE COUNTER FOR SERIAL CORRELATION. C CONSNT REQUIRED TO CALCULATE THE EXPECTED NUMBER OF C L I N E S TO BE PRINTED FOR THE CUMULATIVE AND C MONTHLY RATES OF RETURNS. C F E L T E R . . THE NUMBER OF F E L T E R PERCENTAGES. C XP(10) THE F E L T E R PERCENTAGES. 84 C NI(3) THE INFLECTIONS(-,0, + ) C NR(3) THE RUNS (-,0, + ). C SUMNI SUM OF THE INFLECTIONS. C ACTUAL SUM OF THE RUNS. C E I (3) THE PERCENTAGES OF THE INFLECTIONS C (-,0,+). C ER(3) THE PERCENTAGES OF THE RUNS (-,0, + ) . C TF TRUNT OBJECT TIME FORMAT (RUN T E S T S ) . C TF TMON OBJECT TIME FORMAT (MONTHLY MARKET RETURNS). C TF TCUM OBJECT TIME FORMAT(CUMULATIVE MARKET RETURNS). C TF TSERC OBJECT TIME FORMAT(SERIAL CORRELATIONS). C TF SKIP L ( 2 ) OBJECT TIME FORMAT. FOR SKIPPING LINE. C NUMTIT NUMBER OF T I T L E S FOR OBJECT TIME FORMAT. C IBROKE COUNTER FOR COMPANIES THAT WENT BROKE. C IDEL COUNTER FOR COMPANIES DELETED. C KSTART THE MONTH IN WHICH THE FIRST PRICE APPEARED. C PS TART P (KSTART). C PSTORE THE VALUE OF THE LAST NON MISSING PRICE. C LOGICAL VALUES C LOGB.... SET TO STAR FOR BROKE COMPANIES C STAR "*" . C BLK " ". C C BLOCK DATA C C C PSERT T I T L E PAGE LENGTH FOR SERIAL CORRELATIONS. C CRRT THE T I T L E PAGE LENGTH FOR CUMULATIVE C RATES OF RETURNS. C MRRT SIMILAR FOR MONTHLY RATES OF RETURNS C RTT T I T L E PAGE LENGTH FOR THE RUN TESTS. C CONSNT THE OVERHEAD ON PRINTING A FIRMS RETURN RATES. C FELTER THIS VARIABLE IS THE NUMBER OF FELTER C PERCENTAGES THAT WE ARE CONSIDERING. C F E L T A ( I O ) . . . . T H I S IS AN ARRAY OF FELTER PERCENTAGES. C NUMLAG THE # OF LAGS FOR SERIAL CORRELATIONS. C C INTEGER CRRT,RTT,CONSNT,FELTER,NUMLAG,PSERCT COMMON/P1/PAGEC(10),SKIPL(2) COMMON/A1/CRRT,MRRT,RTT,PSERCT,NUMLAG,NUMY,CONSNT,FELTER, 1FELTA (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 T I T L E INDEX 1) CUMMULATIVE RATE OF RETURNS. 2) MONTHLY RATE OF RETURNS 3) RUN TESTS. 4) SERIAL CORRELATION COEFFICIENTS. COMMON/P./PAGEC(10),SKIPL(2) COMMON/A1/CRRT,MRRT,RTT,PSERCT,NUMLAG,NUMY,CONSNT,FELTER, * X P ( 1 0 ) , I T I T L E ( 6 0 , 5 ) REAL F l ( 1 2 , l l ) ,P(132) ,RR(132) ,R(132,2) ,DOUBRR(12,11,) ,EI (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, *LASTR,RZERO,ICUM(132),DDICUM(12,11),ICORC(12), 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/ E Q U I V A L E N C E ( I T I T L E ( 1 , 1 ) , T C U M ( 1 ) ) , ( I T I T L E ( 1 , 2 ) , T M O N ( 1 ) ) , * ( I T I T L E ( 1 , 3 ) , T R U N T ( 1 ) ) , ( I T I T L E ( 1 , 4 ) , T S E R C ( 1 ) ) L O G I C A L * l EOF/.FALSE./,MISS/.GALSE./,START,NEGONE,FLOG(8), 1STAR/ 1 * 1/,LOGB, *BLK/' 1 / REAL*8 FIRM(11),LASTFJ/'999'/,BLANKS/ 1 '/ EQUIVALENCE ( N E G , N I ( 1 ) ) , ( Z E R O , N I ( 2 ) ) , ( P O S , N I ( 3 ) ) , *(RNEG,NR(1)), RZERO,NR(2)), RPOS,NR(3)), * ( E X P E C T , E ( 1 ) ) , ( A C T U A L , E ( 2 ) ) , ( D I F F , E ( 3 ) ) , * ( F I R M ( l ) , F L O G ( l ) ) , * (F1,P),(RR,DOUBRR),(RMEAN,RUN,DOUBRN),(CRET,DOUBCR), *(ICUM,DDICUM),(DCUMS,CUMSUM),(MRRK,DDMRRK),(IMRK,DDIMRK) DATA RUN(1)/0./,RR(1)/0.0/,CRET(1)/0.0/,IBROKE/0/,PSTORE/0.0/ C HERE WE I N I T I A L I Z E AS WELL AS READ IN T I T L E S . C WRITE(DEBUG,555) 555 FORMAT('1****DEBUG UNIT****',///) READ(TU,24) NUMLAG 24 FORMAT(12) DO 983 K=l,4 READ(TU,333) ( I T I T L E ( J , K ) , J = 1 , 6 0 ) WRITE(DEBUG,444) ( I T I T L E ( J , K ) , J = l , 6 0 ) 444 FORMAT( 1 ',30A4,/,IX,30A4) 333 FORMAT(60A4) 9 83 CONTINUE DO 798 K=l,10 798 P A G E C ( K ) = l DO 984 K=l,121 IMRK(K)=0 MRRK(K)=0.0 ICUM(K)=0 CUMSUM(K) = 0 . 0 984 ICUM(K) = 0 C 86 C C SET THE LINE COUNTERS TO THE T I T L E LENGTHS, AND PAGE COUNTERS C TO 1. C PCRR=CRRT PMRR=MRRT PRTC = RTT PSERC=PSERCT C C C AFTER THE I N I T I A L I Z A T I O N , WE PRINT OUT THE TABLE HEADINGS ON C THE.VARIOUS UNIT NUMBERS. C C WRITE(SCC,TSERC) ONE,NUMLAG,,(K,K=l,NUMLAG) WRITE(CWB,882) 882 FORMAT ('1***THE FOLLOWING COMPANIES WENT BROKE*** '",//, *'**FIRM**',12X,'MONTH 1,4X,'YEAR',//) WRITE(DEL,8888) 8888 FORMAT. ('1***THE FOLLOWING COMPANIES WERE DELETED FROM THE 1SURVEY',//, *'**FIRM**',12X,'MONTHS IN STUDY',//) WRITE(MRR,TMON) ONE WRITE(CRR,TCUM) ONE WRITE(RT,TRUNT) ONE DO 10 1=1,1000 LASTY=-1 I F (EOF) GOTO 9999 I F (1-1) 177,178,177 177 NUMY=NUMY+1 LASTFJ=FIRM(JKEEP) DO 13 K=l,12 13 F1 ( K , 1 ) = F 1 ( K , J K E E P ) YEAR (1 ):=YEAR (JKEEP) FIRM(1)=FIRM(JKEEP) 178 DO 11 J=JSTART,11 JKEEP=J FIRM(J)=BLANKS READ(5,12,END=340) ( F l ( K , J , K = 1 , 1 2 ) , F I R M ( J ) , Y E A R ( J ) 12 F0RMAT(12F6.3,A7,I1) GOTO 888 340 EOF=.TRUE. 888 CONTINUE I F ( J . E Q . l ) GOTO 931 I F (LASTFJ.NE.FIRM(J).OR.EOF) GOTO 7 C C HERE WE DETERMINE WHEN TO PROCESS THE CURRENT FIRM. 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 87 C C C HERE START WITH THE RATIOS "RR"(RATE OF RETURNS), AND ALSO C CALCULATE THE RUNS. C C C THE RUNS IN THE PRICES ARE CALCULATED IN THE FOLLOWING WAY. C C 1. THE FIRST POSITIVE RUN IS NOT COUNTED, THIS IS DUE C TO THE FACT THAT I F THE STOCK OPENS IT'S RUNNING C VALUE IS MEANINGLESS IN THIS CASE. C C 2. CONSEQUENTLY, THE RUN OF ZEROS BEFORE THE OPENING C OF THE STOCK ARE NOT COUNTED. FURTHERMORE, C THE ZEROS IN THE MIDDLE OF THE STOCKS L I F E C (MISSING DATA) DO NOT COUNT AS PART OF A NEGATIVE C RUN, RATHER THEY COUNT AS A ZERO RUN. C C 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 I F ( P ( K ) . E Q . 0 . 0 ) IMISS=IMISS+1 DO 15 K=1,IZ I F ( P ( K ) . E Q . 0 . 0 ) IMISS=IMISS+1 C C FIND THE FIRST L I S T I N G OF THE STOCK C 609 K1=K+1 IF (P(K)) 93,92,91 C C WE GET HERE I F THE COMPANY WENT BROKE. IN THIS CASE EVERYTHING C FROM HERE ON IN IS ZERO, AND WE BRANCH OUT OF THE LOOP. C 93 IF(NEGONE) 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 KI=K,IZ1 88 RUN(KI)=0.0 RR(KI+1)=0.0 CRET(KI+1)=0.0 16 P ( K I ) = 0 . 0 DO 1112 KK=k,120 1112 ICUM(KK)=ICUM(KK)+1 GOTO 151 91 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) IF(START) GOTO 654 KSTART=K PSTART=P(K) 654 START=.TRUE. 92 RUN(K1) = ( P ( K 1 ) - P ( K ) ) IF(.NOT.START) GOTO 800 IF (P(K1).EQ.0.) GOTO 4 7 IF (K.EQ.KSTART) GOTO 40 MISS=.FALSE. RUN(Kl) = P(K1) - PSTORE GOTO 41 40 PSTORE=P(K) MISS=.TRUE. GOTO 41 4 7 MISS=.TRUE. RUN(Kl) = 0.0 GOTO 60 41 IF(RUN(K1)) 50,60,70 50 NEG=NEG+1 IF(RUN(K).GE.0.) RNEG=RNEG+1 GOTO 80 60 ZERO=ZERO=l IF(RUN(K).NE.0.) RZERO=RZERO+l GOTO 80 70 POS=POS+l IF ( R U N ( K ) . L E . 0 . ) RPOS=RPOS+l 80 CONTINUE 800 CONTINUE C C C NOW FIGURE THE CUMULATIVE RATES OF RETURNS AND THE MONTHLY C RATES OF RETURNS C C IF(K.NE.KSTART) GOTO 15 3 RR(K) = 0 CRET(K) = 0 153 I F ( P ( K 1 ) . N E . 0 . 0 ) GOTO 702 RR(K1) = 1.0 C R E T ( K l ) = CRET(K) IF(K.NE.START) GOTO 701 RR(K1)=1. C R E T ( K l ) = l . GOTO 701 702 IF(KSTART.EQ.-1) GOTO 704 89 RR(K1) = (P (KD/PSTORE C R E T ( K l ) = P(K1)/PSTART 701 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) = CRET(Kl)+CUMSUM(IK) ICUM(IK) = ICUM(IK) + 1 703 IF(RR(K1).EQ.0.0) GOTO 704 IMRK(IK)=IMRK(IK)+1 MRRK(IK) = MRRK(IK) + R R ( K l ) 704 ' CONTINUE 15 CONTINUE 151 I F ( K S T A R T . E Q . - l ) GOTO 4 09 2 RRMEAN=RRSUM/FLOAT(NSTAR) C C C HERE WE PRINT OUT THE RESULTS C C C C C HERE WE PRINT OUT THE HEADINGS FOR THE VARIOUS F I L E DESTINATIONS. C (MONTHLY RATES OF RETURNS ...MRR,CUMULATIVE RATES OF RETURNS..CRR) C WE ALSO CHECK TO SEE I F WE NEED TO RESET THE PAGES. C C PCRR = NUMY + CONSNT + PCRR PMRR = NUMY + CONSNT + PMRR PRTC = 1 + PRTC PSERC = 1 + PSERC IF(PCRR.GT.PAGEL) CALL RESET(PCRR,CRR,1) I F (PRTC.GT.PAGED CALL RESET (PRTC, RT, 3) I F (PMRR. GT. PAGED CALL RESET (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) 533 FORMAT(IX,/,IX, 1 ** 1,A7, * (' , 1 4 , A l , ') 1,14X, * ' S U M ( P ( T + l ) / P ( T ) ) = 1 , F 1 0 . 4 , 2 X , 1 , N = 1,15,2X,',MEAN= 1,F10.5, *4X, 1,MISSING=',13,/, *8X,'*',35X, 1 MONTHS ',10X,/, * 8 X , ' * ' , / , l X , 1 3 2 ( ' * ' ) , / , *2X,' Y E A R ' , 1 X , ' * • , 1 2 ( 4 X , I 2 , 4 X ) , 3 X , , / , 8 X , ,123 ('-'),'*') 532 FORMAT (8X, 1 * 1,35X, ' MONTHS ',/,8X, 1 * , / , I X , 1 3 2 ( ' * ' ) , / , *2X,' Y E A R ' , 1 X , 1 * ' , 1 2 ( 4 X , I 2 , 4 X ) , 3 X , 1 * ' , / , 8 X , ' * ' , 1 2 3 ( ' - ' ) - ' * ' ) WRITE(6,32) LASTFJ,NUMY,(K,K=1,12) 32 FORMAT('-FIRM = * * * * 1 , A 4 , 1 * * * * NUMBER OF YEARS IN STUDY =',15,// *8X,'*',35X,' MONTHS 1 , / , 8 X , ' * ' , / , I X , 1 3 2 ( 1 * ' ) , / , *2X, ' YEAR' ,1X, ,12 (4X, 12, 4X) ,3X, '*' ,/,8X, '"*' ,123 ( ' - ' ) , ' * ' ) DO 131 K=l,10 KKEEP=K IR=12 YEAR(K)=YEAR(K)+1 WRITE(MRR,231) YEAR(K),(DOUBRR(L,K),L=1,IR) 90 231 FORMAT(4Z,12,2X,1 *' ,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,1 *',IX,12(IX,F7.4,2X) ,2X, 1 *',/,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,'* 1 ,/,8X, '*',123X,'* 1) 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,',1, C *I5,' YEARS STUDIES,',2X,15,1 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 EI(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) 91 579 FORMAT (IX,Al,A7, 1(',14, 1)',IX,2(2X,F8.4,IX), *3X,3(IX,'/',1X,I3,]X,F4.2,1X),1X,'/'/3('/',IX,13,2X,F4.2,2X)) C C C NOW WE START THE CORRELATIONS C 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) 111 CONTINUE IF (IC-1) 110,110,271 271 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) 113 RSQ2=RSQ2+RK2**2 RRT=RSQ1*RSQ2 IF (RRT.NE.0.) COR(LAG) =RS/SQRT(RRT) ICORC(LAG) = IC 110 CONTINUE C C C HERE WE. PRINT C 1) SERIAL CORRELATION COEFFICIENTS UNIT=SCC C -2) MONTHLY RATES OF RETURNS UNIT=CRR C 3) CUMULATIVE RATES OF RETURNS UNIT=CRR C C C WRITE(SCC,697) LOGB,FIRM(1),1,(COR(L),ICORC(L),L=1,NUMLAG) 697 FORMAT(IX,A1,A7,' ( 1 ,14, ') ',IX.7(IX,'/1,IX,F7.4,2X,13,2X)) GOTO 10 4092 WRITE(DEL,4093) FIRM(1),I,IZ1 4093 FORMAT(' **',A7,' * 1 ,14,') 1,9X,13) IDEL=IDEL+1 10 CONTINUE 92 9999 1=1-1 WRITE(SUMMRY,9) I,IBROKE,IDEL 9 FORMAT( 11',//,1X, '****THE TOTAL NUMBER OF•FIRMS. STUDIES WAS', * l 4 f " *****',/,IX.'****THE NUMBER OF COMPANIES GOINT BROKE=',I4, */,IX.'****THE NUMBER OF COMPANIES DELETED FROM THE DATA=',I4) C C C WE GET HERE WHEN WE ARE FINISHED. WE PRINT OUT: C C 1) CUMULATIVE RATES OF RETURNS (MARKET) UNIT=CRRM C 2) MONTHLY RATES OF RETURNS (MARKET) UNIT=MRRM C C WRITE (MRRM, 859). 859 FORMAT('1 ****MONTHLY RATES OF RETURNS(MARKET)****',//) 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) 54 3 FORMAT .(2X, 12, 3X, ' * ' , IX. 12 (1X,F7 . 2 , 2X) , 2X, ' * • ,/., *8X, ' *•' ,1X,12 (3X,I5,2X) ,2X, ' *• ,/, * 8 X , , 1 X , 1 2 ( 1 X , F 7 . 4 , 2 X ) , 2 X , • * ' , / , 8 X , ' * • , 1 2 3,'*') 54 4 CONTINUE WRITE(MRRM,54) WRITE(CRRM,857) 857 FORMAT('1****CUMULATIVE RATES OF RETURNS(MARKET)****',//) WRITE(CRRM,532) (K,K=1,12) CLAL CALCU(DCUMS,DDICUM,RMEAN) DO 564 K=l,10 WRITE(CRRM,543) K,(DCUMS(L,K),L=1,12),(DDICUM(L,K),L=1,12), 564 CONTINUE WRITE(CRRM,54) RETURN END 93 SUBROUTINE GETMON(YEAR,K,II,IK,IMON,IYEAR) C C THIS SUBROUTINE GETS THE MONTH AND YEAR GIVEN ANY K. C INTEGER YEAR(10),IYEAR(1),IMON(l),11(1),IK(1) II(l)=MOD(K f12) IF(II (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 94 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 12 XMEAN(J,K) = XX(J,K)/FLOAT(IX(J,K)) 10 CONTINUE 11 CONTINUE RETURN END 95 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)) non THIS SUBROUTINE RESETS THE PAGE/LINE COUNTERS AND THEN C TO THE NEXT PAGE. c /-I PAGEC(INDEX)=PAGEC(INDEX)=1 GOTO (10,10,30,30),INDEX 10 IPAGE = IT(INDEX) + NUMY + CONSNT GOTO 100 30 IPAGE = IT(INDEX) + 1 100 CONTINUE GOTO (11,21,31,41),INDEX 11 WRITE(IUNIT,TCUM) PAGEC(INDEX) GOTO 200 21 WRITE(IUNIT,TMON) PAGEC(INDEX) GOTO 200 31 WRITE(IUNIT,TRUNT) PAGEC(INDEX) GOTO 200 41 WRITE(IUNIT,TSERC) PAGEC(INDEX),NUMLAG,(K,K=l,NUMLAG) WRITE(IUNIT,SKIPL) 200 CONTINUE WRITE (0,2)IPAGE,IUNIT,INDEX,IT(INDEX),CONSNT,NUMY 2 FORMAT(' ***RESET ***',6I10) RETURN . 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