UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Relative value analysis Ney, David James 1968

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1968_A4_5 N84.pdf [ 6.56MB ]
Metadata
JSON: 831-1.0102383.json
JSON-LD: 831-1.0102383-ld.json
RDF/XML (Pretty): 831-1.0102383-rdf.xml
RDF/JSON: 831-1.0102383-rdf.json
Turtle: 831-1.0102383-turtle.txt
N-Triples: 831-1.0102383-rdf-ntriples.txt
Original Record: 831-1.0102383-source.json
Full Text
831-1.0102383-fulltext.txt
Citation
831-1.0102383.ris

Full Text

RELATIVE VALUE ANALYSIS by DAVID JAMES NYE B.Com., U n i v e r s i t y of B r i t i s h Columbia,  1965  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION  i n the Department of Commerce and Business A d m i n i s t r a t i o n  We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA June  1968  iii  In p r e s e n t i n g  this thesis i n p a r t i a l fulfillment  the requirements f o r an advanced degree a t the  of  University  of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e for reference  and  study.  I f u r t h e r agree  that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may  be granted by the Head of  Department or by h i s r e p r e s e n t a t i v e s .  my  I t i s understood  copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l s h a l l not be allowed without my  written  permission.  David J .  Department of Commerce and  Business  The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date August 13, 1968.  Nye  Administration  gain  that  ABSTRACT T h i s study i s an e m p i r i c a l a n a l y s i s of a t e c h n i c a l s t o c k s e l e c t i o n technique. the p e r i o d 1956  - 1967.  A random sample i s s t u d i e d f o r  P o r t f o l i o s are c o n s t r u c t e d  and  managed by b u i l d i n g a model c o n t a i n i n g three v a r i a b l e s — r e l a t i v e earnings, prices.  The  r e l a t i v e price-earnings  and  relative  o b j e c t i v e of the study i s to gather evidence  which w i l l t e s t the hypothesis t h a t r e l a t i v e value  analysis  s e l e c t s p o r t f o l i o s whose r a t e of a p p r e c i a t i o n i s g r e a t e r than that of a buy-and-hold s t r a t e g y or that of the market. The With few  r e s u l t s of the a n a l y s i s support the  exceptions  the s t r a t e g i e s ' r a t e s of a p p r e c i a t i o n are  up to s e v e r a l percentage p o i n t s higher a p p r e c i a t i o n of both the market and  than the r a t e of  the buy-and-hold  Secondly, p o r t f o l i o s which are c o n s t r u c t e d amental a n a l y s i s and higher  r a t e s of  r e l a t i v e value a n a l y s i s show even  appreciation.  several s p e c i f i c conclusions  general conclusion  (a)  a  general  are reached.  The  formed i s t h a t r e l a t i v e value a n a l y s i s i s  a p r o f i t a b l e stock s e l e c t i o n technique. it  strategy.  u s i n g both fund-  As a consequence of the r e s u l t s o b t a i n e d , c o n c l u s i o n and  hypothesis.  i s concluded t h a t : Trends i n stock p r i c e s do e x i s t .  More s p e c i f i c a l l y ,  (b)  Fundamental a n a l y s i s serves selecting  (c)  securities  an important f u n c t i o n i n  to maximize p o r t f o l i o  returns.  The a n a l y s t who uses the r e l a t i v e value method w i l l make buy and s e l l d e c i s i o n s which r e s u l t  i n the  s e l e c t e d p o r t f o l i o outperforming the market.  TABLE OP CONTENTS CHAPTER I.  II.  PAGE 1  INTRODUCTION . Purpose and Scope of the Study  2  D e f i n i t i o n of Terms Used  4 15  THE CONCEPT OF RELATIVE VALUE ANALYSIS The  Five-Stage  15  Theory  Risk III. IV.  V.  22  RELATIVE VALUE - REVIEW OF THE LITERATURE  . . .  2? 61  DEVELOPMENT OF THE MODEL Development o f the Model  6l  R e s u l t s of the T e s t  ?2  CONCLUSIONS  82 86  BIBLIOGRAPHY APPENDIX i :  EXCHANGE LISTING REQUIREMENTS  APPENDIX I I .  TABLES 10 - 13  APPENDIX I I I .  GRAPHS A - D  . . . .  . . . .  89 91 100  LIST OF TABLES TABLE  PAGE  1.  Summary of Whitbeck & K i s o r T e s t R e s u l t s  2.  Summary o f R. Levy's Test R e s u l t s  3.  R e s u l t s o f T e s t i n g the V a l i d i t y o f the  . . . . . .  . : .  47  . . : . .  49  T r a n s i t i o n Matrix  5.  Study No.  6.  R e s u l t s of M u l t i p l e R e g r e s s i o n A n a l y s i s  7.  Percent of T o t a l Number of Purchases  . . .  1952-1963  42  45  4.  - Test Results  36  ; • . .  F i v e - S t a g e Hypothesis  1  . . .  . . .  56  Executed During I n i t i a l 20% of Sample 71  Time P e r i o d  8.  Summary of R e s u l t s o f Study No.  9.  Compound Growth Rate of Study No. 1 on a D o l l a r Commitment B a s i s  10-13.  Appendix I I  1 - 1964-1967.  72 79  91  LIST OP FIGURES FIGURE  PAGE  A.  Graph of S u p e r i o r E a r n i n g s Performance  . . . . .  5  B.  Graph of Average E a r n i n g s Performance  . . . . .  5  C.  Graph of Below Average Earnings Performance . . .  D.  Graph of F i v e - S t a g e C y c l e . . . . . . . . . . . .  E.  Expected D i s t r i b u t i o n of R e l a t i v e P r i c e i n P e r i o d t+1 G i v e n a L e v e l of y i n Year t . . . .  F.  R e l a t i v e P r i c e - Dynamic and S t a t i c Models  G.  S. & P. Composite p-e R a t i o  . . .  5 14  25 60 69  CHAPTER I INTRODUCTION T r a d i t i o n a l l y , each i n v e s t o r has had  one  or more of  the f o l l o w i n g o b j e c t i v e s : (a)  The  (b)  The p r e s e r v a t i o n of the purchasing the d o l l a r .  (c)  To earn an adequate r e t u r n on  (d)  To maximize r e t u r n on  Various an i n v e s t o r may achieve  p r e s e r v a t i o n of c a p i t a l .  investment.  investment.  techniques have been suggested i n order p r o p e r l y manage h i s p o r t f o l i o and  his objectives.  evaluated  power of  that  thereby  T r a d i t i o n a l l y , f i r s t of a l l one  stocks on the b a s i s of e i t h e r fundamental a n a l y s i s i  or t e c h n i c a l a n a l y s i s . of Random Walk  has  More r e c e n t l y , however, the Theory  been g a i n i n g acceptance as a good  d i c t o r of s e c u r i t y p r i c e f l u c t u a t i o n s . As a r e s u l t , Theory has been used to c r i t i c i z e the use  prethe  of t e c h n i c a l  a n a l y s i s , s i n c e the l a t t e r assumes the e x i s t e n c e of  trends  i n stock p r i c e movements. The  next s t e p i n the management of p o r t f o l i o s was  determine not only the percent  d i s t r i b u t i o n of s e c u r i t i e s i n  i & < i p i e r e f e r to S e c t i o n I I of t h i s chapter d e f i n i t i o n of termsL e a S  to  for  2 the p o r t f o l i o hut a l s o how t h i s d i s t r i b u t i o n should  vary  over time. In s p i t e of the l a r g e amounts of e f f o r t which have been devoted t o d e t e r m i n i n g the best a l l o c a t i o n o f i n v e s t o r resources notable  i n order  t o meet s p e c i f i c o b j e c t i v e s , t h e r e  isa  l a c k of investment techniques which a r e a b l e t o s a t i s f y  the i n v e s t o r whose aim i t i s t o "outperform" the market.3 I . PURPOSE AND SCOPE OP THE STUDY Purpose.  T h i s study was undertaken i n order  (1) t o  i n v e s t i g a t e the hypothesis t h a t r e l a t i v e value a n a l y s i s enables the i n v e s t o r t o make buy and s e l l d e c i s i o n s which permit him t o a t t a i n h i s o b j e c t i v e of outperforming the market; (2) t o o f f e r support t o the " t r e n d i s t " s c h o o l , which advocates that t e c h n i c a l a n a l y s i s of stock p r i c e data i s a p r o f i t a b l e technique; (3) t o answer c r i t i c i s m s ^ of my previous  study.5  3"Outperforming" the market i s an e x p r e s s i o n used t o i n d i c a t e t h a t the s e l e c t e d p o r t f o l i o e x h i b i t e d a g r e a t e r growth r a t e than t h e market, as measured by an Index. ^The c o n c l u s i o n reached i n t h i s study was that i t was p o s s i b l e t o c o n s i s t e n t l y outperform the market. T h i s c o n c l u s i o n was c h a l l e n g e d on two grounds. F i r s t of a l l , the time p e r i o d s e l e c t e d (1952-1963) was one of g e n e r a l l y r i s i n g p r i c e - e a r n i n g s r a t i o s and t h e r e f o r e one d i d not need t h i s technique t o outperform the market. Secondly, the u n i v e r s e of f i r m s from which the sample was s e l e c t e d was n e i t h e r s u f f i c i e n t l y l a r g e ( i t contained only 70 f i r m s ) nor was i t r e p r e s e n t a t i v e of the stock market as a whole. ^Davld J . Nye, R e l a t i v e Value A n a l y s i s , unpublished B a c h e l o r of Commerce T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, May, 1965.  3 The scope of the study i s very narrow but i s nevert h e l e s s of c o n s i d e r a b l e s i g n i f i c a n c e . Importance of the Study. because,  The study i s important  f i r s t of a l l , i t e x p l o r e s a s t o c k s e l e c t i o n technique  which has not been thoroughly i n v e s t i g a t e d to d a t e . with the " a r t " of i n v e s t i n g and attempts body of knowledge i n t h i s a r e a .  to c o n t r i b u t e t o the  The word " a r t " i s used  r a t h e r than s c i e n c e f o r the f o l l o w i n g r e a s o n . s t o c k market approaches  the economist's  market, i . e . , e x c l u d i n g those who  I t deals  Given that the  i d e a l of a p e r f e c t  have both the means and the  a b i l i t y t o m a i n t a i n ^ a market i n a p a r t i c u l a r s e c u r i t y or a c t on the b a s i s of " i n s i d e " i n f o r m a t i o n , the s u c c e s s f u l  investor  i s more of a b e h a v i o r l s t than a s c i e n t i s t . The past t e n years has seen a n o t a b l e Increase i n the use of q u a n t i t a t i v e techniques i n s e c u r i t y v a l u a t i o n and s e l e c t i o n and they may  s a f e l y be c a l l e d p r o g r e s s .  the most s o p h i s t i c a t e d model must s t i l l  i n c l u d e one  v a r i a b l e — p e o p l e and t h e i r e x p e c t a t i o n s . of  However, important  Our present l e v e l  technology i s improving i n i t s a b i l i t y to understand,  measure and p r e d i c t the a c t i o n s of people but much remains to be done.  T h i s , of course, excludes the " s p e c i a l i s t s " employed by the New York Stock Exchange, whose f u n c t i o n i t i s t o m a i n t a i n an o r d e r l y market f o r the b e n e f i t of a l l i n v e s t o r s . See Baumol, The Stock Market and Economic E f f i c i e n c y .  A second reason why t h i s study i s important i s the I m p l i c a t i o n which s u c c e s s f u l t e c h n i c a l a n a l y s i s has with r e g a r d to t h e r o l e of fundamental  a n a l y s i s of s e c u r i t i e s .  I f p r o f i t s , i . e . , a p p r e c i a t i o n i n the p r i c e of a s e c u r i t y , can be earned which a r e equal t o or b e t t e r than those a t t a i n a b l e by the use of fundamental  a n a l y s i s i n stock evaluation,  then the a l l o c a t i o n a n n u a l l y of s u b s t a n t i a l r e s o u r c e s by the investment  Industry c o u l d be c r i t i c i z e d on the grounds t h a t  the funds a r e not being put t o t h e i r most p r o d u c t i v e u s e . I I . DEFINITION OF TERMS USED Relative Earnings:  R e l a t i v e earnings a r e d e f i n e d as  the earnings per share of the f i r m f o r a 12-month p e r i o d d i v i d e d by the earnings per share of the market index f o r the same 12-month p e r i o d .  M a t h e m a t i c a l l y , t h i s may be  expressed a s : X  it  =  ^ l t E  Where:  X e  =  lt  E  t  t  the 12-month r e l a t i v e earnings per share of the i t h s e c u r i t y a t time t earnings per share o f the i t h company's stock f o r the 12-months ending a t time t  =  =  the earnings per share of the market index f o r the 12 months ending a t time t  Relative  earnings may be computed f o r a s e r i e s of  time periods and p l o t t e d on semi-log graph i n the f o l l o w i n g  paper, as shown  figures:  A S u p e r i o r Earnings Performance  B Average E a r n i n g s Performance  C Below Average Earnings Performance  Relative Value (Log s c a l e )  Time As  i s shown i n the f i g u r e s , X may be t r e n d i n g upward,  downward or h o r i z o n t a l l y , i . e . , the s l o p e of the r e l a t i v e earnings l i n e may be p o s i t i v e , negative or z e r o . the f o l l o w i n g ,  Consider  i f we l e t :  e = de = the r a t e o f change of the f i r m ' s earnings dt with r e s p e c t to time. E = dE = the r a t e of change of the Index's earnings dt with r e s p e c t to time. Then:  Case (a) a r i s e s when ( I ) e > £ ( l i ) -e > -E Case (b) a r i s e s when ( i ) e = £ ( i i ) -e = -E Case ( c ) a r i s e s when ( i ) e < E ( i i ) -e < -E  Then dX w i l l be p o s i t i v e (Case (a) ) when ( i ) e > E , dt ( i i ) -e > -E. S i m i l a r l y , dX w i l l be negative (Case (c) ) dt when ( i ) e < S or ( i i ) -e < -E and dX w i l l equal zero when dt ( i ) e = E or ( i i ) -e = -E. Relative Price:  R e l a t i v e p r i c e i s d e f i n e d as the  p r i c e o f a stock a t a p a r t i c u l a r p o i n t i n time d i v i d e d by the p r i c e o f a market index a t t h a t same p o i n t i n time. For purposes o f t h i s study, r e l a t i v e p r i c e i s r e p r e sented as  and i s equal t o p ^ where:  *T p  l t  P  t  As  = the p r i c e of the 1 t h s e c u r i t y a t time t = the p r i c e of the market index a t time p e r i o d t . i n d i c a t e d i n the case o f r e l a t i v e e a r n i n g s , the  s l o p e of the r e l a t i v e p r i c e l i n e dY may be e i t h e r p o s i t i v e , dt n e g a t i v e or z e r o . By determining whether dY i s g r e a t e r than dt or l e s s than z e r o , the a n a l y s t i s a b l e t o measure whether a Thus, i f dY i s > 0 dt f o r a s e c u r i t y , then t h a t s e c u r i t y i s outperforming the market s e c u r i t y i s outperforming the market.  Relative Price-Earnings R a t i o :  The r e l a t i v e  price-  earnings r a t i o i s d e f i n e d as the p r i c e earnings r a t i o o f the stock d i v i d e d by the p r i c e - e a r n i n g s r a t i o of the market  7it  index.  should be noted t h a t dY may be p o s i t i v e , although dt the change inp^. f o r the same p e r i o d i s n e g a t i v e and v i c e v e r s a  T h i s may be expressed mathematically a s : Z  it  =  P lt e  PE Where: p e  l t  t  = the p r i c e - e a r n i n g s r a t i o o f the i t h s e c u r i t y a t time t  PE. = the p r i c e - e a r n i n g s r a t i o of the market index. The s l o p e o f the r e l a t i v e p r i c e - e a r n i n g s l i n e  ( d e f i n e d as dZ) dt o f f e r s a reasonably good measure of i n v e s t o r "enthusiasm" f o r  a security.  I f dZ i s p o s i t i v e f o r a reasonably long p e r i o d dt of time, e.g., 2-3 y e a r s , the s l o p e o f the l i n e i n d i c a t e s  t h a t the s e c u r i t y enjoyed p e r i o d o f time.  investor popularity during that  C o n v e r s e l y , i f dZ i s n e g a t i v e f o r a s i m i l a r dt  p e r i o d , t h i s i s good evidence t h a t the stock i s out of favour and t h e r e f o r e should be avoided i n most c a s e s . R e l a t i v e Value A n a l y s i s :  R e l a t i v e value a n a l y s i s i s  the use o f the v a r i a b l e s ( r e l a t i v e e a r n i n g s , r e l a t i v e  price  and r e l a t i v e p r i c e - e a r n i n g s ) t o decide when a stock should be i n c l u d e d and when i t should be e l i m i n a t e d from a p o r t f o l i o . Fundamental A n a l y s i s :  Fundamental a n a l y s i s i s the  a n a l y s i s and f o r e c a s t i n g o f economic, i n d u s t r y and f i r m f a c t o r s i n order t o determine the i n t r i n s i c value of a s e c u r i t y a t a s p e c i f i c  or t h e o r e t i c a l  p o i n t i n time.  The l o g i c  behind t h i s method i s that i f the t h e o r e t i c a l value i s g r e a t e r than market p r i c e , the stock should be purchased.  Conversely,  8 it  should be s o l d i f the i n t r i n s i c  market v a l u e .  Opposed t o t h i s idea a r e the membeis o f the  technical analysis  school.  Technical Analysis: of s e c u r i t y p r i c e s only decision.  v a l u e i s l e s s than the  This analysis  Technical  analysis  i s the study  i n order t o make an investment i s founded upon the b e l i e f that a l l  factors a f f e c t i n g a security are r e f l e c t e d i n i t s price eventually p r i c e trend  and one has only t o i n t e r p r e t c o r r e c t l y the stock's i n order t o p r e d i c t a c c u r a t e l y  i t s price  fluctuations. T h i s method o f a n a l y s i s assumes the e x i s t e n c e i n successive has  price differences.  been s e v e r e l y  criticized  o f trends  L a t e l y , t h i s assumption  by some members o f the academic  community, who have proposed, as an a l t e r n a t i v e , the Theory of Random Walk. Random Walk Theory: is defined  here t o mean that p r i c e changes o f a s t o c k a r e  statistically learned series. chart  B r i e f l y , the Random Walk Theory  independent o f each o t h e r .  Nothing can be  about the f u t u r e by l o o k i n g a t the stock's p r i c e Thus, buying a s t o c k based on s i g n a l s from a p r i c e  w i l l produce r e s u l t s no b e t t e r  f l i p p i n g of a f a i r  coin.  than those from repeated  9 Growth Stock;  Since the concept o f a growth stock  i s q u i t e important to the Theory of R e l a t i v e Value A n a l y s i s , more space than u s u a l i s devoted t o i t s d e f i n i t i o n . As  i n other areas of f i n a n c e , the t h e o r i e s of  d e f i n i t i o n and v a l u a t i o n o f growth common stocks have moved from a g e n e r a l l y q u a l i t a t i v e approach, such as that taken by Jenks, K o t l e r and B e r n s t e i n , t o a q u a n t i t a t i v e method, such as that suggested by B u r r e l l , Solomon, and, more r e c e n t l y , Mao. B e r n s t e i n ^ makes an important d i s t i n c t i o n between a growth company and a growth s t o c k .  To him, a growth company  i s not one whose s a l e s and earnings  i n c r e a s e merely as a r e s u l t  of the f i r m ' s response t o f a v o u r a b l e population  e x t e r n a l f a c t o r s , such as  i n c r e a s e ; r a t h e r , he sees true growth as being  "inner d i r e c t e d . "  I n other words, the management o f a growth  f i r m i s the d r i v i n g f o r c e .  "The a b i l i t y t o c r e a t e i t s own  market i s the s t r a t e g i c , the dominating, and the s i n g l e most d i s t i n g u i s h i n g c h a r a c t e r i s t i c o f a t r u e growth company."9 Opposed t o t h i s view i s K o t l e r ' s somewhat d e f i n i t i o n o f a growth s i t u a t i o n .  loose  "... a growth stock i s the  stock o f a company which has shown f o r a number of years i s showing annual percentage i n c r e a s e s i n net earnings  and/or  which  °P. B e r n s t e i n , "Growth Companies versus Growth S t o c k s , " Harvard Business Review, v o l . 34, No. 5 (September-October 1956),  pp. 87-98. 9  I b i d . , p. 91.  s u b s t a n t i a l l y exceed the l o n g run growth r a t e i n the economy A®  11 To Jenks,  x  a growth company means "a company t h a t  e v e n t u a l l y be s u c c e s s f u l and phase of r a p i d development."  t h a t i s now He  will  i n or e n t e r i n g a  enumerates s e v e r a l  character-  i s t i c s of growth companies such as h i g h m u l t i p l e s , low y i e l d s , plus s e v e r a l other t e c h n i c a l p r i c e p a t t e r n s . article  i s easy to r e a d ,  represent  i t i s a t a low  l e v e l and does not  a s i g n i f i c a n t c o n t r i b u t i o n t o the  B u r r e l l , ^ w r i t i n g In  I960,  Although the  theory.  suggests that two  Important  f a c t o r s i n v a l u i n g growth companies are the h i s t o r i c a l growth r a t e of the d i v i d e n d and  investor expectations.  that a measure of i n v e s t o r expectations s h i p of d i v i d e n d s being  current The  two  i s the past  suggests relation-  to market p r i c e with an a d d i t i o n a l i n d i c a t o r  stock market  current  He  levels.  p r i c e i s the sum  e l e m e n t s — t h e present  value  f u t u r e date plus the present  of the present  values  of  of the s e l l i n g p r i c e a t some  value  of an annuity  of  the  P . K o t l e r , "Elements i n a Theory of Growth Stock V a l u a t i o n , " Readings i n F i n a n c i a l A n a l y s i s and Investment Management. (Ed. E, M. L e r n e r ) . Homewood, I l l i n o i s , R i c h a r d D. I r w i n , Inc., 1963, pp. 355. i U  Hj.  P.  C. Jenks, " I n v e s t i n g  i n Growth S t o c k s , " i b i d . ,  325.  0 . K. B u r r e l l , "A Mathematical Approach to Growth Stock V a l u a t i o n , " i b i d . , p. 338. 1 2  expected i n c r e a s i n g d i v i d e n d s .  Thus, B u r r e l l must assume  a growth r a t e i n d i v i d e n d s , the d u r a t i o n of the growth, an appropriate  c a p i t a l i z a t i o n r a t e and  an a p p r o p r i a t e  discount  rate. According  to B u r r e l l , the c u r r e n t market p r i c e i s  then equal t o : P  0  = D r  ' (l+ff?  D  (l+r)  n  n  +  £  D  1=1  0  /l±_f \l+rj  Where: P D r  Q  = the proper p r i c e to pay  0  = the c u r r e n t d i v i d e n d per Q  r The  f o r the stock today share  = the r a t e which an i n d i v i d u a l i n v e s t o r uses t o c a p i t a l i z e a constant s i z e income stream i n perpetuity = the d i s c o u n t r a t e which an i n d i v i d u a l i n v e s t o r a p p l i e s to a f u t u r e d o l l a r first  term i s an estimate  of the present  value  of the stock's expected market p r i c e i n years hence and second term i s an estimate expected d i v i d e n d  of the present  income over the  the  value of the  period.  A more c u r r e n t d e f i n i t i o n of a growth company i s that of Mao's: "... a company which has  s p e c i f i c o p p o r t u n i t i e s to  i n v e s t funds at a p e r p e t u a l a f t e r - t a x annual r e t u r n of r , where r i s g r e a t e r than the s t o c k h o l d e r ' s r e t u r n , y."*3  He  r e q u i r e d r a t e of  summarizes two models of permanent growth  3James C. T. Mao, Q u a n t i t a t i v e A n a l y s i s of F i n a n c i a l D e c i s i o n s . unpublished manuscript, U n i v e r s i t y of B r i t i s h Columbia, 1968. Chapter 10, p. 30. 1  as developed  "by Solomon*^ and M o d i g l i a n i and M i l l e r ^ ^ and  then develops a model which i n c o r p o r a t e s e x p o n e n t i a l growth of e a r n i n g s , constant growth and d e c l i n i n g growth. It and  i s important  to note t h a t these models r e c o g n i z e  i n c o r p o r a t e the investment  o p p o r t u n i t i e s approach.  Thus,  i n the f i n a l a n a l y s i s , d i v i d e n d s are a f u n c t i o n of earnings, which i n t u r n a r e a f u n c t i o n o f the o p p o r t u n i t y of the f i r m to i n v e s t i t s funds a t a r a t e g r e a t e r than y.  Solomon, The Theory o f F i n a n c i a l Management, New York, Columbia U n i v e r s i t y Press, 1963. 5 f . M o d i g l i a n i and M. M i l l e r , "Dividend P o l i c y Growth, and the V a l u a t i o n o f Shares," J o u r n a l of B u s i n e s s , v o l . 34 (October 196l), pp. 421-449. 1  CHAPTER I I THE CONCEPT OF RELATIVE VALUE ANALYSIS In Chapter  I the hypothesis was  s t a t e d , and  i n this  chapter the u n d e r l y i n g theory which l e d to the hypothesis will  be g i v e n .  I n a d d i t i o n , the concept  of r i s k and i t s  r e l a t i o n t o r e l a t i v e value w i l l be d i s c u s s e d . I. THE  FIVE-STAGE THEORY  T h i s theory s t a t e s t h a t , g i v e n a s i t u a t i o n of i n c r e a s i n g r e l a t i v e e a r n i n g s , the market i n i t i a l l y respond  fails  f a v o u r a b l y to the improved e a r n i n g s , and then  i n an exaggerated upon the premise  manner.  to  responds  In other words, the theory r e s t s  t h a t human beings i n g e n e r a l r e a c t i n a  manner which i s not p r o p o r t i o n a t e to the o r i g i n a l  stimuli.  Benjamin F. Graham expressed e s s e n t i a l l y the same i d e a when he  said: One t h i n g badly needed by i n v e s t o r s — a n d a q u a l i t y they r a r e l y seem to h a v e — i s a sense of f i n a n c i a l h i s t o r y . 1 ° Yet the market tends to greet each upsurge as i f i t were the b e g i n n i n g of an endless growth and each d e c l i n e i n earnings as i f i t pressaged u l t i m a t e extinction.*7  B . Graham, The I n t e l l i g e n t I n v e s t o r , 3rd Harper & Row, New York (1965), p. 13. 1 D  1  ? I b l d . . p.  14.  edition,  14 In order t o b e t t e r understand t h i s i d e a , i t i s convenient  t o d i v i d e t h i s process  of under and o v e r - r e a c t i o n  Into f i v e stages, as shown i n F i g u r e D. FIGURE D Graph o f 5-Stage C y c l e Stage 1  2  3  4  5  R e l a t i v e Value (Log S c a l e )  Time  During  Stage 1, r e l a t i v e  sloped while the r e l a t i v e slope.  earnings a r e p o s i t i v e l y  p r i c e - e a r n i n g s l i n e has a negative  T h i s means t h a t the f i r m ' s earnings  g r e a t e r r a t e than those  of the index.  a r e growing a t a  A t the same time, a  f a l l i n g r e l a t i v e p r i c e - e a r n i n g s l i n e i n d i c a t e s that the f i r m ' s m u l t i p l e i s r i s i n g a t a slower r a t e than the m u l t i p l e of the market i s r i s i n g .  On the other hand, i t may i n d i c a t e  that the f i r m ' s m u l t i p l e i s f a l l i n g a t a r a t e g r e a t e r than t h a t o f the market.  The  impact  of the r e l a t i v e earnings and  relative  p r i c e - e a r n i n g s change upon r e l a t i v e p r i c e w i l l depend upon t h e i r comparative mathematically Chapter  I , we X^  t  movements.  T h i s idea may  i n the f o l l o w i n g manner.  As  be  expressed  indicated i n  have:  = the r e l a t i v e earnings per share of the i t h s e c u r i t y a t time t = the r e l a t i v e p r i c e of the i t h s e c u r i t y a t time t = the r e l a t i v e p r i c e earnings r a t i o of the i t h s e c u r i t y a t time t .  Values of X, Y and Z f o r a number of time periods may calculated.  be  Having c a l c u l a t e d these values and p l o t t e d them  on s e m i - l o g a r i t h m i c graph  paper as i n F i g u r e D,  i t is  p o s s i b l e t o r e g r e s s these values a g a i n s t time and o b t a i n an e q u a t i o n of the form y = a + bx. the  In our case we would o b t a i n  following: (1) X = a +o<T  (2) Y = b + £ T (3) Z = c  +TT  Where: a, b and c are c o n s t a n t s . oC = the s l o p e of the r e l a t i v e earnings  line.  ^  = the slope of the r e l a t i v e  price  line.  if  = the slope of the r e l a t i v e line.  price=earnlngs  16 Then i f : (a)  ©< = ~Y .  (b)  <<  >  1$  >  0  (o)  c<  <  nr ; ? <  0  Stage 1 has  behavioural  ;  £  been c a l l e d a "base b u i l d i n g " stage s i n c e  the market l a r g e l y ignores the f i r m .  P = o  the improving earnings p i c t u r e of  T h i s i s an i n t e r e s t i n g occurrence from a p o i n t of view and  bears f u r t h e r d i s c u s s i o n .  Proceeding from the p o s i t i o n t h a t an earnings i n c r e a s e i s " b e t t e r " from the point of view of an o u t l e t f o r h i s funds, why words, why  should  should ^ be n e g a t i v e ?  i n v e s t o r s be w i l l i n g to pay  l e s s f o r i n c r e a s i n g earnings? not aware of the  i n v e s t o r seeking  The  In  an  other  relatively  p o s s i b i l i t y that they are  i n c r e a s e can s a f e l y be  ignored.  Another  p o s s i b i l i t y i s t h a t they are aware of the s i t u a t i o n but b e l i e v e the  Increase to be only a temporary r e v e r s a l of a  long term downtrend as evidenced by previous  data.  This  c o u l d be case (c) mentioned p r e v i o u s l y , where °< K if and s e c u r i t y p r i c e i s being adjusted r e v i s e d l o n g term  downwards on the b a s i s  the  of  expectations.  I n case ( a ) , <=*£. = 1$ , i . e . , the slope of l i n e X i s equal to the s l o p e of l i n e Z.  Under these c o n d i t i o n s ,  investors  appear to b e l i e v e t h a t earnings w i l l r e t u r n to a "normal" l e v e l and  t h e r e f o r e , the adjustment i n B r e f l e c t s these  expectations.  In  case (b) i t c o u l d be argued t h a t some i n v e s t o r s  b e l i e v e the i n c r e a s e t o be a fundamental  improvement and,  on t h i s b a s i s , the f a l l i n g r e l a t i v e p r i c e earnings r a t i o does not completely o f f s e t the r i s i n g r e l a t i v e e a r n i n g s . In  t h i s s i t u a t i o n there a r e enough " b e l i e v e r s " t o more than  o f f s e t the " d i s b e l i e v e r s " and as a r e s u l t Q i s p o s i t i v e . E x p e c t a t i o n s a r e f o r continued improved  earnings but they  a r e by no means unanimous. By f o c u s s i n g on r e l a t i v e e a r n i n g s , we have excluded many other explanatory v a r i a b l e s and they must now be mentioned.  A c c o r d i n g t o K i n g , ^ market and i n d u s t r y f a c t o r s a r e very  important i n the e x p l a n a t i o n o f s e c u r i t y p r i c e changes. However, by d i v i d i n g f i r m data by market d a t a , we have excluded the market and i n d u s t r y impact. more t o the f i r m and the impact  T h i s b r i n g s us once  that other v a r i a b l e s such as  d i v i d e n d s , cash flow and l e v e r a g e w i l l have on s e c u r i t y Rather than attempting t o determine  prices.  the i n f l u e n c e o f  each o f these v a r i a b l e s as s t o c k p r i c e determinants, they a r e merely mentioned and the d i s c u s s i o n w i l l continue to be c e n t e r e d on earnings as an important v a r i a b l e i n determining stock p r i c e changes.  • Benjamin F. King, "Market and Industry F a c t o r s i n Stock P r i c e Behaviour," J o u r n a l of F i n a n c e , v o l . 39, No. 1, Part I I (January 1966), p. 139. LO  18 A good d i s c u s s i o n of the concept of changed earnings and  Investor  expectations  i s provided  by Whitbeck and  Kisor. ? 1  In t h e i r paper they p o i n t out that d u r i n g a business c y c l e the m u l t i p l e s of many f i r m s behave i n a c o n t r a - c y c l i c a l manner. versa.  Thus, as earnings r i s e , the m u l t i p l e f a l l s and Obviously  vice  i n v e s t o r s have some n o t i o n of "normal"  earnings f o r the f i r m and  the occurrence of a Stage 1 merely  i n d i c a t e s that they expect the f i r m to continue to behave i n a c y c l i c a l fashion.  As  earnings r i s e , t h e i r expectations  do  not change and,  as a r e s u l t , the p r i c e of the s e c u r i t y remains  f a i r l y constant  and  the m u l t i p l e c o n t r a c t s .  When earnings  f a l l because of a d e c l i n e i n economic a c t i v i t y ,  investors  expect them to i n c r e a s e when the economy resumes i t s growth. Therefore,  s e c u r i t y p r i c e s are maintained and  the  multiple  expands. Stage 2 i s d e f i n e d as one continue to i n c r e a s e  ( i . e . °<  earnings r a t i o remains constant  >  i n which r e l a t i v e earnings 0) but ( Y  the r e l a t i v e p r i c e  = 0).  T h i s stage i n the  c y c l e i n d i c a t e s that i n v e s t o r s are r e v i s i n g t h e i r about the f u t u r e earnings of the f i r m and  expectations  as a r e s u l t are  w i l l i n g to pay r e l a t i v e l y more f o r each share i n the  belief  !9v. S. Whitbeck and M. K l s o r , J r . , "A New T o o l i n Investment D e c i s i o n Making." R e p r i n t e d i n F r o n t i e r s of Investment A n a l y s i s (Ed. E. Bruce F r e d r i k s o n ) . Scranton, Pennsylvania, I n t e r n a t i o n a l Textbook Company, 1965, pp.  335-350.  19 that r e l a t i v e  earnings w i l l continue t o expand.  As w i l l "be  I n d i c a t e d l a t e r , t h i s stage does not p l a y a s i g n i f i c a n t i n the concept mainly because of d e f i n i t i o n a l  role  inadequacies.  During Stage 3 r e l a t i v e earnings continues to expand and,  i n a d d i t i o n , the r e l a t i v e p r i c e earnings r a t i o expands,  resulting  i n r e l a t i v e p r i c e s u b s t a n t i a l l y outperforming  market.  the  During t h i s stage i n the c y c l e i n v e s t o r s appear to  have confirmed t h e i r b e l i e f that t h i s i s a growth f i r m . b e l i e v e t h a t t h i s above average continue  u  They  earnings growth i s going to  and a r e , t h e r e f o r e , w i l l i n g t o pay more f o r each  share. Stage 3 i s i n t e r e s t i n g  t o c o n s i d e r with r e f e r e n c e t o  the Whitbeck and K i s o r theory and the b e h a v i o u r a l l s t I t would appear t h a t i n v e s t o r s view the f i r m from a p o i n t of view u n t i l Stage 3 o c c u r s .  approach. cyclical  A t t h i s time, the over-  r e a c t i o n takes p l a c e and the value of the r e l a t i v e  price  earnings r a t i o i n c r e a s e s to a l e v e l which i s not j u s t i f i a b l e when s u b j e c t e d t o r a t i o n a l  analysis.  Stage k i s d e f i n e d as having s t a b l e r e l a t i v e while r e l a t i v e p r i c e earnings continue t o i n c r e a s e . s t o c k i n t h i s stage w i l l continue to outperform i n Stages average  earnings, Thus, a  the market as  2 and 3 (and p o s s i b l y i n Stage 1 a l s o ) but the above  performance i s due  s o l e l y to an i n c r e a s i n g m u l t i p l e  ^ I t i s d i f f i c u l t t o determine what i s each i n v e s t o r ' s time h o r i z o n f o r t h i s expected growth. u  20 and  i s thus a p o t e n t i a l l y dangerous s i t u a t i o n from the  s t o c k h o l d e r ' s p o i n t of view.  The r e a s o n i n g behind the  occurrence o f Stage 4 i s as f o l l o w s . increase,  through Stages  1,  As r e l a t i v e  earnings  2 and 3> a n I n c r e a s i n g number  of i n v e s t o r s become aware o f the s u p e r i o r earnings gains being r e p o r t e d by the f i r m .  As t h i s number becomes s u f f i c i e n t -  l y l a r g e , demand f o r the stock i s i n i t i a l l y then e q u a l , and f i n a l l y exceeds supply.  l e s s than supply,  Stage k r e f l e c t s  the s i t u a t i o n o f c o n t i n u i n g excess demand r e s u l t i n g i n the expanding m u l t i p l e . What i s the reason f o r t h i s apparent I t i s suggested  excess demand?  that i t i s a g a i n the r e s u l t o f f a v o u r a b l e  investor expectations.  I f e x p e c t a t i o n s a r e i n f l u e n c e d by  h i s t o r i c a l data (and i t would appear t h a t they are) i n v e s t o r s , n o t i n g the uptrend purchase  then  i n e a r n i n g s , continue to  the stock i n the e x p e c t a t i o n that t h i s uptrend  will  continue. Stage 5 occurs when both r e l a t i v e earnings and r e l a t i v e p r i c e earnings s l o p e downward, r e s u l t i n g i n a s u b s t a n t i a l d e c l i n e i n share v a l u e t o those h o l d i n g the s e c u r i t y d u r i n g t h i s stage.  As i s i n e v i t a b l e , almost a l l f i r m s experience an  earnings d e c l i n e a t some time or another.  When such a r e l a t i v e  earnings d e c l i n e i s experienced, concurrent with i t i s a r e l a t i v e p r i c e earnings r a t i o d e c l i n e — a g a i n the r e s u l t of r e v i s e d e x p e c t a t i o n s based  on new i n f o r m a t i o n .  21 In a l l p r o b a b i l i t y  i t i s unrealistic  t o t h i n k that  i n v e s t o r s never expect a f i r m ' s earnings t o d e c l i n e  since  the mathematical i m p l i c a t i o n s o f a h i g h growth r a t e compounded f o r even a l a r g e f i n i t e time p e r i o d a r e absurd.  The q u e s t i o n  then becomes: why would the s e c u r i t y continue t o be purchased d u r i n g Stage kl  Obviously  the answer i s t i m i n g .  Investors  expect earnings t o d e c l i n e e v e n t u a l l y but not i n the r e l a t i v e l y near f u t u r e i  When the d e c l i n e occurs,  the downward s l o p i n g  r e l a t i v e p r i c e earnings r a t i o i m p l i e s t h a t the downtrend i n r e l a t i v e earnings i s expected to continue f o r a time.  Other-  wise, r e l a t i v e p r i c e earnings would i n c r e a s e , based on the b e l i e f t h a t the r e l a t i v e earnings d e c l i n e was only  temporary  ?1  and  t h a t t h e growth would q u i c k l y be resumed. T h i s i s the very broad framework w i t h i n which we s h a l l  be d e a l i n g and i t i s expected t h a t there w i l l be which a r e not explained very naive explained  by t h i s t h e o r y .  exceptions  Indeed, i t would be  t o c l a i m that s e c u r i t y p r i c e movements can be by only one v a r i a b l e .  However, we s h a l l attempt  to a t t a i n t h e p r e v i o u s l y mentioned o b j e c t i v e by means of r e l a t i v e value a n a l y s i s . One  of the p o i n t s t o be noted here i s that  value a n a l y s i s i s not, nor i s i t claimed which stocks may be v a l u e d .  relative  to be, a method by  Rather, i t focuses  on the problem  ^•"•Some support i s l e n t t o t h i s by B. Graham's p r e v i o u s l y mentioned statement (see f o o t n o t e 1 7 ) .  22 that, given a c e r t a i n  s e c u r i t y and  i t s p r i c e , w i l l i t be  profitable  investment, i . e . , w i l l i t outperform the  We  r e a l l y concerned with whether the  are  not  valued or overvalued but  market?  stock i s under-  only whether that s e c u r i t y , i f  purchased, w i l l r i s e i n p r i c e more than the market or i n price less  than the  a  fall  market. I I . RISK  No sidering  d i s c u s s i o n of r i s k , and  w i t h i n the For kinds of  investments i s complete without con-  i n t h i s s e c t i o n r i s k w i l l be  context of r e l a t i v e our  purposes the  studied  values.  i n v e s t o r may  be  said  to f a c e  two  risk.  First  of a l l , he  f a c e s what we  w i l l c a l l Internal r i s k  op and  t h i s r i s k i s d e f i n e d as  The  use  of the  of the firm  word "chance  failing.  the 0  chance of the  firm  i m p l i e s some known  However, when one  failing.  probability  c o n s i d e r s that  Internal  21  r i s k i n c l u d e s both b u s i n e s s r i s k and d e r i v a t i o n of a p r o b a b i l i t y impossible, task.  financial risk,  J  f u n c t i o n i s a complex, but  I n t e r n a l r i s k i s reduced to the  the not  extent  " F a i l u r e " i s d e f i n e d as the c o n d i t i o n where the f i r m has i n s u f f i c i e n t resources to meet o b l i g a t i o n s as they f a l l due, or, i n Donaldson's words, there e x i s t s a s i t u a t i o n of "cash i n s o l v e n c y . " 2 2  3 " B u s i n e s s r i s k " and t r a d i t i o n a l meaning. 2  " f i n a n c i a l r i s k " have  the  23 p o s s i b l e by l i m i t i n g stocks  e l i g i b l e f o r i n c l u s i o n i n the  sample to those l i s t e d on the New June 30,  1955» ^ 2  York Stock Exchange as a t  No attempt w i l l be made i n t h i s p r o j e c t to  quantify i n t e r n a l r i s k .  To  the extent  t h a t a l l firms must  meet these minimum standards, the p r o b a b i l i t y of f a i l u r e i s maximized a t a c e r t a i n l e v e l with the l a r g e r firms presumably having a p r o b a b i l i t y lower than t h i s maximum. In a d d i t i o n to i n t e r n a l r i s k * the i n v e s t o r a l s o  faces  e x t e r n a l r i s k , which i s d e f i n e d as the r i s k of a d e c l i n e i n the value risk!  of the f i r m due  The  two  to a l l f a c t o r s other  types of r i s k may  than I n t e r n a l  be measured by the  i n the market p r i c e of the s e c u r i t y .  In some work to be  cussed i n a l a t e r chapter i t i s evident  dis-  that s e c u r i t y p r i c e  f l u c t u a t i o n s are a f u n c t i o n of market, i n d u s t r y and Thus, even though an i n v e s t o r may  variance  firm factors.  purchase an i n t e r e s t i n a  f i r m , not only because of i t s demonstrated earning  power but  a l s o because of i t s o p p o r t u n i t i e s f o r p r o f i t a b l e investment, he n e v e r t h e l e s s value  i s exposed t o the r i s k of a d e c l i n e i n the  of h i s shares due  to f o r c e s e x t e r n a l to the f i r m .  He  thus f a c e s , f o r example, the f o l l o w i n g anomaly; l e t us assume  24 .Y.S .E. l i s t i n g requirements are summarized i n Appendix I i n a d d i t i o n t o the requirements of the s m a l l e r , r e g i o n a l exchanges. I t i s i n t e r e s t i n g to note that the f i r s t N.Y.S.E. L i s t i n g Committee was formed i n 1866 and, over the y e a r s , standards have g r a d u a l l y been r a i s e d . However, s i n c e no e x i s t i n g c o n t r a c t i s bound by l a t e r agreements, the improved standards a p p l i e d only to the l a t e s t agreements and, l e g a l l y , a p r e v i o u s l y l i s t e d f i r m was not bound by the new standards. N  2k t h a t our  investor  t r u l y able  i s one  of those g i f t e d i n d i v i d u a l s who  t o f o r e c a s t the f u t u r e b e t t e r than most as  r e s u l t of h i s e x c e l l e n t a n a l y t i c a b i l i t y , both with to economic f a c t o r s and bought an able  human b e h a v i o r .  Our  investor  a v a i l a b l e to the  a  respect  i n t e r e s t i n a f i r m based on h i s f o r e c a s t of  investment o p p o r t u n i t i e s  is  has profit-  firm.  Subsequently a government department announces a p o l i c y change which i s expected t o a d v e r s e l y industry.  affect this particular  T h i s announcement r e s u l t s i n changed e x p e c t a t i o n s  of present and  p o t e n t i a l i n v e s t o r s and,  consequently,  the  supply of t h i s s e c u r i t y exceeds demand, r e s u l t i n g i n a lower p r i c e .  However, to what extent would  investors'  e x p e c t a t i o n s be r e v i s e d as a r e s u l t of l o g i c a l This  i s an extremely d i f f i c u l t  e m p i r i c a l evidence but, Our  i n v e s t o r has  i s of the o p i n i o n  obtain  would say not  enough.  assessed the s i t u a t i o n , however,  t h a t f a c t o r s e x i s t which w i l l m i t i g a t e  e f f e c t s of the p o l i c y change. a n a l y s i s may  analysis?  q u e s t i o n on which to  i n t u i t i v e l y , we  new,  Although the  and the  investor's  be c o r r e c t , he w i l l s u f f e r a l o s s or have h i s  p r o f i t s reduced, should he be f o r c e d to l i q u i d a t e h i s h o l d i n g s b e f o r e market p r i c e has  a d j u s t e d to the  " t h e o r e t i c a l " or  "intrinsic" price. R e c o g n i z i n g t h i s e x t e r n a l r i s k , the i s not  to minimize v a r i a n c e  but  investor's  objective  to choose a s e c u r i t y whose  expected d i s t r i b u t i o n of f u t u r e r e l a t i v e p r i c e s i s  negatively  skewed, (see F i g u r e E) d u r i n g the time he owns shares i n t h a t company. FIGURE E Expected D i s t r i b u t i o n of R e l a t i v e P r i c e i n p e r i o d t+1 g i v e n a l e v e l of y i n year t  Frequency  X H  As Markowitz pointed  out, v a r i a n c e  of r i s k s i n c e t h i s Implies  Hooe  i s not a t r u e measure  that d e v i a t i o n s on both s i d e s of  the r e g r e s s i o n l i n e are e q u a l l y u n d e s i r a b l e .  However, p o s i t i v e  d e v i a t i o n s are i n f i n i t e l y more d e s i r a b l e than negative  ones.  Thus, a measure such as the semi-variance i s more meaningful but  i t i s a l s o a much more complex programming problem.  In t h i s chapter the concept of r e l a t i v e value has been g i v e n and, i n a d d i t i o n , the n o t i o n of r i s k has been r e l a t e d to the s u b j e c t of the study. In the next chapter the l i t e r a t u r e on r e l a t i v e value w i l l be reviewed and the subsequent chapter e x p l a i n the development of the model.  will  CHAPTER I I I RELATIVE VALUE - REVIEW OF THE Although the use appealing very few  of r e l a t i v e values  i s an i n t u i t i v e l y -  concept, a review of the l i t e r a t u r e i n d i c a t e s that w r i t e r s have d e a l t with the s u b j e c t e x p l i c i t l y .  Most i n v e s t o r s r e a l i z e against  LITERATURE  some standard  that performance must be measured and  one  need only r e f e r ,  f o r example,  to the prospectus of any mutual fund or investment s e r v i c e to see the use interesting  of r e l a t i v e v a l u e .  point to note i s t h a t very  few  advisory  However, the i n v e s t o r s appear  to have i n v e s t i g a t e d the r e l a t i o n s h i p between the s e c u r i t y and  the standard  i n order to determine i f a meaningful  consistent pattern The was  and  exists.  e a r l i e s t reference  t h i s w r i t e r was  a b l e to f i n d  that of Rose,25 where r e l a t i v e values were used more as  a d e s c r i p t i v e t o o l , r a t h e r than an a n a l y t i c a l s e l e c t i o n technique. Rose Rose's main purpose was achieved  to study the r a t e s of r e t u r n  by f i n a n c i a l i n s t i t u t i o n s  p o r t f o l i o and  h i s r e l a t i v e value  on t h e i r  securities  technique i s shown i n an  ^Dwight C. Rose, A S c i e n t i f i c Approach to Investment Management. New York, Harper & B r o t h e r s , 1928. 2  28 appendix e n t i t l e d  " R e l a t i o n of Stock P r i c e Trends i n Each  Major I n d u s t r y to the P r i c e Trend of a l l S t o c k s . "  As the  heading i m p l i e s , Rose summed the market value of the stocks i n a p a r t i c u l a r group, d i v i d e d t h i s sum by the market  and  p l o t t e d t h i s r a t i o on semi-log c h a r t s f o r the p e r i o d January 1,  1918—December 31,  1927.  I n a d d i t i o n , he employed a s c a l e  on the v e r t i c a l a x i s which i n d i c a t e d the percent v a r i a t i o n of the group from a l l the s t o c k s .  One must suppose t h a t the  c h a r t s were u s e f u l t o Rose as i n d i c a t o r s of past performance of a group, e.g., h i s automobile group i n c l u d e d : 1. 2. 3. 4.  General Motors W i l l y s Overland Studebaker Corp. White Motor  5. Packard Motor Car  6. 7. 8. 9.  C h r y s l e r Motors Chandler C l e v e l a n d Preference Mack Truck Pierce Arrow  10. Hupp Motor Car  However, the v a l i d i t y of h i s index would be open to q u e s t i o n because o f the weighting system he used.  Apparently  i t d i d not occur to him that he should study f u r t h e r the r e l a t i o n s h i p s i n v o l v e d to see i f a n y t h i n g meaningful c o u l d be uncovered.  By 'meaningful' I have i n mind a s e l e c t i o n  technique a b l e to choose stocks which w i l l outperform the market. Rhea The d i s c o v e r y of an a p p a r e n t l y meaningful r e l a t i o n s h i p  ^°Rose d i d not I n d i c a t e , however, which stock market index he used.  r e p o r t e d i n a 1933  was made by Robert Rhea, who  i s s u e of  Barron's^? t h a t he had had some success i n u s i n g a r e l a t i v e value technique. Rhea began with the simple o b s e r v a t i o n t h a t d u r i n g the course o f a s t o c k market c y c l e some i s s u e s f l u c t u a t e more widely than others i n r e l a t i o n t o the Dow-Jones I n d u s t r i a l Average.  A s t o c k ' s v o l a t i l i t y was measured by i t s Index  number and Rhea assumed t h a t a s t o c k which h i s t o r i c a l l y been v o l a t i l e would continue t o e x h i b i t The  s e c u r i t y p r i c e was  had  volatility.  r e l a t e d t o the market  the use of an a p p r e c i a t i o n index number d e r i v e d as  through follows:  (1)  Determine the percentage change i n the f o r time p e r i o d t  security  (2)  Determine the percentage change i n the index f o r time p e r i o d t  industry  (3)  D i v i d e (1) by (2); then (3) i n d i c a t e s the g a i n which would have been made on an investment i n the s e c u r i t y r e l a t i v e t o the g a i n r e c o r d e d by the index.  Example  $ Change ( t ^ - t )  % Change ( t ^ - t )  Security  105i75  -  94:25  12.00  (1)  24i65  -  20;90  17.94  (2)  Index  (1)  Q  \ (2) = 12.00 _ I7.9Z4. -  »  o b  °  Thus, t h i s s e c u r i t y d i d r e l a t i v e l y poorer than the index Ri H i Rhea, "Stock H a b i t s - A Simple Method t o F o l l o w Issues t h a t F l u c t u a t e More Widely than the Averages," Barron's, New York, May 8, 1933, P» !• Cf  30 s i n c e , f o r every $51.00 a p p r e c i a t i o n of the index, the stock went up o n l y $ .668. A s i m i l a r f i g u r e can be d e r i v e d f o r d e c l i n e s i n the index. Rhea then determined  these index numbers f o r the 10  d e c l i n e s and 10 r a l l i e s ^ which had occurred i n the 15-month 2  p e r i o d January 1,  1932—May, 1933*  He averaged these f i g u r e s  to a r r i v e a t one advance index and one d e c l i n e index f o r each stock.  These stocks were then d i v i d e d i n t o three groups o f  '15 each, a c c o r d i n g t o the f o l l o w i n g Group I  criteria.  - " l i v e l y " s t o c k s — t h o s e t h a t move with the market but with g r e a t e r v a r i a t i o n i n advances than declines. Characteristics: (a) absence  of d i v i d e n d payers  (b) "heavy" leverage Group I I  - P r i c e v a r i a t i o n "approximates"  that o f the average.  Characteristics: (a) mostly d i v i d e n d payers Group I I I - P r i c e v a r i a t i o n i s u s u a l l y l e s s than that o f the average. Characteristics: (a) i n c l u d e s many h i g h e r p r i c e d stocks (b) d i v i d e n d payers a r e i n the m a j o r i t y The r e s u l t s o f h i s t e s t were as f o l l o w s : Group I showed a $3.00 g a i n f o r every $1.00 g a i n . r e c o r d e d by.Group I I I . ^°A peak was s a i d t o have occurred i f the index d e c l i n e d more than 10$ from a g i v e n l e v e l . T h i s d e c l i n e was s a i d t o have continued u n t i l the index had r i s e n 10% from a given l e v e l .  31 A l t h o u g h Rhea's method i s not a t a l l r i g o r o u s and a n a l y t i c a l , i t does take the f i r s t  step i n using  relative  v a l u e s as a technique t o a i d i n the s e l e c t i o n o f above average s e c u r i t i e s as w e l l as d e s c r i b i n g t h e i r h i s t o r i c a l performance. Kourday A l t h o u g h i t i s p o s s i b l e t h a t many i n v e s t o r s may have used r e l a t i v e values apparently  t o a i d t h e i r investment d e c i s i o n making,  none of them f e l t  i n c l i n e d to report  i t , s i n c e the  next a r t i c l e d i d not appear u n t i l the e a r l y 1960's. time M. Kourday p u b l i s h e d Analysts  Journal.  an a r t i c l e ^ 2  A t that  i n the F i n a n c i a l  H i s purpose i n w r i t i n g was to p u b l i c i z e  a h y p o t h e s i s which he had developed and t e s t e d d u r i n g h i s c a r e e r as a s e c u r i t y a n a l y s t .  He f e e l s t h a t r e l a t i v e  value  a n a l y s i s Is a u s e f u l technique f o r comparing s e c u r i t i e s with one another, s e l e c t i n g the best one, i . e . , the stock which w i l l outperform the averages, and determining when an i s s u e should be e l i m i n a t e d  from a p o r t f o l i o .  s t a t e s t h a t t h i s a n a l y s i s should  However, he a l s o  not be the s o l e d e c i s i o n -  making t o o l but that i t i s best used i n c o n j u n c t i o n  with  fundamental a n a l y s i s . His b a s i c premise i s that s e c u r i t y p r i c e s a r e a f u n c t i o n of e a r n i n g s .  As earnings i n c r e a s e , so should  the stock's  29 . Kourday, " R e l a t i v e Values r- A Method f o r Outperforming the Market," F i n a n c i a l A n a l y s t s J o u r n a l , v o l . 19, No. 6 (November-December 1963), p. 35. M  32 pricei  S i m i l a r l y , as r e l a t i v e earnings  p r i c e should a l s o r i s e .  increase, r e l a t i v e  Thus, the share p r i c e of the company  whose earnings a r e growing f a s t e r than average should show b e t t e r than average p r i c e performance. e x i s t s f o r the opposite r e l a t i v e earnings price decline;  This c o r r e l a t i o n also  s i t u a t i o n , so Kourday c l a i m s .  d e c l i n e should be r e f l e c t e d i n a r e l a t i v e  Where a c o r r e l a t i o n does not e x i s t , then there  e x i s t s an o p p o r t u n i t y  to buy  earnings are i n an uptrend  or s e l l .  For example, i f r e l a t i v e  but r e l a t i v e p r i c e has not shown any  growth,3° the stock should be purchased. apparently  A  f l a g r a n t c l a i m of a good and  However, Kourday's consistent c o r r e l a t i o n  over time i s q u a l i f i e d by a d d i t i o n a l hypotheses d i s g u i s e d as " f a c t s " i n other s e c t i o n s of h i s paper. even though t h e r e may  Thus,"As i s w e l l known,  be a time l a g i n earnings  r e p o r t s , the  r e l a t i v e market performance of a stock can r e f l e c t a m a t e r i a l change."3l The r e l a t i v e p r i c e - e a r n i n g s r a t i o i s a measure of the under or o v e r v a l u a t i o n of a s e c u r i t y .  Thus, the amount by  which the r e l a t i v e p r i c e - e a r n i n g s r a t i o i s g r e a t e r than provides a measure of the premium which i n v e s t o r s are T h i s may  be compared to the a n a l y s t s ' and  100$  paying.  others' forecasts  of share p r i c e to determine whether the premium, i n t h e i r  3° he reader w i l l remember t h a t t h i s has been d e f i n e d as Stage 1. T  3%i  Kourday, op. c i t . , p.  36.  opinion, i s j u s t i f i e d . The u s e r of Kourday*s method i s r e q u i r e d t o f o r e c a s t not only the earnings of the s e c u r i t y under study but a l s o the earnings of the Dow-Jones I n d u s t r i a l Average.  For  example, i n September the a n a l y s t should f o r e c a s t the  last  earnings.3  q u a r t e r earnings and a l s o the f o l l o w i n g year's From t h i s d a t a , and u s i n g c u r r e n t p r i c e s , he may  2  determine  r e l a t i v e v a l u e s and evaluate the s e c u r i t y from a r e l a t i v e standpoint. Kourday's paper i s very i n t e r e s t i n g to read; however, he i s not a b l e to p r o v i d e any s i g n i f i c a n t e m p i r i c a l support f o r h i s h y p o t h e s i s other than a few examples mentioned i n the t e x t of h i s paper. b a s i c assumptions,  In a d d i t i o n , h i s r e a s o n i n g proceeds  from  f o r which there i s not e m p i r i c a l evidence.  However, as mentioned e a r l i e r , the theory i s i n t u i t i v e l y a p p e a l i n g and d e s e r v i n g of a d d i t i o n a l thought  and  testing.  Whitbeck and K i s o r ^ u t i l i z e d the r e l a t i v e  earnings  Whitbeck and K l s o r  concept  i n t h e i r e m p i r i c a l work which was  They addressed  themselves  reported i n  to the problem of how  196ji  much to pay  3 The accuracy of t h e i r f o r e c a s t s i s i n c o n s i d e r a b l e doubt. See the a r t i c l e by J , G. Cragg and B. C. M a l k i e l . 2  V . S. Whitbeck and M. K i s o r , J r . , "A New 'Tool Investment Decision-making," F i n a n c i a l A n a l y s t s J o u r n a l , v o l . 19, No. 3 (May-June 1963), pp. 55-62. 3 3  34 f o r a g i v e n s t o c k and determining what the proper m u l t i p l e should  be. By p l o t t i n g earnings per share over time on a  a r i t h m i c s c a l e and f i t t i n g a l e a s t squares  l i n e , they  logdetermine  the slope of the l i n e , i . e . , the average annual growth i n earnings per share and the v a r i a b i l i t y of the earnings as measured by the standard d e v i a t i o n . Proceeding from the a s s e r t i o n t h a t r e l a t i v e  earnings  and r e l a t i v e p r i c e earnings move i n a c o n t r a c y c I l e a l f a s h i o n , they i n f e r t h a t the market has a concept " c y c l i c a l average"  of "normal" or  earnings f o r the f i r m i n q u e s t i o n .  This  "normal" earnings l e v e l i s d e f i n e d as "... that l e v e l of net income which would p r e v a i l c u r r e n t l y i f the economy as a whole were e x p e r i e n c i n g m i d - c y c l i c a l business c o n d i t i o n s . 3 ^ Working i n the b e l i e f t h a t there should be a r e l a t i o n s h i p between the p r o j e c t e d r a t e of earnings growth and the r a t i o , the authors conducted stocks o f "general investment growth r a t e was  the f o l l o w i n g t e s t .  p l o t t e d a l o n g the x a x i s and the  p-e r a t i o a l o n g the y a x i s .  The  earnings  "normalized"  "normalized" p-e r a t i o  determined  by d i v i d i n g c u r r e n t (6/8/62) p r i c e by  earnings.  A r e g r e s s i o n l i n e was  was  "normalized"  then f i t t e d , which y i e l d e d  3 Whitbeck and K i s o r , i b i d . , p. 158. 1+  135  For  i n t e r e s t , " the expected  p-e  35 the  following:35  Y = 9.3 + 1.5X In t h i s case Investors were a p p a r e n t l y w i l l i n g t o pay 9»3  X  earnings f o r a f i r m with no p r o j e c t e d growth and, a f t e r t h a t , each percentage  p o i n t of growth was worth an a d d i t i o n a l  1.5  multiples. The  second part of t h e i r e m p i r i c a l work c o n s i s t e d of  r e g r e s s i n g what they c o n s i d e r t o be the three  principal  f a c t o r s of common stock v a l u a t i o n , growth, s t a b i l i t y and payout upon the p-e r a t i o .  T h e i r a n a l y s i s produced the  f o l l o w i n g equation:36  y = 8.2 + 1.5*!  + 6.7x  - O.2X2  2  Where: y  = price-earnings r a t i o  x^ = growth r a t e x  = payout  2  = standard d e v i a t i o n of earnings Having determined  the "proper" m u l t i p l e with which t o  m u l t i p l y "normal" e a r n i n g s , Whitbeck and K i s o r a r e a b l e to a r r i v e a t the t h e o r e t i c a l p r i c e o f the s e c u r i t y .  This price  may be expressed as a r a t i o of c u r r e n t a c t u a l p r i c e and they  35since no value f o r r t h a t i t was not s i g n i f i c a n t . 36 ee footnote 35 f ° S  r  2  was g i v e n we can only assume  comment r e g a r d i n g the r ^ v a l u e .  36  thus have an index w i t h which t o measure under or overvaluation. G i v e n t h i s t h e o r e t i c a l p r i c e , t h e i r h y p o t h e s i s then becomes "... the market p r i c e o f the s t o c k w i l l seek t h i s l e v e l f a s t e r than the t h e o r e t i c a l p r i c e i t s e l f change . . . " 3 ?  Why?  will  Because "... changes i n market  psychology come, by and l a r g e , i n a slow and o r d e r l y ..."38  fashion  To t e s t t h e i r h y p o t h e s i s , they d i v i d e d the stocks i n t o the f o l l o w i n g  groups:  (a) Undervalued  group: Market P r i c e Theoretical Price  (b) Overvalued  *  group: Market  Price  i> 1 e  i»±5  Theoretical Price The r e s u l t s o f the study a r e shown i n T a b l e  1.  TABLE 1 Undervalued Group 3 months' Cumulative Change Change  Date  S & P 500 3 months'' Cumulative Change Change  %  %  n;9  11.9  6.6  16.8  30.7  12.3  3/24/61  3i0  34.6  6/23/6I  3.2  38.9  9/23/60 12/23/60  %  8  %•  %  6.6  5.7  5-7  19.7  8.3  14.5  1.0  20.9  (1.4)  12.9  2.4  23.8  2.1  15.3  Whitbeck and K i s o r , op. c i t . , p. 6 0 3 Ibid.  Overvalued Group 3 months' Cumulative Change Change  Thus, f o r each three-month p e r i o d , the undervalued group outperformed the S. & P. 500, which i n t u r n o u t performed the overvalued group. Smllen and S a f i a n In 1964 K. B. S m i l e n and K. Safian39 d i s c u s s e d concept and use of r e l a t i v e e a r n i n g s .  They  their  enthusiastically  support the concept of r e l a t i v e earnings but argue t h a t not a l l companies  should be r e l a t e d t o one s t o c k market average.  To r e l a t e a c y c l i c a l f i r m and a growth f i r m t o the same average i s u n f a i r . the Dual Market  Thus they o r i g i n a t e d t h e i r concept of  Principle.  They developed the C y c l i c a l Average of the Dual Market P r i n c i p l e , which i s composed of a r e p r e s e n t a t i v e group of 23 prime c y c l i c a l s e c u r i t i e s whose earnings a r e c l o s e l y r e l a t e d to the l e v e l of economic a c t i v i t y . f i r m s would be compared  For example, automobile  to the C y c l i c a l Average.  T h e i r Dual Market Principle,*s Growth Average i s composed of 25 s e c u r i t i e s which the authors c o n s i d e r to have v a r y i n g degrees of growth p o t e n t i a l .  I n the case of f i r m s  whose earnings are dependent upon e x t e r n a l f a c t o r s , these a r e c l a s s i f i e d as s a t e l l i t e f i r m s and a r e a l s o r e l a t e d t o the Growth Average. 3 K. B. S m i l e n and K. S a f i a n , " R e l a t i v e E a r n i n g s - A F r e s h P e r s p e c t i v e , " F i n a n c i a l A n a l y s t s J o u r n a l (SeptemberOctober 1964), v o l . 20: No. 5, pp. 104-107. 9  A p p a r e n t l y b e l i e v i n g t h a t t h e i r terms have been adequately d e f i n e d , they then proceed, a i d e d and abetted by h i n d s i g h t , t o a n a l y z e a f i r m ' s earnings and make t h e i r investment d e c i s i o n s . In a d d i t i o n t o the absence o f e m p i r i c a l support, the reasoning  o f Smilen and S a f i a n i s f a u l t y .  In this  writer's  o p i n i o n they have f a i l e d t o j u s t i f y the use of two averages w i t h which t o compare f i r m s ;  We w i l l proceed from the b a s i c  premise t h a t the fundamental purpose o f r e l a t i v e values Is to enable the u s e r t o compare a l l f i r m s ^  Smilen and S a f i a n ,  u s i n g t h e i r method, a r e unable to do t h i s .  To compare a  c y c l i c a l f i r m t o a c y c l i c a l average is;to study a subset of the u n i v e r s e .  I t c a r r i e s with i t an i m p l i e d assumption t h a t  the u s e r has a l r e a d y  decided  that he w i l l i n c l u d e a f i r m from  a p a r t i c u l a r i n d u s t r y i n h i s p o r t f o l i o and t h a t h i s d e c i s i o n now i s which one t o i n c l u d e . the c a r t before  the h o r s e .  Obviously,  this i s putting  I t i s p o s s i b l e t o conceive o f a  s i t u a t i o n where a f i r m ' s earnings may be i n c r e a s i n g r e l a t i v e to the C y c l i c a l Average but d e c r e a s i n g market.  r e l a t i v e t o the  I n t h i s case they would make an i n c o r r e c t investment  decisioni  Russell In t h e book A.Treasury o f Wall Street.. Wisdom H. D. S c h u l t z , A Treasury o f Wall S t r e e t Wisdom (Edi Samson Coslow), P a l i s a d e s Park, New J e r s e y , Investors Press, I n c i , 1966, pp. 90-92.  t  39 R i c h a r d R u s s e l l has a s h o r t s e l e c t i o n on the use of r e l a t i v e s t r e n g t h as an investment h i s suggested  procedure  selection criterion.  Basically,  i s as f o l l o w s :  (a) S e l e c t those groups o f stocks which have shown the best r e l a t i v e s t r e n g t h , i . e . , those groups which a r e now s t a r t i n g to i n c r e a s e a f t e r long declines. (b) From these groups p i c k the stocks with the best r e l a t i v e strength. (c) From these stocks p i c k those with the best a c t u a l technical patterns. Those stocks s e l e c t e d should be s o l d when any o f the following situations  occurs  (a) The stocks no longer outperform  the market.  (b) When the r e l a t i v e s t r e n g t h l i n e r e v e r s e s . (c) When the g e n e r a l market r e g i s t e r s a s e l l Although R u s s e l l ' s technique  signal.  sounds very l o g i c a l and  p r o f i t a b l e , i t l a c k s r i g o r o u s d e f i n i t i o n and e m p i r i c a l support. However, the present study attempts t o c o r r e c t s e v e r a l o f these  deficiencies.  Levy's Study Perhaps the most i n t e r e s t i n g r e l a t i v e value reported, t o date i s that o f L e v y ' s ^  study  which.offers strong  R o b e r t A. Levy, " R e l a t i v e S t r e n g t h as a C r i t e r i o n f o r Investment S e l e c t i o n , " J o u r n a l o f F i n a n c e , v o l ; 22, No. 4, (December, 1967)* PPi 595-610.  support  i n favour of the T r e n d i s t s .  A l t h o u g h he has  not  r e f u t e d the Random Walk Theory, he has been a b l e to e f f e c t a p o s s i b l e r e c o n c i l i a t i o n between the two G e n e r a l l y speaking,  opposing camps.  Levy found that a s e r i a l c o r r e l a t i o n  study of performance ranks r a t h e r than s u c c e s s i v e  first  d i f f e r e n c e s detected the e x i s t e n c e of trends over the term (26  long  weeks) but not over the short term (4 weeks).  the "co-movement" of stock p r i c e s , found by K i n g ,  24,2  Thus  could i n  f a c t c o n c e a l e x i s t i n g dependencies i n s u c c e s s i v e p r i c e changes.  Then, Levy suggests t h a t , by u s i n g ranks which  measure r e l a t i v e s t r e n g t h , the v e i l of the g e n e r a l market movements may  be parted and the u n d e r l y i n g s t r u c t u r e  analyzed. I n order to i n v e s t i g a t e h i s h y p o t h e s i s , chose 200 stocks and October 24, designed  Levy randomly  s t u d i e d them over the 260-week p e r i o d  i 9 6 0 — O c t o b e r 15,  1965.  He c o n s t r u c t e d  to measure h i s t o r i c a l s t r e n g t h and  ratios  f u t u r e performance.  Thus he used h i s t o r i c a l s t r e n g t h as a means f o r s e l e c t i o n at time p e r i o d t and  subsequent r a t i o s as a measure of h i s  investment r e s u l t s . A f t e r c a l c u l a t i n g the f o l l o w i n g three p r i c e r a t i o s : (a) C/A  26 - c u r r e n t week's p r i c e d i v i d e d by the average of 26 previous weeks' p r i c e and i n c l u d i n g the c u r r e n t week.  Benjamin P. King, "Market and Industry F a c t o r s i n Stock P r i c e Behaviour," J o u r n a l " o f Business, v o l . 39» No. 1, Part I I (January 1966), pp. 139-190.  41 (b) 4/C  - c u r r e n t week's p r i c e d i v i d e d i n t o the p r i c e 4 weeks subsequent t o the c u r r e n t p r i c e ;  (c) 26/C  - c u r r e n t week's p r i c e d i v i d e d i n t o the p r i c e 26 weeks subsequent  t o the c u r r e n t week:  The ranks l i s t e d below were determined f o r the 200 s t o c k s : (1) R e l a t i v e S t r e n g t h Ranks - the h i g h e s t r a t i o was g i v e n a rank of 000. (2) V o l a t i l i t y Ranks - the c o e f f i c i e n t of v a r i a t i o n d e f i n e d as was used as a r a n k i n g c r i t e r i o n with the h i g h e s t r a t i o r e c e i v i n g the lowest rank (000): (3) Market Ranks - each week the C/A 26 r a t i o s were summed and the t o t a l s ranked. (4) Divergence Ranks - the d i f f e r e n c e between the average of the C/A 26 r a t i o s of the 20 s t r o n g e s t s t o c k s and the average of the 200 s t o c k s was determined and ranked w i t h the l a r g e s t divergence r e c e i v i n g a rank of 001. S i m i l a r l y , the long term weak divergence ranks were determined. Levy's r e s u l t s were extremely e n l i g h t e n i n g : T r a d i t i o n a l l y , i t has. been maintained t h a t h i s t o r i c s t r e n g t h tends t o c o n t i n u e f o r a p e r i o d of time: the 4/C 26/C  relative  Although  ranks and r a t i o s d i d not support t h i s h y p o t h e s i s , the  ranks and r a t i o s showed that the 10% h i s t o r i c a l l y s t r o n g  stocks gained on average 9*6% w h i l e the 10% weakest gained on average only 2l9%i  In a d d i t i o n , he found good c o r r e l a t i o n  between past performance  groupings and 26-week f u t u r e perform-  ance groupings, as shown i n Table  21  kz TABLE 2 26 Relative Strength Rank Group Number C/A  Group Performance I n d i c a t o r Based Upon 26/C Average 26/C Average Group R a t i o s Group Ranks  1  1  1  2  2  2  3  3  5  6 7 8 9  10  r*  =  3  7  6  8 5 6 9  8 5 7 9  10  10  .87  .92  F u r t h e r i n v e s t i g a t i o n of h i s p r e l i m i n a r y r e s u l t s l e d Levy t o the f o l l o w i n g c o n c l u s i o n s : (a) S e l e c t i o n of stocks which h i s t o r i c a l l y had been both r e l a t i v e l y s t r o n g and r e l a t i v e l y v o l a t i l e r e s u l t e d i n p r o f i t s g r e a t e r than those p o s s i b l e by random s e l e c t i o n ^ (b) F o l l o w i n g from the r e s u l t s f i t s t mentioned, he t h a t s u p e r i o r performance c o u l d be achieved by stocks i n a market which h i s t o r i c a l l y had been Thus c o n t i n u a t i o n of r e l a t i v e s t r e n g t h appears to the g e n e r a l case (the market) as w e l l as to securities I Nye-Study No: The  1  next study to be considered  BiComm. graduating e a r l i e r was  found purchasing strongi to apply individual  essay.  The  i s the  Five-Stage  f o r i t s v a l i d i t y and  author's  Theory d e s c r i b e d  f o r i t s a b i l i t y to outperform  the market. The  sample c o n s i s t e d of 30 U.S.  the N.Y.S.E.  industrials listed  These companies were being f o l l o w e d by  the  on  43 Research Department of Eastman D i l l o n , Union S e c u r i t i e s  and  Company, a l a r g e U n i t e d S t a t e s investment house based i n New  York, and i n c l u d e d f i r m s from almost a l l major i n d u s t r i e s . For purposes  of t h i s t e s t , a g i v e n stage was  said to  have o c c u r r e d i f the t r e n d of r e l a t i v e earnings or r e l a t i v e p r i c e earnings was Although t h i s was  e s t a b l i s h e d f o r a minimum of f o u r q u a r t e r s . an a r b i t r a r y f i g u r e i t was  f e l t t h a t t o take  any p e r i o d l e s s than t h a t might not permit a t r e n d t o be c l e a r l y enough e s t a b l i s h e d , whereas t o postpone  the d e c i s i o n s  past f o u r q u a r t e r s might r e s u l t i n l o s t investment  opportunities.  In order t o t e s t f o r v a l i d i t y , a p a r t i c u l a r stage first  was  of a l l chosen and then the movements of r e l a t i v e  earnings and r e l a t i v e p r i c e earnings were s t u d i e d , both b e f o r e and a f t e r the occurrence of the g i v e n s t a g e . t h i s t e s t w i l l be g i v e n i n the next  The r e s u l t s of  section;  The next p o r t i o n of the study was  devoted t o t e s t i n g  the a b i l i t y of the system t o a c h i e v e above average results.  F i r s t of a l l ,  investment  t h i r t y c h a r t s were randomly chosen  coded from the o r i g i n a l seventy.  Following t h i s ,  and  quarterly  p l o t t i n g s of r e l a t i v e e a r n i n g s , r e l a t i v e p r i c e earnings and r e l a t i v e p r i c e were made from the coded c h a r t s onto new c h a r t s by an I m p a r t i a l p a r t i c i p a n t i n the study.  I t should be  p o i n t e d out t h a t the author d i d not know the name of the company whose f i g u r e s were on the c h a r t nor was he aware of  44 the year f o r which t h e f i g u r e s were b e i n g  plottedi  After  each p l o t t i n g , the c h a r t s were g i v e n t o t h e a u t h o r , who s t u d i e d them, made buy o r s e l l d e c i s i o n s i f i n d i c a t e d and returned  t h e c h a r t s t o the p a r t i c i p a n t , who then made another  quarterly plotting.  I n t h i s way, seven years o f data were  p l o t t e d on t h e c h a r t s and s t u d i e d . Buy and s e l l d e c i s i o n s were based on the f o l l o w i n g criteria,  A stock was purchased a t the end of Stage 1 and  h e l d i n the p o r t f o l i o u n t i l Stage 5 had o c c u r r e d . q u e s t i o n was a l s o s t u d i e d .  One f u r t h e r  T h i s was the e f f e c t , i f any, o f  the l e v e l o f r e l a t i v e p r i c e - e a r n i n g s a t t h e time of purchase on the performance o f the p o r t f o l i o . c a r r i e d out:  Thus two t e s t s were  The f i r s t one c o n s i s t e d o f buying on a Stage 1  with r e l a t i v e p r i c e - e a r n i n g s a t any l e v e l , while t h e second t e s t c o n s i s t e d o f buying a f t e r Stage 1 only i f r e l a t i v e p r i c e - e a r n i n g s were l e s s than 100: Results 8 F i r s t o f a l l , t h e r e s u l t s o f the t e s t of the v a l i d i t y of t h e 5-stage hypothesis page f o l l o w i n g .  a r e summarized i n Table  3 on the  45 TABLE 3 Results  of Testing  the V a l i d i t y of the F i v e - S t a g e Hypothesis % Frequency R.P.E.  R.E.  Increased S t a b l e Decreased  Increased S t a b l e  Decreased  Stage 1 (a) P r i o r (b) A f t e r  78 80  4 10  18 10  17 40  12 22  ?1 38  67 4  67 36  4 28  29 36  Stage 2 (a) P r i o r (b) A f t e r  29 96  Stage 3 (a) P r i o r (b) A f t e r  15 27  30 7  55 66  67 30  20  13  10 4  70 83  87  57 57  3 5  40  12  21  7  60  56  11  3  10  60 52  13 5  27 43  Stage 4 (a) P r i o r (b) A f t e r  33  Stage 5 (a) P r i o r (b) A f t e r  38  Stage 1 was most o f t e n preceded by I n c r e a s i n g p r i c e earnings (R.P.E.) and d e c r e a s i n g (R.E.).  T h i s tendency was very  indicate;  relative  relative  earnings  s t r o n g , as the f i g u r e s  A f t e r Stage 1, R.P.E. i n c r e a s e d  80$ o f the time,  while the R i E i movements i n d i c a t e d no strong t r e n d i n e i t h e r direction!  Stage 2 o f the c h a r t s s t u d i e d was most o f t e n  preceded by d e c l i n i n g R.P.E. and I n c r e a s i n g R i E .  Following  Stage 2, 21 out o f 22 cases showed an R.P.E. i n c r e a s e  while  R i E i was more or l e s s evenly d i s t r i b u t e d between i n c r e a s i n g , s t a b l e , and d e c r e a s i n g  movements.  Stage 3.was preceded by  d e c l i n i n g o r s t a b l e R.P.E. 85$ of the time.  During t h i s  p e r i o d R i E i was i n c r e a s i n g with a frequency o f 67$.  After  Stage 3 R i P i E i and R.E. decreased 66$ and 60$ of the time, respectively!  Movements p r i o r t o Stage 4 i n d i c a t e that de-  c l i n i n g R.P.E. and i n c r e a s i n g R.E. were predominant;  This  was a l s o the case f o r movements of R i P i E . and R i E i a f t e r Stage hi'  Movements o f R.P.E. p r i o r t o Stage 5 were r o u g h l y d i v i d e d  between i n c r e a s e s and decreases, whereas R i E . e i t h e r or remained s t a b l e 73$ o f the t i m e i  increased  A f t e r Stage 5 had occurred,  R.P.E. i n c r e a s e s were made s l i g h t l y more than h a l f the time and R i E . movements were f a i r l y evenly mixed between i n c r e a s e s and  decreasesi The  theory  of Markov chains  t r a n s i t i o n a l matrixi  was used t o generate a  Thus, g i v e n a c e r t a i n movement o f R.Ei  47 and B.P.E., i t was  p o s s i b l e to determine the p r o b a b i l i t y of  another stage f o l l o w i n g the g i v e n s t a g e . a r e summarized  These  probabilities  i n T a b l e 4. TABLE 4 Transition Matrix To Stage  From Stage  1  2  3  4  5  1  .02  .05  • 35  .50  .08  2  .00  .00  .36  .59  .05  3  .34  .00  .00  .31  .35  4  .45  .00  .09  .09  .37  .38  .00  .14  .43  .05  5  .  f i g u r e s were c a l c u l a t e d u s i n g the data from the sample c h a r t s . Given Stage 1, T a b l e 4 shows t h a t there was a p r o b a b i l i t y of i85 t h a t e i t h e r Stage 3 or 4 would f o l l o w .  This  would  i n d i c a t e t h a t an investment a t the end of Stage 1 would have a v e r y good chance of outperforming the market, w h i l e the chance of s u b s t a n t i a l l o s s , i . e . , Stage 5> was only 8%, Stage 2,  Given  the r e s u l t s a r e even more i n t e r e s t i n g s i n c e the  p r o b a b i l i t y of g a i n through e i t h e r Stage 3 or 4 was A f t e r the development  .95*  of Stage 3 t h e r e was almost an even  chance of e i t h e r Stage 1, 4 or 5»  A g a i n , g i v e n Stage 4,  48 the most l i k e l y outcome was the  p r o b a b i l i t y was  figures  .81  e i t h e r Stage 1 or 5«  1  f o r e i t h e r Stage 1 or 4.  I n d i c a t e t h a t g i v e n Stage 1 or 2,  the  These  probability  above average r e s u l t s was  very h i g h .  a t the  a g r e a t l y reduced p r o b a b i l i t y  end  of Stage 3 had  substantial  gain since  T h i s p r o b a b i l i t y was  the  However, an  chance of Stage 4 was  f u r t h e r reduced a t the  end  only  of •31i  of Stage  investment a t the  of  investment  4,  when the combined p r o b a b i l i t y of e i t h e r Stage 3 °r 4 was expected, an  5»  I* Stage  i18•  As might be  end  5 had  a good chance of performing as w e l l as or b e t t e r  only  of Stage than  the market! The  r e s u l t s of the  page i n T a b l e 5* two  s i g n a l was  on a per  indicated,  second b a s i s  one  stock was  i n the  of a l l , the  share b a s i s .  following  s i g n a l was  stock was  that  results  purchased.  assumed  In a d d i t i o n ,  assumed that $1,000  stock every January 1st.  cash d i v i d e n d s .  as was  A l s o of note was  f a c t that a l l gains shown r e p r e s e n t c a p i t a l a p p r e c i a t i o n the v a l u e of the  buy  of d o l l a r commitments.  g i v e n , i t was  purchased.  h e l d , i t was  test,  Thus whenever a  share of that  t h a t $1,000 worth of stock was  invested  First  of c a l c u l a t i o n was  In t h i s c a s e , when a buy  l o n g as the  shown on the  In c a l c u l a t i n g the r e s u l t s of the  d i f f e r e n t bases were used.  were c a l c u l a t e d  The  2 t e s t s are  s t o c k plus stock d i v i d e n d s but  the in  exclude a l l  49 TABLE 5 Study No. 1 - Test R e s u l t s  D o l l a r Commitment  Per Share Test #1  I952-I963  Test #2  Test #1  Test #2  Market  1952  5.7  11.2  1953  4.5  8.7  1954  93.2  41.2  1955  55.0  104.0  47.0  91.0  1956  28.2  19.3  36.O  36.I  1957  33.5  (11.1)  12.1  (7.4)  (12.2)  1958  84.2  93.2  69.0  58.9  34.0  1959  55.0  42.2  52.0  36.I  15.2  I960  12.6  36.6  14.0  42.7  10.0  1961  51.3  62.5  27.0  55.1  17.4  1962  (22.6)  22.0  35.0  30.1  (10.0)  1963  23.0  42.7  30.0  31.1  I6.5  Average Annual Gain  35.3  45.7  31.9  41.5  12.5  11.7 (0.3) 43.8 20.2  3.6  Of the 2? stocks  purchased a t one time or another  d u r i n g t h e p e r i o d 1952-1963, 22 or 85$ o f t h e purchases appreciated  i n value.  Considering  the t e s t #1 r e s u l t s f i r s t ,  these show t h a t the p o r t f o l i o outperformed t h e market i n 10 out o f 12 y e a r s .  U s i n g the a r i t h m e t i c mean of the annual  r e s u l t s , the average g a i n per year was 35*3$ while the market's average g a i n per year was only 12.5$;  Calculated  on a d o l l a r commitment b a s i s , the r e s u l t s show that the p o r t f o l i o a g a i n outperformed the average i n 10 out o f 12 years but  the mean g a i n was 31*9$ or 3.4$ l e s s than the per share  method: The  t e s t #2 r e s u l t s show that both methods of c a l -  c u l a t i o n r e s u l t e d i n the p o r t f o l i o outperforming t h e market i n n i n e out of nine y e a r s .  I n both cases t h e average y e a r l y  g a i n was b e t t e r under t e s t #2 than under t e s t #1;  The per  share b a s i s showed a g a i n o f 45.7$ v s . 35:3$ while the d o l l a r commitment b a s i s showed a 41.5$ v s i a 31.9$ g a i n ; Conclusions s The a 1-3-5  r e s u l t s o f the sequence v a l i d i t y t e s t showed t h a t  s e r i e s of movements was more l i k e l y .  However, the  p o i n t t o be noted was that an investment made a t the end o f Stage 1 had a h i g h p r o b a b i l i t y o f outperforming the market s i n c e a move i n t o e i t h e r Stage 2, 3 o r 4 w i l l u s u a l l y r e s u l t i n above average r e t u r n s .  T h i s type of a n a l y s i s  permitted  51 an I n t r o d u c t i o n o f a q u a l i t a t i v e judgment concerning  risk  s i n c e , once t h e stock had moved through Stages 1 t o 4, the r e l a t i v e p r i c e earnings  was q u i t e h i g h and as a r e s u l t t h e  stock p r i c e was v u l n e r a b l e !  I t may be argued that the reason  f o r t h i s was t h a t the market was d i s c o u n t i n g expected f u t u r e earnings  increases;  Thus, i f they d i d not m a t e r i a l i z e , the  best t h a t c o u l d be hoped f o r was a n average market performance! On t h e other hand, t h e company's f a i l u r e t o achieve the expected earnings with  would l i k e l y r e s u l t  i t s resulting capital losses!  i n a multiple contraction  S i m i l a r l y , we may say that  an investment made a t Stage 3 i s s u b j e c t t o a higher r i s k than the same investment made a t Stage 1.  Good r e s u l t s may  a f t e r Stage 5 because t h e r e l a t i v e p r i c e - e a r n i n g s usually increases:  However, the r i s k s t i l l  occur  ratio  e x i s t s that  this  i n c r e a s e may be o f f s e t by a f u r t h e r d e c l i n e i n r e l a t i v e earnings! On the b a s i s of the r e s u l t s of t e s t s #1 and #2, i t was shown t h a t r e l a t i v e value a n a l y s i s was a u s e f u l technique i n a c h i e v i n g an above average investment performance:  I t appeared  t h a t , r e g a r d l e s s o f the method.of I n v e s t i n g , i . e . , e i t h e r on a per share b a s i s or a d o l l a r commitment b a s i s , or the l e v e l of the r e l a t i v e p r i c e earnings,  t h i s technique permitted the  i n v e s t o r to outperform t h e market.  52 The  study i s , however, open t o s e v e r a l major c r i t i c i s m s .  These a r e the time p e r i o d d u r i n g which i t was undertaken, p o s s i b l e b i a s e s i n the sample and imprecise d e f i n i t i o n of variables! In the f i r s t one  p l a c e , the time p e r i o d o f the study was  i n which stock p r i c e s underwent a s u b s t a n t i a l r e -  e v a l u a t i o n by i n v e s t o r s .  Large amounts o f funds were committed  to the s t o c k market by the p u b l i c , not o n l y i n d i v i d u a l l y but through other channels such as Mutual Funds and Pension  Funds.  As a r e s u l t , the p r i c e - e a r n i n g s r a t i o o f the S. & P. Composite r o s e from 10;3 i n 1953 t o 22.? i n 1961 but by 1963 had d e c l i n e d t o 17i8.  Thus, one c o u l d argue t h a t the success  r e l a t i v e value technique  o f the  was due i n a l a r g e part t o t h i s  m u l t i p l e expansion; Secondly, the t e s t sample was b i a s e d i n t h a t i t cont a i n e d only f i r m s which one investment house p e r c e i v e d t o be growth f i r m s !  They were h i s t o r i c a l l y s u c c e s s f u l companies,  which had been o p e r a t i n g f o r many years and had a proven earnings r e c o r d !  Therefore  c o u l d have achieved  i t i s q u i t e p o s s i b l e t h a t one  the same r e s u l t s by merely randomly  s e l e c t i n g a p o r t f o l i o from the group o f 70 s e c u r i t i e s . T h i r d l y , the slope of t h e r e l a t i v e earnings and r e l a t i v e p r i c e - e a r n i n g s l i n e s was determined v i s u a l l y and as a r e s u l t i t was not p o s s i b l e t o i n c r e a s e the s e l e c t i v i t y o f the buy c r i t e r i a and determine i t s Impact.  53 Nye-Study No: 2 In order t o f u r t h e r i n v e s t i g a t e the r e l a t i o n s h i p between earnings and the p-e m u l t i p l e , a second study was undertaken * This the  study was conducted i n an e f f o r t t o determine  p r e d i c t i v e s i g n i f i c a n c e of two v a r i a b l e s  q u a r t e r l y changes i n s e c u r i t y p r i c e s .  i n forecasting  For each of 35  companies the change i n p r i c e of the s t o c k a t the end of q u a r t e r t + 1 was p r e d i c t e d a t the end o f the t t h  quarter!  The change i n p r i c e was measured i n d o l l a r s and, i f a c c u r a t e l y predicted,  then p r i c e i n p e r i o d t plus the change i n p r i c e  from t t o t + 1 should g i v e a r e a s o n a b l y good estimate of what the p r i c e of the s e c u r i t y w i l l be a t the end of p e r i o d t + l i This  p r e d i c t i o n o f change i n p r i c e i n v o l v e d  fore-  c a s t i n g the earnings per share of the company i n q u e s t i o n ! T h i s f o r e c a s t was f o r the percentage change i n earnings per share from p e r i o d t t o t + 1 and was made a t the end o f p e r i o d ti  This  p r e d i c t i o n thus i m p l i e d an a d d i t i o n a l  forecast—that  of the earnings per share a t the end o f p e r i o d t .  For  example, a t September 30 the percentage change i n earnings per share from the end of September to December 31 must be forecasted!  T h i s means that the earnings per share f o r the  p e r i o d ending September 30 must be known but, s i n c e the f i r m w i l l not y e t have published  t h i s data, an estimate must be made.  54 Relevant to t h i s d i s c u s s i o n i s the work done by Green and 43 Segall.  J  I n t h e i r a r t i c l e they developed and t e s t e d s i x  d i f f e r e n t models to f o r e c a s t earnings per share. models were: (a) Annual 1:  EP3  (b) Annual  2:  EPS t+1 = EPS  (c) Annual  3:  EPS  t  t + 1  +  1  = EPS  = EPS  t  + (EPS t  ± (EP3 r  (d) I n t e r i m 1:  EPS  (e) I n t e r i m 2:  EPS  ( f ) I n t e r i m 3:  Regress  t  The s i x  E  p  t  t  s  « EPS _ ) t  1  - EPSj^) t - i  )  = 4 (1st Quarter E P S ) t  t + 1  = EPS  t  + (I Q. E P S  (  _  t + 1  _  - I Q. E P S ) I Q.EPS t  _  )  I Q. EPS^. on p r e v i o u s f i v e q u a r t e r s .  They concluded t h a t f o r e c a s t s u s i n g f i r s t  quarter  i n t e r i m r e p o r t s are not c l e a r l y s u p e r i o r to those u s i n g only annual d a t a !  However, they s t a t e d that some knowledge  ( i i e i , t h r e e months* earnings) i s b e t t e r than a twelve-month forecast;  A l s o they found t h a t , i n companies with r e l a t i v e l y  l a r g e changes i n earnings per share, the I n t e r i m 3 model provided the best  results.  ^Di Green and J . S e g a l l , " T h e . P r e d i c t i v e Power of F i r s t Quarter Earnings Report," J o u r n a l of B u s i n e s s , v o l i 40, Noi 1 (January, 1967), pp. 44-55!  t  55 Hypothesis: The  hypothesis  of common stocks  o f f e r e d was  t h a t the change i n p r i c e  i s a f u n c t i o n of two  percentage change i n earnings  variables—the  per share of the stock  the l e v e l of i t s r e l a t i v e p r i c e - e a r n i n g s r a t i o i  and  Thus, f o r  a given s e c u r i t y :  i t+l  =  p  Where: ^P^+i i  E F S  lt jPE  t+l " iEPS  j t  =  5  1  5  f  ( l (  E P S  t+l - l iEP3  E  F  S  t  t  ; I  i f t ) PE ) t  the change i n p r i c e of the i t h s e c u r i t y from p e r i o d t t o t+1 ^ the percentage change i n earnings per share o f the i t h s e c u r i t y from p e r i o d t to t+1 = the p r i c e - e a r n i n g s r a t i o of the s e c u r i t y a t the end of p e r i o d t d i v i d e d by the p r i c e - e a r n i n g s r a t i o of the Dow-Jones I n d u s t r i a l Average a t the end of p e r i o d t i  ra  t  The  data used was  q u a r t e r l y p r i c e and  share as a t March Jl, June 30>  September 30,  earnings  and December Jl  f o r the p e r i o d i960 to the second q u a r t e r of 1967, t o t a l of 30 o b s e r v a t i o n s  per  for a  f o r each of the 35 companies s t u d i e d .  S i m i l a r l y , data f o r the Dow-Jones was To t e s t the h y p o t h e s i s ,  used f o r the same d a t e s .  the computer was  used to run a  m u l t i p l e r e g r e s s i o n on the data of each of the 35 companies.  Thus an equation  of the form shown below was  obtained  for  each company*s s t o c k : jX t+l 0  =  jA + ^  1  X  1  t + 1  + b i  ±  2  X  2  t  Where: .X 1  (t+1)  = the d o l l a r change i n p r i c e from p e r i o d t to t+1 of the i t h s e c u r i t y !  0  jX.. (t+1)  = the percentage change i n earnings per share of the i t h s e c u r i t y from p e r i o d t to t+1  .X  = the l e v e l of the r e l a t i v e r a t i o at period t :  2  (t)  = a ^0  + ^bg  price-earnings  constant  = regression coefficients  The  r e s u l t s of the r e g r e s s i o n are shown i n Table  6,  TABLE 6 R e s u l t s of M u l t i p l e R e g r e s s i o n Constant  Regression Coefficients X  C ompany  Analysis  l  X  2  2 r  8.7  .45  -.06  .07  A l l i e d Chemical Company  -7.8  .23  .07  .13  American Home Products  55.1  -1.7  6.2  .04  Abbot  Laboratories  Armstrong Cork B r i s t o l Myers  -  Celanese  -5.1  Chrysler  Corporation  C l u e t t Peabody  .66  .90 -  .16  -.3  .13  -.02  .003  .004  .01  .13  .08  19.8  .32  -.27  .42  22.6  .18  -.28  .24  5? TABLE 6 (continued) Constant  Regression Coefficients X  Company  l  X  2  r  2  17.6  -.10  -.13  .10  Dupont  54.0  .81  -.41  .10  P.M.C. C o r p o r a t i o n  30.0  • 38  -.20  .15  G e n e r a l Cable  -7.0  -.03  .16  .19  G e n e r a l Motors  17.2  -.003  -.20  .06  Georgia  26.1  .19  -.23  .21  38.4  -.70  -.21  :i3  1.16  .02  Corn  Products  Pacific  Honeywell I n c . Inland S t e e l  -105.7  -1.08  -2.82  -.39  .05  .03  Jones & L a u g h l i n  -.17  -.06  .006  .06  Lockheed A i r c r a f t  3.5  .16  -.04  .06  36.6.  .08  -.27  .37  8.7  • 56  -.09  .12  3.47  .006  -.05  .02  29.1  .63  -.27  .27  9.3  .12  -.06  .05  Polaroid  37.0  .21  -.10  .10  R.C .A.  19.6  .26  -.14  :i4  9.0  .71  -.10  .09  Safeway  12.3  .29  -.14  .14  Smith, K l i n e & French  29.2  .80  -.21  .27  4.8  .10  -.06  .04  I n t e r n a t i o n a l T. & T.  Magnavox Monsanto  Chemical  North American A v i a t i o n Owen I l l i n o i s G l a s s Pepsi  R. J . Reynolds  Standard O i l  58 TABLE 6  (continued)  Constant Company  Regression Coefficients X« X„ 1  T  d  S t e r l i n g Drug  12.0  .44  -.08  .05  Textron  -2.5  -.02  .09  ;12  U.S.  37.0  .18  -.34  :28  Warner-Lambert  10.1  -.30  -.06  .06  Xerox  72.0  -.01  -.14  .17  Freight  In g e n e r a l , the r e s u l t s i n d i c a t e t h a t t h i s model has no p r e d i c t i v e value and t h e r e f o r e the h y p o t h e s i s as i t i s p r e s e n t l y formulated must be  rejected.  Looking f i r s t a t the c o r r e l a t i o n c o e f f i c i e n t s , s i g n i f i c a n t r e l a t i o n s h i p was P and X  2  -i25to  or X^ and Xgi ;59  The range of r f o r P and  2  the range was  and 7 p o s i t i v e s i g n s .  -!60  X^, was  with 15 n e g a t i v e s i g n s and 20 p o s i t i v e  For P and X ,  — i39 to i72  e x h i b i t e d between P and  no  signsi  to i43 with 28 n e g a t i v e s i g n s  S i m i l a r l y , f o r X^ and X » 2  r ranged  from  with 15 n e g a t i v e s i g n s and 20 p o s i t i v e s i g n s ;  Thus, i n some cases, the v a r i a b l e s moved i n o p p o s i t e d i r e c t i o n to each other while i n the remaining cases they moved t o g e t h e r i n the same d i r e c t i o n , but there was results.  no c o n s i s t e n c y i n the  I n a d d i t i o n , the h i g h e s t r was  .72  and almost a l l  others were f a i r l y c l o s e t o z e r o , thus i n d i c a t i n g t h a t they v a r i e d randomly.  Looking a t the  v a l u e s , the range was .003 t o i42,  i n d i c a t i n g t h a t the best " f i t " e x p l a i n e d only k-2% of the total error. C o n s i d e r i n g the P - r a t l o s , a t a 5$ l e v e l of s i g n i f i c a n c e the value of F had t o exceed 4;5» we can conclude  A t values g r e a t e r than 4! 5  t h a t there i s r e g r e s s i o n i n the p o p u l a t i o n  and the improvement brought about by f i t t i n g the r e g r e s s i o n plane was not due t o chance. frequency  The f o l l o w i n g l i s t  of F v a l u e s g r e a t e r than  X  l  shows the  4;5:  - 3 oases  *2 " 5 cases ~2  „  2  Chrysler  .42 Cluett-Peabody  !24  O w e n s - I l l i n o i s Glass  .27 General Cable  il9  Smith, K l i n e & French  .27 G e o r g i a - P a c i f i c  ;21  Magnavox  •37  U.S. F r e i g h t Although  i28  the F - l e v e l d i d i n d i c a t e an improvement,  which was not due t o chance, i n a s m a l l number of cases the r  2  f i g u r e s show t h a t i t was not a s i g n i f i c a n t  improvement.  Conclusion: As mentioned e a r l i e r , the r e s u l t s of t e s t i n g the hypothesis  show t h a t i t had no p r e d i c t i v e v a l u e ;  In fact  s e v e r a l cases r e s u l t e d i n the standard d e v i a t i o n of the p r e d i c t e d v a l u e being g r e a t e r than the standard d e v i a t i o n of the mean!  60 Perhaps  the r e a s o n the r e s u l t s compared so unfavourably  w i t h the r e s u l t s of Study No. 1 p r e v i o u s l y mentioned the former model i s a s t a t i c dynamic;  Thus, because  was  that  one whereas the l a t t e r i s  the v a r i a b l e s have a wide movsment  over time, the " f i t " of the l i n e i s not good.  On the other  hand, the r e l a t i v e v a l u e system appears to be a b l e t o permit the u s e r t o take advantage illustrates this  of these v a r i a t i o n s ;  Figure F  point; FIGURE F  R e l a t i v e P r i c e - Dynamic and S t a t i c Models Dynamic Model  Relative Price  Static Model  Time A l t h o u g h the s t a t i c r e g r e s s i o n model was not v a l u a b l e as a p r e d i c t i v e t o o l , these " s t a g e s " s t i l l occur and, i f i t i s p o s s i b l e t o develop a dynamic model, then the r e s u l t s might be  improved;  CHAPTER IV DEVELOPMENT OF THE MODEL AND  THE  TEST OF THE HYPOTHESIS I . DEVELOPMENT OF THE MODEL D e s c r i p t i o n of the T e s t As mentioned p r e v i o u s l y , the Study No. 2 r e s u l t s tended to support the r e l a t i v e v a l u e h y p o t h e s i s . However, as a r e s u l t of the e a r l i e r mentioned c r i t i c i s m s , the Study No. 1 t e s t was of  f i r s t of a l l continued to the second quarter  1967. In a d d i t i o n , because of the p o s s i b i l i t y that the  sample was b i a s e d i n favour of s u c c e s s f u l companies shares were e a g e r l y sought by i n v e s t o r s , a new was chosen.  whose  sample of f i r m s  The t e s t was then conducted from the second  quarter of 1956  t o the second quarter of 1967» p r o v i d i n g a  time span o f more than t e n y e a r s . S e l e c t i o n o f the Sample The Standard & Poor's  '500'  index was  chosen as r e p r e -  s e n t a t i v e o f the market r a t h e r than the Dow-Jones I n d u s t r i a l Average  i n view of the r e c o g n i z e d d e f i c i e n c i e s of the l a t t e r . In order t h a t a l l s e l e c t e d p o r t f o l i o s c o u l d be compared  with the market, only those stocks which were i n c l u d e d i n the  62 S; & P. index as a t December 31, 1966 as l i s t e d  i n Standard  & Poor's Trade and S e c u r i t i e s S t a t i s t i c s , 1966 e d i t i o n were e l i g i b l e f o r i n c l u s i o n i n the sample. Having thus d e f i n e d the u n i v e r s e , a t o t a l o f 50 f i r m s was s e l e c t e d f o r the sample.  The procedure  was as f o l l o w s :  each stock i n the Index was a s s i g n e d a number from 001 t o 500.  A Random Number Table was then used to generate the  sample.  Once picked by a random number, the stock had t o be  l i s t e d on the N.Y.S.E. f o r the e n t i r e time p e r i o d .  In a d d i t i o n ,  i t must have been i n c l u d e d i n Moody's Handbook o f Common Stocks, Second Q u a r t e r l y 1956 e d i t i o n , and a l s o the T h i r d Q u a r t e r l y 1967  edition.  I n a d d i t i o n , q u a r t e r l y earnings f i g u r e s had  t o be a v a i l a b l e . requirements  I f the stock f a i l e d t o meet any of these  i t was excluded from the sample and another  s e c u r i t y was randomly chosen.  Oh t h i s b a s i s the stocks o f  the f o l l o w i n g companies were i n c l u d e d i n the sample: Abbot L a b o r a t o r i e s , I n c . Addressograph-Multigraph Corp. A i r Reduction Company, I n c . A l p h a P o r t l a n d Cement Company Aluminum Co. of America Amerada Petroleum Corp. American A i r l i n e s , I n c . American B a k e r i e s Company American Potash & Chemical Corp. American Smelting & R e f i n i n g Co. American Tobacco Company A r c h e r - D a n i e l s - M i d l a n d Company B e a t r i c e Foods Company Beckman Instruments, I n c . B e n e f i c i a l Finance Company B u c y r u s - E r i e Company  Dupont (E.I.) De Nemours and Co. Foremost D a i r i e s G e n e r a l Foods C o r p o r a t i o n G e n e r a l Instrument C o r p o r a t i o n General P o r t l a n d Cement Company Goodrich (B.F.) Company Grant (W.T.) Company Gulf O i l Corporation Hudson's Bay Mining & Smelting Company, L t d . Keebler Company Lockheed A i r c r a f t C o r p o r a t i o n May Department Stores Company Merck & Company, I n c . M o t o r o l a , Incorporated North American A v i a t i o n , I n c .  63 Burlington Industries, Inc. Burroughs C o r p o r a t i o n Case ( J . I . ) Company Chemetr.on C o r p o r a t i o n C o l g a t e - P a l m o l i v e Company Columbia B r o a d c a s t i n g System, Inc. C o n s o l i d a t e d E d i s o n Company . of New York, I n c . D i s t i l l e r s Corporation-Seagrams, Ltd. Dr.  Peabody C o a l Company Penn-Dixie Cement C o r p o r a t i o n P r o c t o r & Gamble Company S c o v i l l Manufacturing Company Sears, Roebuck and Company S h e l l O i l Company S u p e r i o r O i l Company Westinghouse E l e c t r i c C o r p o r a t i o n Whirlpool Corporation Wrigley (Wm.) J r . Company  Pepper Company These f i r m s comprise 24 i n d u s t r i e s with one or two  f i r m s from each i n d u s t r y .  However, t h e r e i s a c o n c e n t r a t i o n  of Food Producing and P r o c e s s i n g f i r m s (8) and Petroleum companies ( 4 ) .  The sample Includes f i r m s i n both  cyclical  industries  ( B u i l d i n g M a t e r i a l s ) and r e l a t i v e l y n o n - c y c l i c a l  industries  (Food).  sented  I n a d d i t i o n , growth i n d u s t r i e s a r e r e p r e -  ( O f f i c e Equipment, E l e c t r o n i c s ) while s t a b l e o r de-  clining industries  (Coal) a r e a l s o a p a r t o f the sample.  S i n c e the f i r m ' s stock had t o be l i s t e d and  i n both  1956  1967J the sample Is b i a s e d towards f i r m s which have been  a b l e t o remain i n business d u r i n g t h a t time.  Thus the r i s k  o f a complete l o s s o f c a p i t a l through bankruptcy has been avoided.  However, the sample does not c o n t a i n o n l y s u c c e s s f u l  f i r m s s i n c e the raw data shows t h a t many o f them, although they were a b l e t o m a i n t a i n t h e i r l i s t i n g s , experienced earnings.  deficit  I n some cases these d e f i c i t s o c c u r r e d as f r e q u e n t l y  as s i x out of the e l e v e n years and t h e i r share p r i c e s suffered accordingly.  Data Q u a r t e r l y data f o r the p e r i o d 1955 q u a r t e r 1967 Standard  f o r the S. & P. Composite was  obtained from  & Poor's Trade and S e c u r i t i e s S t a t i s t i c s  (1966  The data i n c l u d e d 12-month earnings f o r the quarters  edition).  ending March 31,  June 30, September 30 and December 30.  l e v e l of the Index was as was  to the second  The  a l s o obtained f o r corresponding p e r i o d s ,  i t s price-earnings r a t i o . Q u a r t e r l y p r i c e s f o r each stock were obtained  Barron's  from  and were checked from t h a t source to ensure t h a t no  r e c o r d i n g e r r o r s had been made.  I n a d d i t i o n , random checks  were made u s i n g the Wall S t r e e t J o u r n a l to guard a g a i n s t possible printing errors. s e n t a t i v e p r i c e was consequently Although  I t was  decided t h a t the most r e p r e -  the average of the B i d and Ask  t h i s was  determined  i n each case and  i t i s p o s s i b l e that e i t h e r the B i d or Ask  p r i c e s and recorded. p r i c e would  have been a c c e p t a b l e s i n c e most of the stocks were a c t i v e l y t r a d e d , some s e c u r i t i e s d i d e x h i b i t a f a i r l y wide spread t h e r e f o r e i t was  decided to use  the a r i t h m e t i c mean. A l l  p r i c e s were a d j u s t e d f o r stock s p l i t s and Q u a r t e r l y earnings data was  stock d i v i d e n d s .  obtained from v a r i o u s i s s u e s  of Moody's Handbook of Common Stocks and was s p l i t s and  stock d i v i d e n d s .  and  a d j u s t e d f o r stock  E i g h t of the companies had a  year d i f f e r e n t from the calendar year and  t h i s presented  fiscal certain  65 data problems.  The  e i g h t companies were:  Addressograph-Multigraph C o r p o r a t i o n B e a t r i c e Foods Company Case ( J . I . ) Company D i s t i l l e r s Corporation-Seagrams, L t d . G e n e r a l Instrument C o r p o r a t i o n Grant (W.T.) Company May Department Stores Company S e a r s , Roebuck and Company In the case where the f i r m ' s quarter January Jl  or February 28,  Index's March 31 d a t a . and  i t s earnings was  the data was  Thus an  made.  ended on e i t h e r  compared to  the  i m p l i e d f o r e c a s t of the Index  I t c o u l d be argued that a b e t t e r  method would have been t o r e l a t e the d a t a t o the December figures.  31  However, the main o b j e c t i o n t o t h i s i s t h a t i t would  have i n c r e a s e d  considerably  the complexity of the computer  programming while p r o v i d i n g only d o u b t f u l  returns.  Methodology The  first  s t e p was  were R e l a t i v e E a r n i n g s , Earnings R a t i o .  to d e f i n e the v a r i a b l e s .  R e l a t i v e P r i c e and  From the raw  time p e r i o d .  The  l o g a r i t h m i c values  were then determined and against  e  i t  these values  time on a f o u r - q u a r t e r  To repeat  the R e l a t i v e P r i c e -  data the computer was  to c a l c u l a t e the three r e l a t i v e values  These  instructed  f o r each q u a r t e r l y  of these r e l a t i v e f i g u r e s were then  regressed  basis.  from Chapter I , l e t : = the 12-month earnings per share of the 1 t h s e c u r i t y a t time p e r i o d t  66 p p  = the p r i c e o f the i t h s e c u r i t y a t time p e r i o d t  i t  it  e  =  t  h  P "" s s r a t i o of the i t h s e c u r i t y time p e r i o d t  e  r i c e  at  e a r n i n  = the 12-month earnings per share of the S. & P. Index a t time p e r i o d t P+.  = the p r i c e of the Index a t the end o f time p e r i o d  t  Z  PE.  = the p r i c e - e a r n i n g s r a t i o of the Index a t time period t  Then; fit E  £  %t p— t p  e  =  X..  = the 12-month r e l a t i v e earnings per share o f the i t h s e c u r i t y a t time p e r i o d t  =  Y..  = the r e l a t i v e p r i c e of the i t h s e c u r i t y a t time p e r i o d t  it pg t  =  Z-  t  = the r e l a t i v e p r i c e - e a r n i n g s r a t i o o f the i t h s e c u r i t y a t time,period t  For the time p e r i o d 1 < t £ 4, l o g X ^ , l o g log  &^ 2 +  a n (  ^ 1°8 i t + 3 x  of the form X^ _ r e l a t i v e earnings  w  e  r  e  r e g r e s s e d t o o b t a i n an equation  + ^ ^ T where o<^ i s the slope o f the l i n e o f the i t h s e c u r i t y f o r 1 < t < 4  and T i s time. Similarly! Y^  =  ~b + P^T where ^ ±  for 1 < t < 4  + Y j T where Y ^ equals the slope of Zj_ f o r 1 < t < 4  = Values  equals the slope of  of  ^ j_ and " Y ^ were s i m i l a r l y computed f o r the  time periods 2 < t < 5, 3 < t < 6, . . . , . 4-2' < t < 45.  67 The buy and s e l l c r i t e r i a were then d e f i n e d so as t o evaluate a t o t a l  of 120 S t r a t e g i e s and t o attempt  t o determine  the optimum combination of buy and s e l l d e c i s i o n s i n order t o meet the two o b j e c t i v e s of outperforming the market and maximizing  return.  The c r i t e r i a were as f o l l o w s : were c o n d u c t e d — o n e where the l e v e l the other where Z^ f; 1.0,  As b e f o r e , two t e s t s of Z^ was ignored and  i . e . , the m u l t i p l e of the i t h  s e c u r i t y had t o be equal t o or l e s s than the m u l t i p l e of the S. & P. Index.  The c r i t e r i a a r e then:  S t r a t e g y No.  Buy i f « i  >.10  >0  2  " >.15  " "  4  5 6 7 8  9 10 11 12  H  " >.20 «  II  "  "  "  "  >.30  14  »  15 16 17  "  " "  •» "  >.io "  "  "  19 20 21 22 23  >.15  25 26 27 28 29 30  >.25 w  24  "  >.25  13  18  " "  "  "  " >.20  *» "  " >.30 "  " H  i  Y  1  "  " "  » "  »  <0  »  "  " "  « i  <l.o£  » »  "  "  M  " it  II  "  "  » "  <i.o "  "  "  " "  » "  »  "  "  »  "  "  11  M  M  <-.l5 <-.05 <-.10 ^-.15 <-!o5  <-'.05  "  "  <-.io  "  " ••  "  <-.10 <-!o5  c-.io  »  "  <-.05  "  "  M  »  n M  \  »  " M  Sell i f  »  »  " "•»  <-.l5  <-.io <-.i5 <-.05  <-.io  <-.i5 <-.05  <-.io  <-.i5 <-.05  <-.io  <-.15 <-.05  <-.io  <-.i5 <-!o5 <-.l5 <-.10  68 The remaining 30 S t r a t e g i e s were formulated i n a s i m i l a r manner except f o r a data time l a g , the reason f o r which w i l l be d i s c u s s e d f i r s t .  As the data i s p r e s e n t l y formulated,  F i r m data f o r time p e r i o d t i s compared w i t h Index data f o r time p e r i o d t . For  However, t h i s i n v o l v e s the use of h i n d s i g h t .  example, on September 30,  1966  the l a t e s t earnings which  would be a v a i l a b l e would be those f o r the p e r i o d ending June 30, for  1966.  Thus the v a r i a b l e s were r e - d e f i n e d to account  t h i s time l a g .  Let: X..  = e  i t E  = the 12-month r e l a t i v e earnings per share of the i t h s e c u r i t y a t time p e r i o d t  _i ^  = p^ •5— *t ~  = the r e l a t i v e p r i c e of the i t h s e c u r i t y a t time p e r i o d t  = e  E  lt-l p  ^ r e l a t i v e p r i c e - e a r n i n g s r a t i o of the i t h s e c u r i t y a t the end of time period t e  t-1  With the v a r i a b l e s r e - d e f i n e d as above, the same combinations  of c r i t e r i a were a p p l i e d and these a d d i t i o n a l  30 S t r a t e g i e s may  be c o n s i d e r e d as more r e a l i s t i c  30.  previous For  the next s e r i e s of t e s t s the time p e r i o d  shortened from 1956> second q u a r t e r — 1 9 6 ? , to 1958,  than the  was  second q u a r t e r ,  second q u a r t e r — 1 9 6 7 * second q u a r t e r , and r e f e r e n c e  to. F i g u r e G w i l l i n d i c a t e the reason  why.  JJGUHE-JG.  70 One o f the c r i t i c i s m s o f the previous study was that i t was conducted d u r i n g a p e r i o d o f g e n e r a l l y r i s i n g p-e r a t i o s . Under such circumstances f a v o u r a b l e r e s u l t s might be expected, r e g a r d l e s s of the a b i l i t y o f the model t o s e l e c t s u p e r i o r securities.  The present t e s t s have been conducted d u r i n g a  time when the S. & P. Composite m u l t i p l e r o s e from 13*77 to  17-01.  An a n a l y s i s of the computer output f o r the i n i t i a l  s e r i e s of t e s t s  (see Table 7) shows t h a t , on average,  a l l purchases were made i n the f i r s t period.  hjfo  of  20$ o f the t o t a l t e s t  T h e r e f o r e , i t was d e c i d e d t o conduct  the t e s t d u r i n g  a p e r i o d when the b e g i n n i n g and ending p-e r a t i o was the same. When a buy s i g n a l o c c u r r e d , the computer was to  instructed  purchase $1,000 worth of the s e c u r i t y and t o h o l d i t u n t i l  a sell  s i g n a l occurred.  TABLE ? Percent of T o t a l Number of Purchases Executed During I n i t i a l 20% of Sample Time P e r i o d tegy No.  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30  1  41 46 53 36 36 38 48 48 48 45 45 45 40 40 40 41 45 51 34 34 37 45 45 45 45 45 45 40 40 40  72 II.  RESULTS OF THE TEST  Table 8 shows the r e s u l t s of u p d a t i n g the o r i g i n a l t e s t t o the second q u a r t e r of 19&7•  T e s t #1 a g a i n supports  the r e l a t i v e v a l u e method s i n c e , i n each y e a r , the technique outperformed the market  q u i t e s u b s t a n t i a l l y and the average  annual g a i n was g r e a t l y s u p e r i o r t o t h a t of the market. The average annual g a i n of t e s t #2 was lower than that of the market, outperformed the market  slightly  even though the technique  i n two of the four time p e r i o d s ;  These r e s u l t s were not s u p e r i o r and do not l e n d support t o the r e l a t i v e v a l u e technique. TABLE 8 Summary of R e s u l t s of Study #1 (1964-1967. 2nd Quarter) TEST #1 Qtly.Avge. Annual  %  %  1964  1.6  6.6  1965  8.7  39.6  1966  (0.11)  (0.52)  1967*  11:5  24.3  TEST #2 Qtly.Avge. Annual  Average Annual Change 16.5  *  F i r s t two q u a r t e r s o n l y .  %  (1.14)  3.2 (5.96)  8.2  %  MARKET Qtly.Avge. Annual  %  %  (4.48)  0.10  0.4  13.4  1.7  7.0  (21.79)  17.1 0.15  (4.79)  5.1  (17.83)  10.4 0.5  73 In an e a r l i e r chapter the method of c a l c u l a t i n g the r e s u l t s of the f i r s t should be emphasized.  study was  i n d i c a t e d and one  point  By assuming that $1,000 was  i n the s e c u r i t y every January 1,  the e n t i r e p o r t f o l i o  s o l d on December 31 and repurchased the f o l l o w i n g o b v i o u s l y absurd assumption.  invested was  day—an  In a d d i t i o n , the r e s u l t s were  based on a p o r t f o l i o which a t no time contained a cash reserve.  Thus the r e s u l t s were a t t a i n a b l e only by assuming  a continuous 100$  commitment i n s t o c k s .  When b u i l d i n g the present model, the a r b i t r a r y nature of  the p r e v i o u s assumptions  was  kept i n mind and avoided.  But, as i s t r u e i n any s i t u a t i o n , the e l i m i n a t i o n of some problems c r e a t e s new  ones.  Prom an o v e r a l l p o i n t of view,  however, the present t e s t i s more r e a l i s t i c : was  the p o r t f o l i o  not turned over a t year end; and p r o v i s i o n was made f o r  determining cash balances a t any point i n time. I d e a l l y , the r e s u l t s should be measured i n such a t h a t a meaningful I n d i c a t o r of performance  way  i s used and, a t  the same time, some measure of r i s k i s i n d i c a t e d . The computer output f o r the f i r s t  s e r i e s of t e s t s  l i s t e d the amount of e x t e r n a l funds r e q u i r e d f o r purchases at  any p a r t i c u l a r time p e r i o d , the amount of cash on hand,  and the market v a l u e of s e c u r i t i e s h e l d . was  viewed as a Current Account  The cash account  and, as such, was  not c o n s i d e r e d  to earn I n t e r e s t .  As w i l l be shown l a t e r , t h i s had a d e t r i -  mental e f f e c t on r e s u l t s s i n c e , In c e r t a i n cases, s u b s t a n t i a l cash balances r e s u l t e d from the s a l e of s e c u r i t i e s and the u n a v a i l a b i l i t y of a d d i t i o n a l Investment  opportunities.  S i n c e the prime o b j e c t i v e of t h i s t e s t i s to outperform the market  through a p p r e c i a t i o n i n the v a l u e o f the  p o r t f o l i o , d i v i d e n d s were not i n c l u d e d i n c a l c u l a t i n g the results;  In a d d i t i o n , s i n c e d i v i d e n d s a r e not c o n s i d e r e d  i n measuring the performance of the Index, the c o m p a r a b i l i t y of r e s u l t s i s enhanced. I n attempting to a r r i v e at a meaningful measure of performance i n the c u r r e n t study, the method used i n Study No: 1 was  d i s c a r d e d f o r reasons mentioned p r e v i o u s l y .  a form of p r i c e index was  considered.  Next,  I t was hoped t h a t a  base-weighted a g g r e g a t i v e index, such as that developed by Paasche, would be u s e f u l .  H i s m o d i f i e d formula was  of the  form: Index  =  p-^ X  10  Where: p^  = the c u r r e n t market  p r i c e of the s e c u r i t y  Q-^  = the number of shares c u r r e n t l y o u t s t a n d i n g of the s e c u r i t y  p  = the average p r i c e i n the base p e r i o d of the security  QQ  = the number of shares o u t s t a n d i n g of the s e c u r i t y i n the base p e r i o d  75 An index of t h i s type would have y i e l d e d a measure of performance and, i n a d d i t i o n , c o u l d have been r e g r e s s e d a g a i n s t time i n order t o measure the v a r i a n c e and thus o b t a i n a measure o f r i s k .  Upon study, however, i t became apparent  that the index would not have r e s u l t e d i n a meaningful measure of performance. why!  The f o l l o w i n g example w i l l  C o n s i d e r a p o r t f o l i o which was  explain  s t a r t e d i n time p e r i o d t .  During the next f i v e periods v a r i o u s s e c u r i t i e s were purchased and s o l d i  In p e r i o d t + 6 s e c u r i t y x i s purchased, and a t  time p e r i o d t + 7 we wish t o measure the performance p o r t f o l i o from p e r i o d t + 6 t o t + 7. formula the p o r t f o l i o performance  o f the  By u s i n g the index  f o r t + 6 t o t + 7 would  be i n f l u e n c e d by the p r i c e change of s e c u r i t y x from p e r i o d t t o t + 7 and i s t h e r e f o r e an u n s a t i s f a c t o r y measure. The measure f i n a l l y d e c i d e d upon y i e l d s a f i g u r e which r e f l e c t s r e a l i s t i c a l l y  the r e s u l t of each s t r a t e g y .  The approach taken i s t h a t of an investment p r o j e c t , i . e . , f o r an amount of$x r e q u i r e d i n time p e r i o d t = 1,  the  S t r a t e g y y i e l d e d an amount o f $y i n time p e r i o d t = 45. u s i n g the r a t i o  By  = p, one i s a b l e t o determine the com-  pound r a t e of i n t e r e s t f o r which $1  i n t = 1 i s equal t o  ftp i n t = 45. The amount of $x f o r each s t r a t e g y was  determined by  d i s c o u n t i n g the funds r e q u i r e d i n p e r i o d t over and above  76 the  cash on hand i n p e r i o d t .  Thus i n each s t r a t e g y the  i n v e s t o r ' s b e g i n n i n g equity was $0 but through t r a d i n g he was a b l e t o generate cash f o r h i s subsequent opportunities: to  investment  Any a d d i t i o n a l funds r e q u i r e d were assumed  be a v a i l a b l e a t no out-of-pocket c o s t , e i g . , Savings  Account d e p o s i t s , e s t a t e funds or " r i c h benevolent U n c l e s . " Table 10 (see Appendix first  I I ) shows the r e s u l t s of t h i s  effort. The f i r s t  point t o note i s that the system a c h i e v e d  an annual growth r a t e g r e a t e r than t h a t of the market, w i t h e x c e p t i o n of S t r a t e g y 13.  the of  In a d d i t i o n , the growth r a t e  the buy and h o l d s t r a t e g y was  l e s s than those o f a l l the  o t h e r s t r a t e g i e s ( a g a i n with the e x c e p t i o n of S t r a t e g y In  13)•  terms of maximizing r e t u r n s , S t r a t e g y 3 y i e l d e d  the  l a r g e s t d o l l a r amount ($54»253) w h i l e S t r a t e g y 5 y i e l d e d  the  h i g h e s t growth r a t e  (12.018$).  Studying the s t r a t e g i e s themselves, there i s one r e s u l t which was one:  t o be expected and another r a t h e r  C o n s i d e r i n g the former f i r s t , as the s e l l i n g  ) was v a r i e d from  <C-.05  unexpected criteria  t o </-.10, the r e s u l t s , as measured  by the growth r a t e (Column D) and $ r e t u r n s (Column A minus Column B) improve.  The reason f o r t h i s i s t h a t short-term  d e c l i n e s from an upward s l o p i n g trend l i n e caused the s t o c k s to  be s o l d  ( I n the ^ - . 0 5  case) with two e f f e c t s ;  (a) an above  77 average s e c u r i t y was  eliminated  from the  (b) commission c o s t s were unduly l a r g e . t o <^-ilO, these two  p o r t f o l i o , and When  e f f e c t s were e l i m i n a t e d  improved, except f o r S t r a t e g i e s  16 and  was  and  changed  the  results  17.  By r e d u c i n g ^ t o <-.15» the predominant e f f e c t  For v a l u e s of<=*£of >.10  t h a t of an improved growth r a t e . >!15  and  Z a t any  was  l e v e l , ^ <^-.10 was  the dominant  and  strategy.  However, f o r a l l other combinations the compound annual percentage i n c r e a s e d i f f e r e n c e was  was  l a r g e r and,  not n e g l i g i b l e .  i n most cases,  Graphs A-D  the  c l e a r l y show the  effect; C o n s i d e r i n g next the r e s u l t s obtained by v a r y i n g i t was  >il5.  found t h a t the optimum slope was  r e s u l t s were obtained whenc*^ was y,15'» However, a t values of >.20, were poorer.  increased >.25  ^» i  Improved from >.10  and ^ . 3 0 ,  I t i s suggested t h a t t h i s was  ,=><  due  to  the  results  t o firms  being  s e l e c t e d whose earnings experienced wide v a r i a t i o n s , such as c y c l i c a l companies.  As  a r e s u l t , t h e i r p r i c e performance  dominated t h a t of the one  or two  firms whose R.E.  was  growing  a t a s i m i l a r s u b s t a n t i a l r a t e but were of b e t t e r q u a l i t y , i . e . , were more c o n s i s t e n t .  In a d d i t i o n , the wider p r i c e f l u c t u a t i o n s  meant t h a t the s e c u r i t y was a n d / i ! 5 cases. >  Column E) and  s o l d more f r e q u e n t l y  Thus g r e a t e r  than the  amounts of cash were h e l d  t h i s adversely a f f e c t e d  performance.  >.10  (see  78 I t w i l l be remembered that f o r S t r a t e g i e s 16-30 a d d i t i o n a l c o n s t r a i n t of R.P.E. l e s s than 1.0 Comparing S t r a t e g i e s 1-9  with S t r a t e g i e s 16-24  the growth r a t e f o r the l a t t e r was i n s i x out of nine cases. was  no d i f f e r e n c e .  shows t h a t  g r e a t e r than the former  For the remaining s t r a t e g i e s t h e r e  obtained  i n Study No.  i . Based  study's sample was h i n d s i g h t had  such was  The  comprised of w e l l researched  previous  firms which  would continue t o be s u c c e s s f u l ;  other hand, the present industries.  not the c a s e .  shown to be h i g h l y s u c c e s s f u l and which Eastman-  D i l l o n considered  sample was  biased  i n favour  Evidence f o r t h i s suggestion  i n Table 9» which shows the r e s u l t s of  of  present  r e s u l t s are s u b s t a n t i a l l y b e t t e r than any  r e s u l t s from t h i s study and  present  is  the  o r i g i n a l study c a l c u l a t e d on the same b a s i s as the  regarding  the  the r e s u l t s appear to have been i n f l a t e d  as a r e s u l t of t h i s b i a s .  The  On  randomly chosen from many  As a r e s u l t the former was  s u p e r i o r f i r m s and  study;  on  would have expected S t r a t e g i e s I6-3O to e x h i b i t a  c l e a r s u p e r i o r i t y but  contained  imposed;  This i s a p a r t i c u l a r l y i n t e r e s t i n g r e s u l t  i n the l i g h t of r e t u r n s t h i s , one  was  an  of  exciting implications  the r o l e of Fundamental A n a l y s i s :  the  79 TABLE 9 Compound Growth Rate o f the O r i g i n a l Study on a D o l l a r Commitment B a s i s TEST 2  TEST 1  D0W- -JONES  Year  tfcGain  Portfolio Value*  1952  112  1,112  1953  87  1,199  1954  412  1,611  -  1955  470  2,081  910  1,910  1956  36O  2,441  36I  2,271  1957  121  2,562  (74)  1958  690  3,252  1959  520  I960  Portfolio Value  $Gain  Value  117  1,117  (3)  1,114  438  1,552  202  1,754  36  1,740  2,197  (122)  1,668  589  2,786  340  2,008  3,772  361  3,147  152  2,160  140  3,912  427  3,574  100  2,260  1961  270  4,182  551  4,125  174  2,434  1962  350  4,532  301  4,426  (100)  2,334  1963  300  4,832  311  4,737  165  2,499  C om pound Growth Rate**  25.32$  $Gain  -  -  -  30.32$  7.84;  *  Based on $1,000 o r i g i n a l Investment and $1,000 i n v e s t e d every January 1.  **  Compounded a n n u a l l y .  T a b l e 11 summarizes the r e s u l t s obtained when the t e s t was conducted  d u r i n g a time p e r i o d when the market's  b e g i n n i n g and ending m u l t i p l e was the same.  The r e s u l t s o f  Table 10 may be i n f l u e n c e d by the f a c t that the s; & P i Composite m u l t i p l e i n c r e a s e d from 1956 t o 196?»  As the  reader w i l l remember, t h i s was a major c r i t i c i s m of my  first  study and i t s v a l i d i t y had t o be i n v e s t i g a t e d ; The r e s u l t s v i n d i c a t e the e a r l i e r f i n d i n g s and d i s s o l v e the m u l t i p l e expansion argument;  There a r e s e v e r a l  i n t e r e s t i n g p o i n t s t o note i n these r e s u l t s ! technique outperformed 3^,  F i r s t l y , the  the market (except f o r S t r a t e g i e s 31>  37> 40 and 43) even though the beginning and ending  m u l t i p l e o f the market was the same. which f a i l e d t o outperform (^  F o r those S t r a t e g i e s  the market, the s e l l  !05) had a s i m i l a r but more dramatic  criterion  impact  on the  growth r a t e mentioned e a r l i e r f o r T a b l e 10. C o n s i d e r i n g the r e s u l t s i n the f i r s t h a l f o f Table those o b t a i n e d when cases o f ^^ later  >;i0,  11,  was g r e a t e r than ;15 dominated the >.20,  >.25 and >:30:  (see Tables 12 and 13),  As w i l l be shown  t h i s S t r a t e g y was dominant i n  every c a s e ; As  i n the case o f Table 10, the r e s u l t s o f the second  h a l f o f T a b l e 11 were somewhat d i s a p p o i n t i n g i n that only 7 out o f the 15 s t r a t e g i e s showed h i g h e r growth r a t e s than  81 t h e i r twin s t r a t e g y i n the f i r s t h a l f . or  t r e n d s appeared  A l s o , no p a t t e r n s  which c o u l d be c o n s i d e r e d p a r t i c u l a r l y  significant! T a b l e s 12 and 13 c o n t a i n the r e s u l t s of l a g g i n g the data;  As d i s c u s s e d e a r l i e r , i t was conducted  assess the impact  i n order t o  on performance i f the i n v e s t o r a p p l i e s  t h i s technique under a c t u a l c o n d i t i o n s . The r e s u l t s a r e extremely  interesting i n that, i n  many c a s e s , the I n v e s t o r was a b l e t o m a i n t a i n h i s above average performance, while i n cases where the growth r a t e was (10 cases out of 15), of  lower  only one s t r a t e g y e x h i b i t e d a d e c l i n e  g r e a t e r than 1% i n the annual growth r a t e . In  the case of T a b l e 12,  1? out of 30 s t r a t e g i e s  showed no v a r i a t i o n i n the annual growth r a t e while the r e s u l t s r e p o r t e d i n Table 13 showed an i n c r e a s e i n t h i s to  24!  figure  Of the s i x which d i d change, f o u r of these showed an  i n c r e a s e i n the annual growth r a t e while only two d e c l i n e d ! As b e f o r e , the growth r a t e was maximized when > i l 5 f o r the f i r s t h a l f of T a b l e 12.  ^ was  These s t r a t e g i e s were  a l s o dominant f o r the constant m u l t i p l e case, as shown i n the f i r s t h a l f of Table  13.  When the a d d i t i o n a l c o n s t r a i n t of r e l a t i v e e a r n i n g s , b e i n g l e s s than 1!0,  price-  was added, the r e s u l t s i n  Tables 12 and 13 d i d not vary from those shown i n Tables 10 and 11,  respectively!  CHAPTER V CONCLUSIONS P r e l i m i n a r y Note and Suggestions f o r F u r t h e r Study In the r e s u l t s r e p o r t e d i n Chapter IV an unexpected d i s c o v e r y was made.  E a r l i e r i n t h e study i t was suggested  t h a t , i f the h y p o t h e s i s was accepted, then the r o l e o f fundamental a n a l y s i s would he open t o q u e s t i o n ! the h y p o t h e s i s was accepted, i t i s concluded t h a t  Although fundamental  a n a l y s i s has a g r e a t e r r a t h e r than a l e s s e r r o l e s i n c e the r a t e s o f a p p r e c i a t i o n of the p o r t f o l i o s chosen from the a n a l y z e d sample were s u b s t a n t i a l l y g r e a t e r than those o f the random sample!  Proceeding from t h i s f a c t , the next s t e p  would be t o a n a l y z e , say, a group of 50 s t o c k s .  These f i r m s  would be those which, i n the o p i n i o n o f the a n a l y s t , have expanding  o p p o r t u n i t i e s f o r investment.  A second sample of 50 stocks would be randomly as was done i n the present study!  The buy and s e l l  chosen,  criteria  as formulated would then be used t o c o n s t r u c t p o r t f o l i o s from the two samples and I t i s expected that p o r t f o l i o s from sample one would outperform those of sample two and a l s o the market! I t should be noted that the t e s t c o u l d not be conducted u s i n g h i s t o r i c a l data s i n c e sample one may be c o n s t r u c t e d with  83 the b e n e f i t of h i n d s i g h t .  Thus, the s t a r t i n g p e r i o d would  be a t the time the a n a l y s t makes h i s f o r e c a s t and would continue i n t o the f u t u r e f o r as long as i s . . d e s i r e d : S i n c e the area of r i s k was not i n c o r p o r a t e d model, a f u r t h e r study along  i n the  the f o l l o w i n g l i n e s might be  undertaken! F i r s t l y , d i v i d e the s l o p e o f E!E: and R i P . E i  into  the f o l l o w i n g c l a s s e s R!E! Slope  (CXT )  ("Y^)  R.P.E. Slope  i  0  0  —  i04999  (:04999)  —  i05  —  .09999  (.09999)  --(!05)  ;10  --  !14999  (.14999)  -- ( i l O )  .15  —  .19999  (.19999)  —  .20  —  .24999  (.24999)  — (.20)  .25  —  .29999  (.29999)  ~  >.30  (.15)  (.25)  < (.30000)  U s i n g the buy c r i t e r i a d e f i n e d e a r l i e r i n the model, p o r t f o l i o s would be c o n s t r u c t e d of the above c l a s s e s .  from a l l p o s s i b l e combinations  I n a d d i t i o n , a l l p o s s i b l e time p e r i o d s ,  i : e ! , s t a r t i n g and ending d a t e s ,  would be c o n s i d e r e d .  The  one major v a r i a t i o n , however, would be t h a t the s t r u c t u r e o f the p o r t f o l i o would not change over time.  Thus, once the  p o r t f o l i o had been s e l e c t e d , i t s change i n value c o u l d be  84 compared w i t h that of a market index over time and performance  both  and r i s k e v a l u a t e d .  GENERAL CONCLUSION The r e s u l t s of t h i s r e s e a r c h v i n d i c a t e the c o n c l u s i o n r e p o r t e d i n Study #1 t h a t r e l a t i v e value a n a l y s i s i s a p r o f i t a b l e s t o c k s e l e c t i o n technique. S p e c i f i c Conclusions As i n d i c a t e d i n Chapter I , the purpose of the study was: (1) To i n v e s t i g a t e the hypothesis t h a t r e l a t i v e v a l u e a n a l y s i s enables the Investor t o make buy and s e l l d e c i s i o n s which permit him to a t t a i n h i s o b j e c t i v e of outperforming the market. (2) To o f f e r support to the " t r e n d i s t " s c h o o l , which supports the i d e a t h a t t e c h n i c a l a n a l y s i s of s t o c k p r i c e data i s a p r o f i t a b l e t e c h n i q u e . (3) To answer c r i t i c i s m s of my  previous study.  C o n s i d e r i n g the t h i r d purpose,  the r e s u l t s r e p o r t e d In  Chapter IV i n d i c a t e t h a t these c r i t i c i s m s may justified.  have been  The compound growth r a t e of the p o r t f o l i o s ,  a l t h o u g h lower than t h a t r e p o r t e d f o r Study No. t h e l e s s h i g h e r than t h a t of the market.  1, was  never-  However, t o what  extent the lower growth r a t e s are the r e s u l t of the sample b e i n g random r a t h e r than the l a c k of a g e n e r a l m u l t i p l e expansion i s not known. t = 45  (when there was  But, c o n s i d e r i n g the r e s u l t s when  an o v e r a l l m u l t i p l e expansion)  with  8  the r e s u l t s of Study No.  1, one  non-randomness of the Study No.  i s l e d to suspect  that  5  the  1 sample i n f l a t e d the r e s u l t s  more than the m u l t i p l e expansion. The  second c o n c l u s i o n of t h i s study i s t h a t  p r i c e trends do e x i s t and  t h e r e f o r e , as Levy found, i t i s  p o s s i b l e to p r o f i t a b l y e x p l o i t these Based on c o n c l u s i o n the stock market a n a l y s t who a b l e to d e t e c t and  and  trends.  (2) i s the t h i r d c o n c l u s i o n : that uses r e l a t i v e value a n a l y s i s i s  e x p l o i t these t r e n d s ; and  value a n a l y s i s renders a c c e p t a b l e can make buy  stock  the theory  s e l l d e c i s i o n s which r e s u l t  p o r t f o l i o outperforming the market.  that  relative  that the  investor  i n the s e l e c t e d  BIBLIOGRAPHY BOOKS Baumol, W. J . The Stock Market and Economic E f f i c i e n c y . New York, Fordham U n i v e r s i t y Press, 1965* Drew, G. A. New Methods f o r P r o f i t i n the Stock Market. W e l l s , Vermont, F r a s e r P u b l i s h i n g Company, 1966. Graham, B. The I n t e l l i g e n t I n v e s t o r , 3rd r e v i s e d New York, Harper & Row, 1965.  edition.  , Dodd, D. L., & C o t t l e , S. S e c u r i t y A n a l y s i s . 4th e d i t i o n , New York, McGraw-Hill Book Company, Inc., 1962. Hayes, D. A. Investments: A n a l y s i s and Management. New York, The M a c M i l l a n Co., 1966. Mao, J . C. T. Q u a n t i t a t i v e A n a l y s i s o f F i n a n c i a l D e c i s i o n s . Unpublished manuscript, U n i v e r s i t y o f B r i t i s h Columbia, 1968. Markowitz, H. M. Portfolio Selection. John Wiley & Sons, I n c . , 1959. McNeel, R. Wi B e a t i n g the Stock Market. F r a s e r P u b l i s h i n g Company, 1963.  New York, W e l l s , Vermont,  Rose, D. C. A S c i e n t i f i c Approach t o Investment Management. New York, Harper & B r o t h e r s , 1928. S c h l a l f e r , . R. P r o b a b i l i t y and S t a t i s t i c s f o r Business D e c i s i o n s . New York, McGraw-Hill Book Company, Inc., 1959. S c h u l t z , H. D. A T r e a s u r y o f W a l l S t r e e t Wisdom. (Ed. Samson Coslow). P a l i s a d e s Park, New J e r s e y , I n v e s t o r s Press, I n c . , 1966.  87 ARTICLES Barnes, L. "What D i f f e r e n c e . Does Knowledge Make to I n v e s t o r s ? " F i n a n c i a l A n a l y s t s J o u r n a l , v o l . 21, No. 5 (September-October, 1965)» PP. 60-68. Bernstein,. P.. L. "Growth Companies versus Growth S t o c k s . " Harvard Business Review, v o l . 34, No. 5 (September0ctoner-, 1956), pp. 87-98. R e p r i n t e d i n F r o n t i e r s of Investment A n a l y s i s (Ed. E . Bruce F r e d r i k s o n ) . Scranton, Pennsylvania, I n t e r n a t i o n a l Textbook Company, September, 1966, 2nd E d i t i o n . Birmingham, J . M. "Is A b s o l u t e or R e l a t i v e Judgement Required?" F i n a n c i a l A n a l y s t s J o u r n a l , v o l . 20, No. 2 ( M a r c h - A p r i l , 1964), pp. 62-63. , , "Random or Rational:..Stock P r i c e Behaviour and Investment Returns." F i n a n c i a l A n a l y s t s J o u r n a l , v o l ; 21, No. 5 (September-October, 1965), pp. 52-53B u r r e l l , 0. K. "A Mathematical Approach t o Growth Stock V a l u a t i o n . " Readings i n F i n a n c i a l A n a l y s i s and Investment Management (Ed. E. M. L e r n e r ) , Homewood, I l l i n o i s , R i c h a r d D. I r w i n , Inc., 1963, PP. 338-348. Cragg, J . G. and M a l k i e l , B. C. "The Consensus and Accuracy of Some P r e d i c t i o n s of the Growth of Corporate E a r n i n g s . " J o u r n a l of F i n a n c e , v o l . XXIII, No. 1 (March, 1968), pp. 67-84. F i s h e r , L. "Outcomes f o r Random Investments-, i n . Common Stocks L i s t e d on the N.Y.S.E." J o u r n a l of B u s i n e s s , v o l . XXXVIII, No. 2 ( A p r i l , I965), pp. 149-161. Green, D. and S e g a l l , J . "The Predictive-Power, of F i r s t Quarter Earnings R e p o r t s . " J o u r n a l of B u s i n e s s , v o l . XXXX, No. 1 (January, 1967), pp. 44-55. Hammel, J . E . & Hodes, D. A.- "Factors.. I n f l u e n c i n g P r i c e - . Earnings M u l t i p l e . " F i n a n c i a l A n a l y s t s J o u r n a l , v o l . 23, No. 1 (January-February, 1967), pp. 90-92. Harkavy, 0. "The R e l a t i o n between Retained Earnings and Common^Stock P r i c e s f o r Large, L i s t e d C o r p o r a t i o n s . " J o u r n a l of F i n a n c e , v o l . v i i i , No. 3 (September, 1953),  pp. 283-297.  88 H o l t , C... C. "Influence of Growth D u r a t i o n on Share P r i c e s . " J o u r n a l of Finance, v o l . XVII, No. 3 (September, 1962),  pp. 465-475.  King, B. F. "Market and Industry F a c t o r s i n Stock P r i c e Behaviour." J o u r n a l of Business, v o l . XXXIX, No. Part I I (January, 1966), pp. 139-170,  1,  K o t l e r , P. "Elements., i n a Theory, of Growth Stock V a l u a t i o n . " Readings i n F i n a n c i a l A n a l y s i s and Investment (Ed. E. M. L e r n e r ) . Homewood, I l l i n o i s , R i c h a r d D. Irwin,  Inc., 1963,  pp. 355-369.  Kourday, Mi " R e l a t i v e Values - A Method...of. Outperforming the Market." F i n a n c i a l A n a l y s t s J o u r n a l , v o l . 19, No. 6 (November-December, I963), pp. 35-44. Levy, R. A. " R e l a t i v e Strength as.a C r i t e r i o n f o r Investment S e l e c t i o n . " J o u r n a l of Finance, v o l . XXII}" No. 4 (December, 1967), pp. 595-610. McWilliams, J . D. " P r i c e s , Earnings and P-E R a t i o s . " F i n a n c i a l A n a l y s t s J o u r n a l , v o l ; 22, No. 3 (May-June, 1966), pp. 69-75. Molodovsky, N; "Recent S t u d i e s of P-E R a t i o s . " F i n a n c i a l A n a l y s t s J o u r n a l , v o l . 23, No. 3 (May-June, 1967), pp. 101-108. Smilen, K. B. & S a f i a n , K. " R e l a t i v e Earnings. - A Fresh P e r s p e c t i v e . " F i n a n c i a l A n a l y s t s J o u r n a l , v o l . 20, No. 5 (September-October, 1964), pp. 104-107. T a b e l l , E,_ W. "Case f o r T e c h n i c a l A n a l y s i s . " F i n a n c i a l A n a l y s t s J o u r n a l , v o l . 20, No. 2 ( M a r c h - A p r i l , 1964), ppi o7-76. Whitbeck, V. S. & K i s o r , J r . , M. "A New T o o l i n Investment D e c i s i o n Making." R e p r i n t e d i n F r o n t i e r s of Investment Analysis (Ed. E . Bruce F r e d r i k s o n ) . Scranton, Pennsylvania, I n t e r n a t i o n a l Textbook Company, I965,  PP. 335-350.  MICROFILM Zimmer, R. K. "An E m p i r i c a l A n a l y s i s of Stock Market P r i c e Determinants;" M i c r o f i l m 65-5697, U n i v e r s i t y M i c r o f i l m s L i b r a r y S e r v i c e s , Ann A r b o r , M i c h i g a n .  APPENDIX I LISTING REQUIREMENTS New York Stock Exchange a)  Net earnings a f t e r taxes must equal a t l e a s t a n n u a l l y over a t h r e e - y e a r p e r i o d .  $1,000,000  $10,000,000.  b)  Net t a n g i b l e a s s e t s must be a t l e a s t  c)  There must be a t l e a s t 500,000 shares o u t s t a n d i n g d i s t r i b u t e d among 1,500 s t o c k h o l d e r s , each of which must h o l d a t l e a s t 100 s h a r e s .  American Stock Exchange a)  Net earnings a f t e r taxes must be a t l e a s t $150,000 f o r the past f i s c a l year and average a t l e a s t $100,000 f o r the past t h r e e y e a r s .  b)  Net t a n g i b l e a s s e t s must be a t l e a s t  c)  There must be a t l e a s t 200,000 shares outstanding d i s t r i b u t e d among 750 s h a r e h o l d e r s , of whom a t l e a s t 500 must each h o l d 100 shares or more. A l s o , the stock must have an aggregate market value of $2,000,000 o u t s t a n d i n g and $1,000,000 of p u b l i c l y held shares.  $1,000,000.  Midwest Stock Exchange a)  The company must have an a b i l i t y t o show net earnings of a t l e a s t $100,000.  b)  Net t a n g i b l e a s s e t s must be a t l e a s t  c)  There must be a t l e a s t d i s t r i b u t e d among 1,000  250,000  $2,000,000.  shares o u t s t a n d i n g shareholders.  90 P a c i f i c Coast Exchange a)  The company must have demonstrated earning power of $100,000 a n n u a l l y OR  Source:  $1,000,000.  b)  T o t a l a s s e t s of a t l e a s t  c)  A t l e a s t 250,000 shares must be o u t s t a n d i n g , e x c l u d i n g f a m i l y or c o n c e n t r a t e d h o l d i n g s , d i s t r i b u t e d among 750 s h a r e h o l d e r s .  Cooke, G i l b e r t W., The Stock Market, Simmons-Boardman P u b l i s h i n g C o r p o r a t i o n , New York, 1964, pp. 214-215.  APPENDIX I I  TABLES 10 - 13  92 TABLE 10 RESULTS OF STRATEGIES WITH NO DATA LAG AND t = 45 Strategy Number  Ending Value of P o r t f o l i o ($)* A  Funds Required (I)** B  Profit Ratio C = A B  Annual Growth Rate($)*** D  Average Cash Balance {% of A) E  1  $ 39,120  $ 15,138  2.5843  8.52  32.9  2  60,416  19,400  3.1143  10.22  7.2  3  81,397'  27.144  2.9987  9.88  2.0  4  24,133  7,089  3.4046  11.06  30.9  5  44,122  11,415  3.8654  12.02  8.1  6  45,517  13,610  3.6827  11.74  3.5  7  13,127  5,304  2.4749  8.13  43.9  8  23,878  8,372  2.8522  9.42  16.6  9  28,361  9,767  2.9037  9.58  8.1  10  5,707  2,739  2.0833  9.56  43.9  11  12,990  4,400  2.9524  9.73  18.2  12  16,913  5,825  2.9034  9.67  6.3  13  3,598  1,884  1.9092  5.79  30.4  14  10,427  3,503  2.9253  9.64  22.3  15  14,123  4,912  2.8751  9.48  7.3  * ** ***  Less commission of 1% on purchases and s a l e s . Discounted a t a r a t e of 6% Compounded q u a r t e r l y .  93 TABLE 10 (continued) Strategy Number  Ending Value of P o r t f o l i o (I)  A  Funds Required ($) B  Profit Ratio  Annual Growth Rate($) D  Average Cash Balanc e E  16  $ 22,229  $8,515  2.611  8;6o  34.5  17  28,930  10,762  2.688  8.88  12i6  18  31,673  14,541  2.178  8.98  5.6  19  10,619  2,912  3.647  11.66  60.2  20  14,732  4,064  3.625  11.60  16.2  21  18,022  5,070  3.555  11.42  12.5  22  6,838  2,898  2.360  7.70  63.4  23  7,614  2,898  2.627  8.66  46.0  24  9,363  2,898  3.231  10.55  31.3  25  1,933  942  2.052  6.43  77.1  26  3,549  942  3.767  11.96  47i2  27  4,803  942  5.098  14.70  41.7  28  1,920  942  2.038  6.37  29  3,688  942  3.915  12.29  50 i 3  30  4,754  942  5.046  14!25  43:0  6.53$  Standard & Poor's Composite Buy and H o l d , i . e . , of 50 stocks  $1,000  worth each  7.85$  78.2  94 TABLE 11 RESULTS OF STRATEGIES WITH NO DATA LAG AND t = 37 Strategy Number  Ending Value of P o r t f o l i o (ft)* A  Funds Required (ft)** B  Profit Ratio  Annual Growth Rate($)***  C  D  Average Cash Balance (% o f A) E  31  ft 23,706  ft 13,187  1.798  6.38  32  47,108  16,484  2.878  11.50  7.2  33  63,384  19,818  3.198  12.72  3.6  34  15,739  6,795  2.316  11.78  35  33,653  9,773  3.443  13.56  9.7  36  37,870  10,967  3.453  13.60  6.2  37  9,028  5,803  1.556  38  19,832  6,558  3.024  12.46  19.0  39  22,595  7,009  3.224  12.86  12.8  40  4,353  3,954  1.100  41  12,419  4,661  2.664  10.73  15.3  42  15,108  5,346  2.826  11.38  5.9  43  3,275  2,923  1.120  44  9,928  3,662  2.711  10.93  I8;i  45  12,611  4,347  2.90.1  11.67  7:3  #  See  T a b l e 10.  11  11  it  I*  »l  »•  4.80  1.01  1.43  22.9  21.9  40i9  42.5  43.5  95 TABLE  Strategy Number  Ending Value of P o r t f o l i o (!) A  Funds Required ($) B  1  (continued) Profit Ratio C  Annual Growth Rate($) D  Average Cash Balance E  46  $ 13,933  I 8,535  1.632  5.32  25.2  47  24,075  10,161  2.369  9.46  11.1  48  35,519  12,763  2.783  11.21  49  6,354  2,877  2.209  50  13,745  3,968  3.464  13.64  1.1  51  15,516  3,968  3.910  14.49  9.5  52  3,560  1,900  1.874  6.84  48.3  53  5,945  1,900  3.129  12,53  3.2  54  7,371  1,900  3.879  14.88  2.7  8.65  3.2 24.8  55  .730  1,175  .621  -  56  3,307  1,615  2.048  7.82  1.1  57  4,734  1,615  2.931  11.78  2.0  58  730  1,155  .632  -  -  59  3,267  1,508  2.166  8.43  10.6  60  4,687  1,508  3.108  12.42  2.0  S t a n d a r d & Poor's Composite Buy and H o l d  -  6.98$ 10.52$  96 TABLE 12 RESULTS OF STRATEGIES WITH DATA LAG AND t = 45 Strategy Number  Ending Value of P o r t f o l i o  {*)•  Funds Required  Profit Ratio  Annual Growth Rate(#)#**  C  D  (1)**  Average Cash Balance (% of A) E  A  B  61  $ 39,035  $ 15,239  2.526  8.31  32:8  62  60,082  21,070  2.852  9.41  6:6  63  81,107  27,076  2.996  9.88  1:8  64  24,048  7,182  3.348  10.88  33i3  65  44,024  11,499  3.829  13:02  6:9  66  49,831  13,552  3.677  11.73  3:4  67  13,127  5,304  2.475  8.13  43i9  68  23,644  8,318  2.843  9.38  I5i3  69  28,070  9,486  2.959  9:08  7.6  70  5,546  2,698  2.056  6.44  41.0  71  12,756  4,346  2.9351  9.61  15.6  72  16,623  5,770  2.881  3,386  1,680  73  11.01  4:7  2.016  6:27  40:7 18:7  74  10,014  3,431  2.919  9.62  75  13,833  4,841  2.857  9i43  See  T a b l e 10.  II  It  II  II  II  II  5:0  97 TABLE 12 ( c o n t i n u e d ) Strategy Number  Ending Value of Portfolio (*)  Funds Required (•)  Profit Ratio  Annual Growth Rate($)  A  B  C  D  Average Cash Balance (% o f A) E  76  $ 22,229  1 8,515  2.611  8.60  34:5  77  28,930  10,762  2.688  8.88  12;6  78  31,673  14,541  2.178  8.98  5.6  79  10,619  2,912  3.647  11.66  60.2  80  14,732  4,064  3.625  11.60  16.2  81  18,022  5,070  3.555  11.42  12.5  82  6,838  2,898  2.360  7.70  63.4  83  7,614  2,898  2.627  8.66  46.0  84  9,363  2,898  3.231  10.55  31.3  85  1,933  942  2.052  6.43  77.1  86  3,549  942  3.767  11.96  47.2  87  4,803  942  5-098  14.70  41.7  88  1,920  942  2.038  6.37  78.2  89  3,688  942  3.915  12.29  50.3  90  4,754  942  5.046  14.25  43.0  98 TABLE 13 RESULTS OF STRATEGIES WITH DATA LAG AND t = 37 Strategy Number  Ending Value of P o r t f o l i o ($)*  Funds Required (?)**  A  B  91  $ 23,624  $ 13,187  92  47,006  93  Annual Growth Rate($)***  Average Cash Balance {% of A) E  1.792  6.34  23:0  16,354  2.874  11.57  7:2  63,282  19,701  3.212  12;78  3.6  94  15,657  6,794  2,304  9.12  22a  95  33,552  9,713  3.454  13.60  9:8  96  37,768  10,822  3.490  13.72  6;2  97  9,028  5,803  1.556  4.80  98  19,832  6,558  3.024  12.46  19.0  99  22,595  7,009  3.224  12.86  12.8  100  4,353  3,954  1.100  1.01  42.5  101  12,419  4,661  2.664  10:73  15.3  102  15,108  5,346  2.826  11.38  5.9  103  3,275  2,923  1.120  104  9,928  3,662  2.711  10.93  18;1  105  12,611  4,347  2.901  11.67  7.3  See Table 1 0 11  11  11  11  11  11  Profit Ratio C  D  1.43  43i5  TABLE 13 (continued) Strategy Number  Ending Value of P o r t f o l i o A  Funds Required  Profit Ratio  Annual Growth Rate($)  B  C  D  Average Cash Balance {% of. A) E  106  ft 13,933  ft 8,535  1.632  5.32  25.2  107  24,075  10,161  2.369  9,46  11.1  108  35,519  12,763  2.783  11.21  3,2  109  6,354  2,877  2.209  8.65  24.8  110  13,745  3,968  3.464  13.64  1.1  111  15,516  3,968  3.910  14.49  9.5  112  3,560  1,900  1.874  6.84  48.3  113  5,945  1,900  3.129  12.53  3.2  114  7,371  1,900  3.879  14.88  2.7  115  730  1,175  .621  -  -  116  3,307  1,615  2.048  7.82  1.1  117  4,734  1,615  2.931  11.78  2.0  118  730  1,155  .632  -  -  119  3,267  1,508  2.166  8.43  10.6  120  4,687  1,508  3.108  12.42  2.0  APPENDIX I I I  GRAPHS A - D  GIIA]FH A —  —  —  —  GR 0_ViTE _E A3 !E_ A£ (  J  \  1  )  ><  >.N_ _Q] (cL)  (c  •0r)  : ( <  IB LE _1.0  AJ TO. - f t _E )R .:(  —  (1 )::  (k)  •:(h i )  S.)  14 —  !l2 —  _..  10  /  'i  6  5  ~w  bh  .%  —  -  /  — -  —  —  -  -  /, —  —  /  ——  —  —  /  /  —  -T-  —  •—  y  —  \ r  .:_  Gr  - -  /  8 Jlat  -  /  —  —  — -  —  T —  ?, —  0 I. —  • — •  —--  io:  >a<  :  —  —  0  >  >.3P.  | ;h<  —  c><  •  the s!LofDe ol  =  LO  5  0  > a 5  >  .3 0  5  2. L.In  I  •;  .._|_-  J-R. XV  ....  —  -  E A and su bs eq ue nt g rg 1  i  -  Ca se (a) —  - —  : Th e ti i  —If—  r.  .s ar  —  ..„  . -I:  —  —  - - -  e  re :ac.  £LS'  i s t pc>irit reJ pi*eserlt£ i« II . 2rid  3r  ~n  S i ml l a r-3 y~ ro - J 'r Ca se - ( -b") —  i  n ' i  i  I  fc>i:- O l js it ir  i  i  : :a'ie II  —  i —  •  o:r \  II  II  i  —  H  bh w'i e . t i c < —  I  • —  ti  it  i»  II  >a0  and II  II  < 0.5 < io; <  15  —• -31 o Ca )' .... .....-:- * — Ts —J-... & — i -< OS :...p.  . 1:  -  " " t "  1  L3 L2  i .. . L .  a.t  Hi of Gro  2  .... .... - .......  11  i  1.0. l  :  I'  1  I  —  -  —  i 7„  I 1I  1  i. .  i  i  re  /.  —  — —-  V  ]  y  « —- \\"*• r / i\  \ 1  i .j l i •~r: i  i1  i  j.  1  .  <-  1  I  —  _ 4__ — — fftl -)-•- i — --- 1 '1 $ I T " .... 1• • ] i • - f / ij i | i •! 18• •!i.... 1 i / t  . W . W . A J L . .... J| UJ — — -•—: — — ...  [—i  1  .  (-e  —  i/  — .....  ! ....  1 {  -  !  —i—  l• "T " i  1  ...— —  1  i  i  ....— — -  TO  r  .—— — — I -  —  ! ——  — —  - i  \  —  —  r i  \\-  i / i /  —  -  !  i  7  — 7  :  —  i — i I • 7 i i .... / i— .. . .... - — — i 5 i | ! . ... — — — Ii •— i • • j —- — ii • 3 ii .... —- — — i i 2. T " •I :| --— ... i .... — .... 1 ! i 1 i 1 ^1 i • 10 >.20 > :..l|0J •i2 .... ;30 —- >ab..> .20.) >.3'0< L.l o 0- — • -;U<.0- ' 1 10- 10- 30 >.: ~-  —  I \  — ....— — ---  i  ,) -/—  /\ \  ... i _ ._ .1l ... -~  .... —-  r.  (f  —  •  5.  —  )  —  1  V  — —  t  i  i  i i l  :  •ii. • |  •  i  •  1 1  .i  1  •=!-the s lb  _C  .f_  — >.1-0 >;2-0 >.  >.-301  1  1  e_ R.E, - L i r i e ' i "  :  GRAPH — •  GB  1  TE _I A T E . A£  •(b)"  (a)  -  .  mi ic; ?i.<>N.-o: ..... (c)  C -P- DR  (8 )  (ti )  F T  -T.A B L E -12  (f )  (g)  ':'(h)  )  V L)  14 - —  12  —  10  e  8  th —  'A /  —  /  / / /  6 —  4  _  r  2 —  —  •:  —  0  >i l  —  —  5  0  - - - —  >  >i2 5  i.lo  >  LO  >i-2-0  >i:25  0  •  c  —  th e  -o'l  _o.f  -L::n<  —  —  —  >i'20  >  — -  —  —  ••  '-—  —  -  —  — -  y  —  —  —  —  ----  I  t•  - ;• •  •  .  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0102383/manifest

Comment

Related Items