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The ability of the Value Line Investment Survey to forecast "Probable twelve months market performance.. Staley, Donald Ross 1966

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THE ABILITY OF THE VALUE LINE INVESTMENT SURVEY TO FORECAST "PROBABLE TWELVE MONTHS MARKET PERFORMANCE RANK"  by  DONALD ROSS STALEY B. Com., U n i v e r s i t y o f B r i t i s h Columbia, 1965  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION  i n the Faculty of Commerce and B u s i n e s s  Administration  We a c c e p t t h i s t h e s i s as conforming t o t h e required  standard  THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 1966  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements  for an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i ] a b l e study,  I f u r t h e r agree t h a t p e r m i s s i o n - f o r  f o r r e f e r e n c e and  extensive  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 g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s .  I t i s understood that  or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l w i t h o u t my w r i t t e n p e r m i s s i o n .  Department o f The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8 , Canada Date  copying  g a i n s h a l l n o t be a l l o w e d  ABSTRACT  In t h e t h e s i s t h e author attempts t o d i s c o v e r whether  o r not  The V a l u e L i n e Investment Survey shows e v i d e n c e of an a b i l i t y  to fore-  c a s t "Probable Twelve Months Market Performance Rank," a r a n k i n g o f s t o c k s a c c o r d i n g t o t h e i r p r o b a b l e r e l a t i v e p r i c e performance w i t h i n t h e succeeding twelve months.  To t e s t t h e a b i l i t y t o f o r e c a s t , t h e a u t h o r  determines t h e s i g n i f i c a n c e o f the c o r r e l a t i o n between t h e r a n k i n g o f s t o c k s a c c o r d i n g t o t h e f o r e c a s t and the r a n k i n g of s t o c k s a c c o r d i n g t o the  observed r e l a t i v e p r i c e performance w i t h i n the y e a r .  The  conclusion  drawn i s t h a t The V a l u e L i n e Investment Survey does n o t show evidence o f a consistent a b i l i t y  t o f o r e c a s t "Probable Twelve Months Market Perform-  ance Rank." The author a l s o p r e s e n t s a model o f the p r o c e s s which may the  g e n e r a t i o n of s t o c k market p r i c e changes.  underly  The author t e s t s t h e  assumption of the independence o f p r i c e changes, a p a r t o f t h e model, on the d a t a of t h e t h e s i s and f i n d s t h a t the t e s t r e s u l t s do n o t r e f u t e the  assumption.  The model, t h e "Random Walk H y p o t h e s i s , " i s r e l a t e d t o  the  a b i l i t y o f The V a l u e L i n e Investment Survey t o f o r e c a s t "Probable  Twelve Months Market Performance Rank." L i n e Investment Survey has f a i l e d  I t i s concluded t h a t The V a l u e  t o show t h a t i t s f o r e c a s t s a r e s u p e r i o r  to f o r e c a s t s based s o l e l y on p a s t p r i c e s where t h e market i s assumed t o f o l l o w a random walk.  TABLE OF CONTENTS Chapter I.  Page  INTRODUCTION  1  II.  METHOD USED BY THE VALUE LINE INVESTMENT SURVEY TO FORECAST "PROBABLE TWELVE MONTHS MARKET PERFORMANCE RANK". .  3  III.  NATURE, METHOD AND FINDINGS OF THE RESEARCH PROJECT . . .  8  Nature of the project . . . . . . . . . . . . . . . . . Method of the project . . . . . . . .  . . . 10  Findings of the p r o j e c t IV. V.  VI.  8  12  THE ABILITY OF FORECASTERS TO FORECAST  15  THE "RANDOM WALK HYPOTHESIS" AND ITS RELATION TO THE PRESENT STUDY  19  The hypothesis  19  Findings which may support the hypothesis . . . . . . .  27  R e l a t i o n t o the present study . . . . . . . . . . . . .  30  CONCLUSION  32  SELECTED BIBLIOGRAPHY  34  CHAPTER I  INTRODUCTION  I t i s t h e purpose o f t h i s paper t o p r e s e n t t h e method and f i n d i n g s of  a r e s e a r c h p r o j e c t * undertaken t o t e s t t h e a b i l i t y  Investment  o f The V a l u e L i n e  Survey ^ t o f o r e c a s t "Probable Twelve Months Market  mance Kank"  (hereafter called  "predictions").  Perfor-  The f i n d i n g s a r e i n t e r -  p r e t e d , and t h e n r e l a t e d t o t h e "Random Walk H y p o t h e s i s , " a model -which may d e s c r i b e t h e g e n e r a t i o n o f market p r i c e  changes.  Chapter I I d e s c r i b e s t h e method used by The V a l u e L i n e  Investment  Survey t o make " p r e d i c t i o n s " which a r e p r i m a r i l y based on a c a l c u l a t e d "intrinsic  value."  T h i s method i s t h e n compared w i t h some g e n e r a l l y  r e c e i v e d procedures f o r a p p r a i s i n g t h e v a l u e s o f s t o c k s . In  Chapter I I I t h e method and f i n d i n g s o f t h e author's r e s e a r c h  project are presented.  The p r o j e c t adopts rank c o r r e l a t i o n methods t o  compare d i f f e r e n t r a n k i n g s o f a s e t o f s t o c k s . In Chapter IV t h e f i n d i n g s o f t h e study a r e i n t e r p r e t e d t o d e t e r mine t h e a b i l i t y  o f The Value L i n e Investment  Survey t o f o r e c a s t .  *"' ',•„•..; .* •> m m  for  Inc.  •'•The r e s e a r c h p r o j e c t was conducted by t h e author i n 1965 on d a t a t h e p e r i o d 1961 t o 1964. ^The Value L i n e Investment (a weekly p u b l i c a t i o n ) .  Survey, New York, A r n o l d Bernhard & Co.,  ^A r a n k i n g o f s t o c k s a c c o r d i n g t o t h e i r p r o b a b l e r e l a t i v e market p r i c e performance w i t h i n t h e succeeding twelve months. 1  2  In Chapter V the "Random Walk Hypothesis" i s discussed.  Some  e a r l i e r findings concerning the adequacy of the hypothesis to describe actual stock price changes are presented.  A test of the independence  assumption f o r stock price changes, which i s part of the "Random Yfalk Hypothesis," i s carried out on the findings of the research project. The "Random Walk Hypothesis" i s then related to the study of The Value Line Investment Survey's a b i l i t y t o ""predict." The conclusion follows; i t includes some inferences made i n the e a r l i e r chapters and discusses further some subjects already considered. The present study should be of i n t e r e s t to those persons wishing to adopt the forecasts of short-run price changes as presented i n The Value Line Investment Survey.  I t should also serve students interested  i n a description of the random walk hypothesis of stock market price changes.  CHAPTER I I  METHOD USED BY  THE VALUE LINE INVESTMENT SURVEY TO FORECAST  "PROBABLE TWELVE MONTH MARKET PERFORMANCE RANK"  The method used i n The Value L i n e Investment S u r v e y s i n c e 1957  t o f o r e c a s t "Probable  November  Twelve Months Market Performance Rank" i s t o  a s s i g n ranks to s t o c k s a c c o r d i n g t o t h e r a t i o of the most r e c e n t 52-week average p r i c e of the stock t o i t s "Value L i n e R a t i n g of I n t r i n s i c p r o j e c t e d 12 months ahead,  ( " i n t r i n s i c v a l u e " i s d e s c r i b e d as  Value"  "the  average p r i c e f o r a 12 month p e r i o d t h a t i s s t a t i s t i c a l l y determined t o be the normal p r i c e i n r e l a t i o n t o the s u b j e c t s t o c k ' s ability  i n that year.")  The  1  " i n t r i n s i c v a l u e " i s o b t a i n e d by p e r f o r m i n g  tion analysis  2  dividend-paying  on a group of s i m i l a r " q u a l i t y "  the r e s u l t s t o the p a r t i c u l a r s t o c k . time s e r i e s d a t a f o r approximately  The  3  a multiple correla-  s t o c k s and  applying  c o r r e l a t i o n i s performed  20 y e a r s .  In the a n a l y s i s , p r i c e i s  c o n s i d e r e d t o depend upon e a r n i n g s , d i v i d e n d s , p a s t p r i c e , and sentiment  on  a market  factor.  •'•Arnold Bernhard, The E v a l u a t i o n of Common S t o c k s , Simon and S c h u s t e r , 1959), p. 120.  (New  York,  ^Although d e s c r i b e d as a m u l t i p l e c o r r e l a t i o n a n a l y s i s by Bernhard, the a n a l y s i s should more f i t t i n g l y be d e s c r i b e d as a r e g r e s s i o n a n a l y s i s as " i n t r i n s i c v a l u e " i s assumed t o depend upon the v a l u e s of t h e o t h e r variables involved. Q u a l i t y " r e f e r s t o a composite index of p a s t performance i n growth and s t a b i l i t y o f e a r n i n g s and d i v i d e n d s . F o r a d e r i v a t i o n of the " q u a l i t y " index see A r n o l d Bernhard, The E v a l u a t i o n of Common S t o c k s , pp. 41-57.  3  4  The relationship formulated i s that the independent v a r i a b l e , the logarithm of the annual average price f o r the group, i s dependent upon the regressor variables, the logarithms of: A. A f r a c t i o n of average annual earnings, which i s combined with average annual dividends, where the f r a c t i o n i s determined by the r a t i o of the standard deviation i n the dividends to the 4 standard deviation i n the earnings f o r the period considered. B. The annual average lagged price (the annual average of prices i n the preceding y e a r ) . C. The annual mean y i e l d s of 45 "representative" stocks  over the  period considered. Once the net regressor c o e f f i c i e n t s f o r the group have been determined they are applied as weighting f a c t o r s to the similar variables f o r the p a r t i c u l a r stock i n a r r i v i n g at the stock's " i n t r i n s i c value." The logarithm of the "Value Line Rating of I n t r i n s i c Value" f o r a p a r t i c u l a r stock i s calculated by weighting, with the appropriate net regressor c o e f f i c i e n t s (obtained from the group multiple c o r r e l a t i o n analysis), the variables of: 1.  a combination  of earnings and dividends projected 12 months  ahead, where earnings are multiplied by a r a t i o (the r a t i o of the standard deviation i n earnings of the p a r t i c u l a r stock f o r *The f r a c t i o n , Bernhard states, (Arnold Bernhard, The Evaluation of Common Stocks, p. 99) tends to "equalize the v a r i a t i o n s i n the earnings and dividend series." 5  The y i e l d s are included as a market sentiment  factor.  5  a 10 year period) before being combined with dividends, and 2. the present average annual price, and combining them together with a constant which i s f o r the p a r t i c u l a r stock equal to a 10-year average of i t s log price, minus the appropriate net regressor c o e f f i c i e n t  g  times the 10-year average of log lagged  price, minus the appropriate net regressor c o e f f i c i e n t times the 10-year 7 average of log combined earnings and dividends. The market sentiment factor (the average y i e l d of 45 representat i v e stocks) i s not included i n a r r i v i n g at the "Value Line Rating of I n t r i n s i c Value" f o r a p a r t i c u l a r stock "since market sentiment  i s held  Q  constant." Once the "Rating of I n t r i n s i c Value" f o r a l l the stocks considered i s determined, the stocks are ranked according to the r a t i o of the 52week average price of the stock to i t s "Rating of I n t r i n s i c Value," to arrive at the forecast of "Probable Twelve Months Market Performance Rank." I t should be noted that the ranks are not based solely on past information.  To arrive at " i n t r i n s i c value," both earnings and  divi-  dends must be projected for a year into the future and the results of the projection used i n the formula. °The appropriate net regressor c o e f f i c i e n t i s the net regressor c o e f f i c i e n t of the similar variable determined f o r the group analysis. ^Earnings are m u l t i p l i e d by the r a t i o of the standard deviation of dividends to the standard deviation of earnings f o r the p a r t i c u l a r stock f o r a 10 year period before being added to dividends. g  Arnold Bernhard, The Evaluation of Common Stocks, p.  106.  6  The method f o r a r r i v i n g at " i n t r i n s i c value" d i f f e r s i n form rather than substance from another generally accepted method f o r  q appraising stock values.  Graham, Dodd and Cottle  assume that the  basic components i n common-stock valuation ares 1. The expected future earnings. 2. The expected future dividend. S. The c a p i t a l i z a t i o n rate - or m u l t i p l i e r - of dividends and earnings. 4. The asset value. They present a model f o r the valuation of common stocks which iss V = M(D +  E) -V A  1 0  where? V i s the value of the stock. M i s the earnings m u l t i p l i e r assumed appropriate f o r the type of stock. D i s the expected dividend. E i s the Expected  earnings.  A i s an adjustment f o r asset value i f necessary. In both methods, once the values of the parameters (based on "quality* f a c t o r s ) have been determined, 1  i t s t i l l remains to project  both earnings and dividends f o r the coming year. The choice of projecting earnings rather than or together with  ^B. Graham, D. Dodd and S. Cottle, Security Analysis, 4th ed. (New York, McGraw-Hill Book Company, Inc., 1962). 1 0  I b i d . , p.  518.  7  dividends f o r a period as indicated by Sauvain ^  serves only as a  short-cut to the valuation of stocks based on a consideration of a l l future dividends.  A method which does treat of a l l future dividends  and which i s generally considered more t h e o r e t i c a l l y sound than the 12 methods already considered i s the J.B. Williams  model,  Williams  assumes that the i n t r i n s i c value of a stock i s equal to the present 13 value of a l l future dividends.  The model may be adjusted to take  into account the r i s k of divergence from expected values i n the stream of dividends.  The model, although t h e o r e t i c a l l y sound, i s d i f f i c u l t ,  i f not impossible, to apply, as i t i s impossible to project the  expected  dividends f o r a l l future years. A procedure more generally applied than any of the preceding i s simply to multiply a price earnings r a t i o (often the average price earnings r a t i o of the stock f o r that year) by a projection of earnings f o r the following year. ^ H . Sauvain, Investment Management 2nd ed. (New Jersey, PrenticeH a l l , Inc. 1960), p. 310. J . B . Williams, The Theory of Investment Value (Amsterdam, NorthHolland Publishing Company, 1956). 1 2  l^The discount rates used to a r r i v e at present values are determined by the interest rates sought by the investor.  CHAPTER I I I  NATURE, METHOD AND FINDINGS OF THE RESEARCH PROJECT  NATURE OF THE PROJECT The purpose of the research project i s to determine the s i g n i f i cance of the correlations between given series of stock p r i c e changes as viewed i n The Value Line Investment Survey, during the period 19611964. F i r s t , the c o r r e l a t i o n , or the degree of correspondence, of the ranking of stocks according to t h e i r "Probable Twelve Month Market Performance Rank" ("predictions") with the "observed"  1  ranking f o r the  twelve months following the date of the "predictions" i s investigated. A s i g n i f i c a n t c o r r e l a t i o n may indicate that a system successful i n f o r e casting p r i c e changes has been devised. Secondly, the c o r r e l a t i o n of the "predictions" with the "actual performance" (the ranking of stocks according to t h e i r percentage price appreciations) f o r the s i x months preceding the date of the "predictions" i s determined.  A s i g n i f i c a n t c o r r e l a t i o n may indicate that "predictions"  are primarily based upon past price performance,  iThe "observed" ranking of stocks, according to t h e i r twelve months market performance, i s a ranking of the stocks according t o the maximum percentage price increase i n the stocks achieved during the twelve months considered. The maximum prices are taken from the charts of stock prices as presented i n The Value Line Investment Survey, 8  9  Thirdly, the c o r r e l a t i o n between the "actual performance" f o r the six month period preceding and the "observed" performance f o r the twelve month period following the date of the "predictions" i s determined.  A  s i g n i f i c a n t c o r r e l a t i o n may indicate that stock market price changes are not independent of past price changes, although they are assumed to 2  be independent i n the "Random Walk Hypothesis." The c o r r e l a t i o n between the "predicted"  and "observed" rankings  i s considered a t four phases i n the market cycle: the bottom, the top, the middle of a f a l l i n g market, and the middle of a r i s i n g market. The dates of the phases have been discovered by viewing weekly figures of Standard and Poor's Index of Total Common Stock P r i c e s .  The number of  dates f o r which c o r r e l a t i o n studies have been possible has been limited by the number of surveys available f o r study.  The actual  computations  to obtain c o r r e l a t i o n c o e f f i c i e n t s have been performed on the I.B.M. 7040 computer a t the University of B r i t i s h Columbia. To determine the significance of the c o r r e l a t i o n between two rankings, i t i s f i r s t necessary to compute a c o r r e l a t i o n c o e f f i c i e n t between the rankings.  The formula used i s presented i n the following  section  together with a note regarding a t e s t of the significance of the c o e f f i cients. For a description of the "Random Walk Hypothesis" see Chapter V.  10  METHOD OF THE PROJECT  The following  i s a description of the method and formula used to  determine the degree of correspondence between the d i f f e r e n t rankings in  the study. The c o r r e l a t i o n between two rankings i s obtained from Spearman's  formula:  J t < n  P  \/  where j  3  - f O - t d 1  i  a  - T '  <: /an -n)-2T'X'^Cn -n)) i  3  3  P  =  Spearman's c o e f f i c i e n t of rank c o r r e l a t i o n  n  =  number of ranks used  d^  =  difference i n ranks  T*  =  II  , where t i s a t i e d set of t members and 4  m t y p i f i e s a set of t i e s i n the ranking. The formula takes t i e d ranks into account i n spite of the f a c t that t i e s should not occur i n an objective ordering of ranks.  In the  survey the ranks of 1 to 5 are allocated to stocks according to t h e i r prospect f o r r e l a t i v e price performance. The method used to rank t i e d sets i s to allocate to each member the average of the rank which the members would have possessed had they M.G. Kendall, Rank Correlation Methods, (London, Charles G r i f f i n & Co. Ltd., 1948) p. 28. 3  4  I b i d . , p. 29.  5  I b i d . , p. 28.  11  been distinguishable.  For example, i f a t o t a l of six stocks had the  "predicted" rank of 1, the rank allocated to stocks with the highest prospect f o r r e l a t i v e price performance, then eaoh would be allocated the rank 3.5, the average of the numbers 1 to 6. The r e s u l t i n g c o e f f i c i e n t s of rank c o r r e l a t i o n , P, are tested f o r significance.  As each sample size n (the number of stocks considered  i n each t e s t ) i s greater than 50, the d i s t r i b u t i o n of P i s assumed to be normal.  (For a sample size n greater than twenty, the assumption of  normality i s l i k e l y j u s t i f i e d . ) ^  I f there were no c o r r e l a t i o n between  two rankings the maximum l i k e l i h o o d value of P would be zero; however, for a normally d i s t r i b u t e d v a r i a b l e , the maximum l i k e l i h o o d value and the mean coincide, so that the mean of the d i s t r i b u t i o n of P would be zero. \  The variance of the d i s t r i b u t i o n of P under the assumption of 1 normality and no c o r r e l a t i o n i s given approximately by  var P  s  8  — - .  Hence the standard normal form of the v a r i a b l e (assuming zero population correlation) i s given by Z  =  P \ n-1 •  6  K e n d a l l , Rank Correlation Methods, p. 25.  7  I b i d . , p. 47.  8  I b i d . , p. 48.  12  FINDINGS OF THE PROJECT  Presented below are the findings of the study, that i s , the s i g n i ficance of the correlations between the rankings studied. F i r s t , i t i s found that i n only three cases out of thirteen are there s i g n i f i c a n t ^ correlations between "predicted" and "observed" market performance.  Also, i n no given stage of the market cycle do  the number of s i g n i f i c a n t relations seem large enough to d i s t i n g u i s h that stage from any other.  At the "Bottom of a Market Break," i n only  two out of s i x cases tested are the correlations s i g n i f i c a n t . At the "Top  of a Market Break" only one out of the three cases studied i s  significant.  At the "Middle of a F a l l i n g Market" and"Middle of a Rising  Market,"' i n which only two cases each are tested, none of the c o r r e l a tions are s t a t i s t i c a l l y s i g n i f i c a n t . Second, the c o r r e l a t i o n between "actual performance" f o r the six months preceding publication of the survey and the "predicted"  perfor-  mance i s found to be s i g n i f i c a n t i n three out of the four tests made. Third, i n only one t e s t out of three i s the c o r r e l a t i o n between "actual performance" f o r the six months preceding publication of the survey and the "observed" market performance found t o be s i g n i f i c a n t . The findings are summarized and presented i n the following pages. The Spearman rank c o r r e l a t i o n c o e f f i c i e n t s P, and the P's i n standard form (Z » P ^n-1)  are summarized together with the l e v e l of significance  CC which would make the absolute value of ± Z, of-t  h  e  n  c  e  t  h  e  a  b  s  o  l  u  t  e  v  a  l  u  e  P s i g n i f i c a n t . An asterisk beside an 0\- indicates that the P i s  s i g n i f i c a n t at a o r i t i c a l l e v e l of .050.  ^Significance i s considered to exist at the c r i t i c a l l e v e l of .050.  13  {  Correlation between "predicted" and "observed" market performancej  1. Bottom of a Market Break: Date July 2, 1962 Oct. 29, 1962 Mar. 4, 1963 July 29, 1963 Oct. 4, 1963 Nov. 22, 1963  P 0.1375 -0.0984 0.0837 0.2512 -0.1405 0.3640  Z 1.05 -0.78 0.65 2.10 -1.27 3.30  OL .294 .435 .516 .036 .204 .000  2. Top of a Market Break: Date May 22, 1961 Aug. 20, 1962 Feb. 11, 1963  P 0.2416 0.1427 -0.0161  (X  Z  1.96 1.20 -0.14  .050 .230 .889  3. Middle of a F a l l i n g Market: Date May Oct.  7, 1962 8, 1962  P 0.1746 0.0924  Z 1.45 0.76  .147 .447  4. Middle of a Rising Market: Date Dec. 24, 1962 Apr. 8, 1963  P 0.1623 0.0251  Z 1.42 0.23  .156 .818  ^ ^  14  Correlation between "actual performance" f o r the s i x months preceding publication of the survey and the "predicted" performance: Date May 22, 1961 Oct. 29, 1962 Mar. 4, 1963 Dec. 20, 1963  (X 0.1587 0.2761 0.2649 0.2490  0.14 2.36 2.40 2.32  .889 .018 .016 .020  % ft  Correlation between "actual performance" f o r the s i x months preceding publication of the survey and the "observed" market performance: Date May 22, 1961 Oct. 29, 1962 Mar. 4, 1963  <X -0.0146 -0.3516 0.1981  -0.12 -2.78 1.68  .005 -TfT .093  In Chapters IV and V the findings of the tests are related t o the a b i l i t y of the Value Line Investment Survey to predict "Probable Twelve Months Market Performance Rank."  I  CHAPTER IV  THE ABILITY OF FORECASTERS TO FORECAST  This chapter i s concerned with the a b i l i t y of forecasters of the stock market to predict price changes.  Presented f i r s t i s a summary of  some research attempted to t e s t the forecasting a b i l i t y of d i f f e r e n t concerns.  Following t h i s summary i s the interpretation of the author's  research findings, which should indicate whether or not The Value Line Investment Survey shows any a b i l i t y to predict "Probable Twelve Months Market Performance Rank." A l f r e d Cowles I I I , i n his study of the forecasting a b i l i t y of f o r t y - f i v e professional agencies f o r the years 1928-1932, found that these agencies f a i l e d to demonstrate any s k i l l i n forecasting stock price changes. ^  Of sixteen f i n a n c i a l services, only six showed better returns  than the market average, and even the best record did not indicate a performance better than that to be expected by chance. In Cowles* study of twenty-five f i r e insurance companies, each of which carried more than twenty percent of their t o t a l investments i n common stocks, only s i x showed evidence of forecasting a b i l i t y .  Again  i t was found that the records could not be attributed to s k i l l . He found that, of ninety forecasts of the stock market as a whole over the period 1904-1929 made by William P. Hamilton using the Dow  *Alfred Cowles, "Can Stock Market Forecasters Forecast?" (Economet r i c a , v o l . 1, July 1933, pp. 309-324). 15  16  Theory, only half were successful. He also investigated twenty-four forecasting publications f o r the period 1928-1932.  His analysis f a i l e d to indicate better than random  successes f o r these publications. 2 In h i s "Stock Market Forecasting,"  Cowles extends the records  of eleven of the twenty-four f i n a n c i a l services he had previously studied.  This study covers the period from 1928-1943.  He found that  the records of these services, during varying periods ranging from ten to f i f t e e n years after 1927, f a i l e d to disclose any a b i l i t y to predict the stock market. In another study, "A Study of Mutual Funds,"  by Brown, Herman  and Vickers, i t was found that the average performance of the funds was about the same as to be expected from an unmanaged fund consisting of similar s e c u r i t i e s .  "Both f o r balanced funds and common stock funds  separately, the d i s t r i b u t i o n of funds c l a s s i f i e d by the number of years i n which they demonstrated above-average performance seem completely random or conforming to chance." Wu,  5  i n following the transactions on the New York Stock Exchange  A. Cowles, "Stock Market Forecasting," (Econometrice, Nos. 3-4, July-October, 1944, pp. 206-214). 2  I . Friend, F.E. Brown, E. Herman and D. Vickers, "A Study of Mutual Fundss Investment P o l i c y and Investment Company Performance," ( i n H. Wu and A.J. Zakon, ed. Elements of Investments, New York, Holt, Rinehart and Winston, Inc., 1965). 3  4  I b i d . , p. 383.  H. Wu, "Corporate Insider Trading P r o f i t s and the A b i l i t y to Forecast Stock Prices," ( i n H. Wu and A.J. Zakon, ed. Elements of Investments, New York, Holt, Rinehart and Winston, Inc., 1965). 5  17  of f i f t y common stocks from October to December 1959,  f i n d s that "there  i s very l i t t l e evidence that a d e f i n i t e relationship exists between insider  transactions and subsequent price movements i n r e l a t i o n to the  general market trend."  His tests indicate that the insiders i n the  f i f t y companies did not outperform the market. As indicated, there i s evidence that stock market traders exhibit l i t t l e , i f any, s k i l l i n forecasting the future prices on the stock market.  However, i t i s s t i l l possible that a system has been devised  which may accurately prediot future stock price changes.  I t i s the pur-  pose of t h i s section to interpret the author's research findings regarding  the forecasting a b i l i t y of the Investment Line Survey i n presenting  the "Probable Twelve Months Market Performance Rank" of stocks. To t e s t the forecasting a b i l i t y , the "predicted" ranking i s compared with the actual "observed"  ranking (a ranking of the maximum per-  centage price appreciations achieved by the stocks during the year) of the stocks.  A t e s t of the c o r r e l a t i o n between the two rankings shows that  i n only three out of thirteen tests performed on data taken from d i f f e r ent periods are there s t a t i s t i c a l l y s i g n i f i c a n t c o r r e l a t i o n s .  The results  f a i l to indicate any consistent a b i l i t y of the survey to forecast the r e l a t i v e performance of stocks over the period of 12 months. In the book describing his survey  Bernhard states, " I t i s of  ^Every person who i s the b e n e f i c i a l owner of ten percent of the stock or i s a director or o f f i c e r or issuer of the security i s a corporate i n s i d e r . Wu, "Corporate Insider Trading P r o f i t s and the A b i l i t y to Forecast Stock P r i c e s , " p. 448. 7  8  A r n o l d Bernhard, The Evaluation of Common Stocks.  18  l i t t l e p r a c t i c a l value, under a method based upon yearly evaluation of earnings and dividends to determine that a stock i s overvalued or undervalued i n a p a r t i c u l a r year, i f prices do not perform i n accordance with the recommendation within that year." ^  I t would seem then, by Bern-  hard's own admission, that the survey's predictions of the "Probable Twelve Months Market Performance Rank" are of l i t t l e p r a c t i c a l value, as they f a i l to indicate any consistent a b i l i t y of the survey to forecast. In commencing the research project the author thought that the "predictions" might be more accurate at one stage i n the market cycle than another.  However, the results of the study f a i l e d to support t h i s  assumption; at no stage of the cycle was a consistent a b i l i t y to f o r e cast discovered. The forecasting a b i l i t y of stock market forecasters i s further considered i n the following chapter.  9  Bernhard, The Evaluation of Common Stocks, p. 86.  CHAPTER V  THE  "RANDOM WALK HYPOTHESIS" AND ITS RELATION TO THE PRESENT STUDY  THE HYPOTHESIS In t h i s chapter a model i s presented of a process which may generate stock p r i c e s .  The model, the "Random Walk Hypothesis," once d i s -  cussed, i s related t o The Value Line Investment Survey's  "predictions."  The random walk hypothesis f o r price changes i s actually composed of two separate hypotheses? 1. That successive price changes are independent of preceding price changes, that i s , that P (X  t  = Xt, / X - i , t  X -2>".) t  = P (X  t  = X ) t  where P (Xt = Xt) i s the unconditional p r o b a b i l i t y that  the  variable Xt, the price change during the period t , w i l l assume the value X-fc and where P (X_t = Xt / Xt-1,  Xt-2>»««)  i  s  t  n  e  conditional probability that Xt w i l l assume the value Xt« 2 . That the i n d i v i d u a l price changes conform to probability d i s tributions each with mean zero. * The random walk process i t s e l f i s given by: Xt - Zt - Z t _ i where Zt i s a variable generated a t time t by the process i n such a way  that Xt forms, for successive periods t, a sequence of random,  *The price changes f o r successive periods need not conform t o i d e n t i c a l probability d i s t r i b u t i o n s . 19  necessarily  20  independent  numbers, each conforming  to p r o b a b i l i t y d i s t r i b u t i o n s with  mean z e r o . F o r t h e random walk p r o c e s s as h y p o t h e s i z e d t o h o l d f o r stock p r i c e changes, s u c c e s s i v e p r i c e changes should e x h i b i t t h e same c h a r a c t e r i s t i c s as a sequence o f random independent  numbers, each  conforming  t o p r o b a b i l i t y d i s t r i b u t i o n s w i t h mean zero* 2 I t was L o u i s B a c h e l i e r  who f i r s t h y p o t h e s i z e d t h a t t h e p r o c e s s  u n d e r l y i n g s p e c u l a t i v e p r i c e changes was the random walk. h i s p i o n e e r i n g work remained i n o b s c u r i t y u n t i l l a t e r when H. Yforking  However,  (about 1934)  h y p o t h e s i z e d t h a t t h e r e v e a l e d s p e c u l a t i v e p r i c e changes  were generated by a random walk p r o c e s s . B a c h e l i e r t e s t e d the h y p o t h e s i s on t h e French Bond Market, assumi n g a " f a i r game," t h a t i s , a zero e x p e c t a t i o n o f g a i n . pondence was found t o be expected  A close corres-  t o e x i s t between the d i s t r i b u t i o n o f p r i c e changes  from h i s t h e o r y and t h a t o f t h e observed  p r i c e changes.  F o r h i s study, B a c h e l i e r chose t o c o n s i d e r o n l y one type o f s e c u r i t y a t a time.  Had B a c h e l i e r been working w i t h v a r i o u s types o f s e c u r -  i t i e s as Osborne t o t h e percentage  d i d l a t e r f o r common s t o c k s , he might have been l e d form o f p r i c e changes.  I n t h i s form, i f a s i n g l e  p r o b a b i l i t y d i s t r i b u t i o n f o r a g i v e n p e r i o d were h y p o t h e s i z e d t o generate ^L. B a c h e l i e r , " T h e o r i e de l a S p e c u l a t i o n " (Annales de 1'Boole Wormale S u p e r i e u r e , S e r . 3, XVII (1900), pp. 21-86. H . Working, "A Random-Difference S e r i e s f o r Use i n t h e A n a l y s i s of Time S e r i e s , " ( j o u r n a l o f t h e American S t a t i s t i c a l A s s o c i a t i o n , XXIX (1934), pp. 11-24). 3  %.F.M. Osborne, "Brownian Motion i n t h e Stock Market," t i o n s Research, V o l . 7 ( M a r c h - A p r i l , 1959), pp. 145-173.  (Opera-  21  equal p r o b a b i l i t i e s f o r g i v e n percentage p r i c e changes f o r a l l s e c u r i ties, be  then a " f a i r game" would r e s u l t from t h e model.  equally l i k e l y  a |10  t h a t a $100  That i s , i t would  s e c u r i t y would r i s e o r f a l l  s e c u r i t y would r i s e o r f a l l  $1.  $10,  E m p i r i c a l f i n d i n g s o f approximate  n o r m a l i t y i n the d i s t r i b u t i o n o f percentage p r i c e changes l e n d to  the h y p o t h e s i s  p r i c e changes.  or t h a t  support  t h a t t h e r e i s equal p r o b a b i l i t y f o r g i v e n p e r c e n t a g e However, the apparent l o n g run t r e n d i n s t o c k market  p r i c e s as a whole does not l e n d support t o t h e assumption of a  "fair  game" which i s p a r t of B a c h e l i e r ' s model. Osborne, i n h i s study of the random c h a r a c t e r of the market led  t o c o n s i d e r the l o g a r i t h m of p r i c e as the v a r i a b l e of concern  the "Random Walk H y p o t h e s i s . "  was in  However, i f the d i s t r i b u t i o n of changes  i n the l o g a r i t h m s o f p r i c e s f o r a g i v e n p e r i o d i s h y p o t h e s i z e d  t o gener-  a t e equal p r o b a b i l i t i e s f o r g i v e n changes i n the l o g a r i t h m o f p r i c e , then the model i s no l o n g e r a " f a i r game." E m p i r i c a l f i n d i n g s concerning  the changes i n the l o g s of p r i c e s f o r  a number of d i f f e r i n g s t o c k s from one p e r i o d t o t h e next, tend t o the h y p o t h e s i s  support  t h a t t h e r e i s equal p r o b a b i l i t y f o r g i v e n changes i n the 7  l o g s of p r i c e s .  Such evidence would i n d i c a t e t h a t the model i s o t h e r  ^S. Alexander, " P r i c e Movements i n S p e c u l a t i v e M a r k e t s : Trends o r Random Walks," ( I n d u s t r i a l Management Review, 2 No. 2 (May 1961), pp. 7-26) p . 467. I f t h e r e i s an equal p r o b a b i l i t y o f a change of one on one hundred d o l l a r s the expected amount of g a i n i s : | ($10 + $1000) - $100 = $405. 6  i n the  log-^,  A.B. Moore, "Some C h a r a c t e r i s t i c s of Changes i n Common Stock P r i c e s " ( i n P.H. Cootner, ed. The Random C h a r a c t e r o f Stock Market P r i c e s , Cambridge, Mass., M.I.T. P r e s s , 1964).  22  t h a n a " f a i r game."  I n f a c t , u s i n g l o g p r i c e s as t h e v a r i a b l e of concern  i n t h e "Random Walk H y p o t h e s i s "  a l l o w s f o r e x p e c t a t i o n of g a i n i n t h e  model. I t i s apparent t h a t a l o n g - r u n  t r e n d i n stock market p r i c e s as a  Q  whole does e x i s t .  The market i s n o t a " f a i r game," b u t r a t h e r i s  weighted i n f a v o u r o f t h e i n v e s t o r ( a t t h e moment t h e l o n g - r u n f o r t h e market t o r i s e ) .  The c h o i c e o f l o g a r i t h m o f p r i c e as t h e  v a r i a b l e o f concern i n t h e "Random Walk H y p o t h e s i s " r i s i n g trend i n p r i c e s . Walk H y p o t h e s i s "  trend i s  does a l l o w f o r a  However, i t seems u n l i k e l y t h a t t h e "Random  as f o r m u l a t e d ,  using logs of p r i c e s , i s the "best"  c h o i c e t o d e s c r i b e t h e random n a t u r e  o f t h e market where a r i s i n g  trend  i n p r i c e s i s apparent. A r e v i s e d form o f t h e "Random Walk H y p o t h e s i s " i n t o account i s t h e "Random Walk H y p o t h e s i s " i s : Z^. - Z-t-1 ~ £ t  Wh  e r e  which t a k e s  trend  incorporating d r i f t ,  that  t h e symbols r e f e r t o t h e v a r i a b l e s p r e v i o u s l y  i n d i c a t e d , save t h a t Xj- i s now assumed t o conform t o d i s t r i b u t i o n s  with  means o t h e r t h a n z e r o , chosen so t h a t t h e expected v a l u e o f X-^ accounts f o r the t r e n d i n t h e market. So regarded,  a t e s t o f t h e random n a t u r e  o f stock market p r i c e s may  be made by comparing a c t u a l performance i n s t o c k p r i c e s under a systematic  t r a d i n g r u l e w i t h p r i c e performance p o s s i b l e through a"buy-and-hold"  plan.  I f r e s u l t s indioate that s i g n i f i c a n t l y greater " p r o f i t s " are  a v a i l a b l e t o a systematic  t r a d i n g p l a n , which takes i n t o account only  M.G. K e n d a l l might d i f f e r , (M.G. K e n d a l l , "The A n a l y s i s o f Economic T i m e - S e r i e s , P a r t I : P r i c e s , " ( J o u r n a l o f t h e Royal S t a t i s t i c a l S o c i e t y , V o l . 96, P a r t I (1953), pp. 11-25) p . 11), f o r he found t h a t "In a s e r i e s o f p r i c e s which a r e observed a t f a i r l y c l o s e i n t e r v a l s t h e random changes from one term t o t h e next a r e so l a r g e as t o swamp any s y s t e m a t i c e f f e c t which may be p r e s e n t . " 8  23  past prices, than to a "buy-and-hold" system on the same stocks, then a dependency between past and future prices may be established, and grounds may be made on which to refute the "Random Walk Hypothesis." Alexander  9  has suggested such a scheme, a f i l t e r scheme,  10  and  11  has tested i t  on some commonly used price i n d i c e s .  His o r i g i n a l  r e s u l t s have indicated that, generally, a l l sizes of f i l t e r s  yield  greater p r o f i t s than a simple "buy-and-hold" p o l i c y . 12 However, as Mandelbrot points out, Alexander's trading system 13 14 has incorporated certain computational biases. In h i s second paper, Alexander has tested the "Random Yfelk Hypothesis" a f t e r attempting to remove a l l biases from h i s f i l t e r scheme.  These l a t e r results indicate  that the apparent p r o f i t a b i l i t y of the f i l t e r technique i s d r a s t i c a l l y reduced but s t i l l indicate that the technique should be more p r o f i t a b l e than a "buy-and-hold" policy f o r f i l t e r sizes up to about 10% and over about 40$. ^S. Alexander, "Price Movements i n Speculative Markets" ( i n Wu) and "Price Movements i n Speculative Markets: Trends or Random Walks, No. 2," ( i n P.H. Cootner, ed. Random Character of Stock Market Prices, Cambridge, Mass., M.I.T. Press, 1964). •^Alexander's scheme i s to select a stock and watch i t . price goes up X percent, buy i t . Hold onto i t u n t i l i t s price X percent from a subsequent high price then s e l l the stock and Buy the stock when i t s price r i s e s X percent from a subsequent  If i t s falls go short. low p r i c e .  **A n o n - s t a t i s t i c a l t e s t i s used. •^B. Mandelbrot, "The V a r i a t i o n of Certain Speculative P r i c e s , " (Journal of Business, V o l . 36, No. 4 (October, 1963), pp. 394-419). 13  Ibid», p. 417.  14  S. Alexander, Price Movements i n Speculative Markets: Trends or Random Walks, No. 2."  24  However, as Fama and Blume  p o i n t out, A l e x a n d e r has n o t a d j u s t e d  the p r i c e i n d i c e s f o r d i v i d e n d s which a r e l o s t through a c t i v e  trading  16 of  the s t o c k s .  The r e s u l t s o f t e s t s c a r r i e d out by Fama and Blume  i n d i c a t e that only f o r very small f i l t e r s ,  1.5%  t e c h n i q u e more p r o f i t a b l e t h a n a "buy-and-hold"  and l e s s , i s the policy before  filter  commissions.  They suggest t h a t t h e r e i s a p o s i t i v e dependence i n v e r y s m a l l p r i c e changesj  and evidence o f a n e g a t i v e dependence i n i n t e r m e d i a t e s i z e d  changes (1.5$ t o 12% f i l t e r s ) .  However, when commissions and the time  funds w i l l be i d l e a r e taken i n t o account, the apparent are  not l i k e l y t o i n c r e a s e the p r o f i t a b i l i t y  more t h a n t h a t of the simple "buy-and-hold"  dependencies  of the f i l t e r  scheme t o  policy. 17  In another paper, dependencies  "A new  Look a t C l u s t e r i n g o f Stock P r i c e s , "  a r e found t o e x i s t i n terms o f the exact p r i c e s a t which  s t o c k s are s o l d .  I t i s found t h a t s t o c k s t r a d e a t even e i g h t h s more  o f t e n t h a n a t odd e i g h t h s , and most o f t e n a t whole number p r i c e s l i k e 25,  50, 75 and 100,  a l l even e i g h t h s .  The  same phenomenon has been  10, dem-  18 o n s t r a t e d e a r l i e r by Osborne i n h i s work, A P h y s i c i s t Looks a t Stock P r i c e s . E . Fama and M. Blume, " ' F i l t e r Rules and Stock-Market T r a d i n g , " (The J o u r n a l o f B u s i n e s s , V o l . XXXIX (January, 1966), pp. 226-241). 1 5  •l^Fama and Blume p o i n t out ( E . Fama and M. Blume, " F i l t e r Rules and Stock-Market T r a d i n g , " p. 235) t h a t " I n a s h o r t s a l e t h e borrower of t h e s e c u r i t i e s t y p i c a l l y reimburses t h e l e n d e r f o r any d i v i d e n d s t h a t a r e p a i d w h i l e the s h o r t p o s i t i o n i s o u t s t a n d i n g . Thus a d j u s t i n g f o r d i v i d e n d s w i l l reduce the p r o f i t a b i l i t y o f s h o r t s a l e s and t h e r e b y reduce t h e p r o f i t a b i l i t y o f the f i l t e r t e c h n i q u e r e l a t i v e t o buy-andhold." V . N i e d e r h o f f e r , "A New Look a t C l u s t e r i n g o f Stock P r i c e s , " ( J o u r n a l of B u s i n e s s , V o l . 39, No. 2 ( A p r i l , 1966), pp. 309-313). 1 7  ^ O s b o r n e , A P h y s i c i s t Looks a t Stock P r i c e s ( c i t e d i n A.B. Moore, "Some C h a r a c t e r i s t i c s o f Changes i n Common Stock P r i c e s , " p . 153).  25  A recent paper by Mandelbrot  introduces the thought that stock  prioes may follow a "Martingale" rather than a random walk.  The "Mar-  t i n g a l e " property "implies only that the expected values of future prices w i l l be independent of the values of past prices: the d i s t r i b u tions of future prices, however, may very well depend on the values of past prices."  2  The random walk i s a "Martingale, " but the "Martingale"  0  1  i s not necessarily a random walk.  However, as Fama and Blume point out,  the degree of dependence shown by the "Martingale" i s l i k e l y so small that f o r p r a c t i c a l purposes the random walk hypothesis i s not greatly v i o l a t e d f o r stock price changes. Some s t a t i s t i c a l tests do not reject the assumption of independence i n the "Random Walk Hypothesis" f o r stock price changes. for  Kendall found  B r i t i s h stock price averages that "stock-exchange movements revealed  l i t t l e s e r i a l c o r r e l a t i o n within series &nd l i t t l e lag c o r r e l a t i o n between series."  2  1  Moore  2  2  found that, although there was s l i g h t posi-  t i v e s e r i a l c o r r e l a t i o n i n the differences of the logs of prices f o r successive periods, non-parametric tests of the runs i n the signs of Standard and Poor's 5 0 0 Stock index tended to support the hypothesis of independence i n runs.  * B. Mandelbrot, "Forecasts of Future P r i c e s , Unbiased Markets, and 'Martingale' Models," Journal of Business, v o l . X X X I X (January, 1 9 6 6 ) , 9  pp.  2 4 2 - 2 5 5 . 2 0  p.  E . Fama and M. Blume, " F i l t e r Rules and Stock-Market Trading,"  2 2 6 .  M.G. Kendall, "The Analysis of Economic Time-Series, Part I ; Prices," p. 1 1 . 21  2 2 A . B . Moore, "Some C h a r a c t e r i s t i c s of Changes i n Common Stock Prices," p. 1 4 5 .  26  As only s l i g h t , i f any, dependence i n stock price changes has been observed, for a l l p r a c t i c a l purposes the assumption that successive price changes are independent of preceding price changes may be an adequate description of r e a l i t y where i t seems that the s l i g h t dependencies cannot be used to produce greater p r o f i t s than a "buy-and-hold" p o l i c y . The nature of the probability d i s t r i b u t i o n l i k e l y to underly stock price changes f o r any given period has been explored by some researchers. 23 Kendall,  i n analyzing changes i n both stock price averages and com-  modity prices on the London market, found approximate normality i n the 24 changes.  Osborne,  i n his study of the New York Stock Exchange, found  approximate normality i n changes i n the logarithms of stock prices. 25 Mandelbrot  questions the findings of normality i n stock price changes.  He f i n d s that more observations l i e near the mean and more l i e i n the extreme t a i l s i n the frequency d i s t r i b u t i o n of price changes than would be expected i f the underlying d i s t r i b u t i o n were normal.  He suggests that,  not the mormal d i s t r i b u t i o n which i s a member of the Pareto family of d i s t r i b u t i o n s , but rather, some other member of the family would better " f i t " the empirical data.  However, those candidates of the Pareto family  which might better " f i t " the empirical findings, although they have the 26 additive properties associated with the normal d i s t r i b u t i o n , do not have f i n i t e variances. Tests of significance have not been develogeddfor the M.G. Kendall, "The Analysis of Economic Time-Series, Part I: Prices," p. 17. Osborne, "Brownian Motion i n the Stock Market." 23  2 5  B . Mandelbrot, "The Variation of Certain Speculative P r i c e s . "  ^A l i n e a r combination of normal independent yariables i s i t s e l f normal. 2  27  Pareto family as a whole.  As such i s the case, i f a Pareto d i s t r i b u t i o n  with i n f i n i t e variance i s assumed to underly price changes, then parametric significance tests of the independence of stock price changes 27 cannot be applied.  However, Fama  indicates that the mean deviation,  rather than the variance, may be the basis f o r future  significance  tests f o r the Pareto d i s t r i b u t i o n . FINDINGS WHICH MAY SUPPORT THE HYPOTHESIS Now,  i n the present study, many d i f f e r i n g stocks are considered  at once so that percentage price changes or the difference i n the logarithms of successive prices would be the acceptable variables f o r testing the independence assumption of the "Random Walk Hypothesis" where i t i s assumed that single probability d i s t r i b u t i o n s underly the 28 changes i n common stock prices f o r given periods.  The method chosen  to t e s t the independence assumption i s non-parametric and hence does not involve the parameters of the underlying d i s t r i b u t i o n s .  The ques-  t i o n as to whether or not the underlying d i s t r i b u t i o n s are normal, Paretian,  or even symmetric, or whether or not the means of the under-  l y i n g d i s t r i b u t i o n s are zero or some other value to account f o r d r i f t i n the prices i s circumvented by performing the rank c o r r e l a t i o n study described i n the paper. differences test.  The choice of percentage p r i c e changes or  i n logarithms of prices would y i e l d the same results i n the  In f a c t , the non-parametric rank c o r r e l a t i o n method chosen to 27  Eugene F. Fama, "The Behaviour of Stock Market Prices."  2®S. Alexander, "Price Movements i n Speculative Markets: Trends or Random Walks," p. 15.  28  t e s t the forecasting a b i l i t y of the survey would y i e l d the same results whether r e l a t i v e price changes, r e l a t i v e prices, the log of r e l a t i v e prices, or the difference i n the logs of prices were chosen to conduct the  t e s t s , as there i s a one to one ordered correspondence between each 29  of the variables l i s t e d . If the "Random Walk Hypothesis" i s assumed and i f a single d i s t r i bution does underly p r i c e changes f o r a given period, or i f single d i s tributions underly price changes f o r every f r a c t i o n of a period, then, for any period chosen, a random ordering of stocks should r e s u l t accord30 ing to percentage price changes.  I f single d i s t r i b u t i o n s underly a l l  price changes f o r d i f f e r e n t periods throughout a year, then a random ordering of stocks according to the greatest percentage price appreciations achieved during the year should r e s u l t from cumulations of the random percentage changes. L o g of r e l a t i v e prices equals the difference i n the logs of prices, i . e . 29  log  = log ?t Log of r e l a t i v e prices has r e l a t i v e prices ( r e l a t i v e prices Relative prices have a one  P  t w  - log P  t  a one to one ordered correspondence to i n a l l cases are or can be made positive), to one ordered correspondence to  r e l a t i v e price changes, that i s , has a one to one correspondence t+i - ^ h to Pt P *•»" P p Proof» "fc* i s the same as - 1 Pt Pt t+1 " t t+l Hence and have a one to one ordered correst P pondence, as they d i f f e r only by a constant -1. p  1  P  p  t  p  p  t  I f the single d i s t r i b u t i o n s are themselves each Paretian (including normal) then the percentage price changes over a number of periods w i l l appear to have been generated by a single Paretian d i s t r i bution. 3 0  29  Assuming that a single d i s t r i b u t i o n does underly stock price changes f o r d i f f e r e n t stocks i n a market characterized by a random walk, and hence that a random ordering of stocks according to percentage price changes i s the r e s u l t , the comparison of the orderings f o r periods should not reveal any  successive  s i g n i f i c a n t c o r r e l a t i o n ; that i s , they  should indicate independence i n price changes. undertaken i n the research project, and,  Such comparisons were  as indicated i n the findings  of Chapter I I I , the c o r r e l a t i o n between the "observed" (future) actual past market performance was  and  found to be s i g n i f i c a n t at the  l e v e l of significance i n only one t e s t out of three.  b%  These results are  not adequate to refute the hypothesis that price changes are independent. However, i t might be f r u i t f u l to make more tests of the independence hypothesis between prices i n a period during which most prices are f a l l i n g and a succeeding period i n which most prices are r i s i n g , as was case for the one t e s t which was  s i g n i f i c a n t . Such a t e s t may  that there i s a c o r r e l a t i o n between price changes i n the two thus may  the  indicate periods and  be grounds f o r refuting the assumption of independence.  Then  again, i f the prices are found to be dependent using the present t e s t , but independent using other t e s t s , the assumption that single d i s t r i b u tions underly a l l stock price changes, rather than the assumption of i n dependence, may  be f a l s e .  Benjamin King f i n d s , through factor analysis,  "that the movemeat of a group of security price changes can be broken 31  down into market and industry components; that the assumption of a single underlying  his results seem to indicate d i s t r i b u t i o n may  not be correct.  B . F . King, "Market and Industry Factors i n Stock P r i c e Behavior," (Journal of Business, V o l . XXXIX (January, 1966), pp. 139-190), p. 163. 31  30  RELATION TO THE PRESENT STUDY  Assuming that the "Random Walk Hypothesis" i s applicable to stock market price changes, i t should be c l e a r that any forecast of future price changes based wholly on past p r i c e changes i s not l i k e l y to y i e l d accurate r e s u l t s .  In the author's study, the c o r r e l a t i o n c o e f f i c i e n t  between "actual past performance" and performance i s determined.  "predictions" of future p r i c e  I t i s found that, i n three out of four t e s t s ,  the c o r r e l a t i o n between the two performances i s s i g n i f i c a n t . Such consistent s i g n i f i c a n t correlations might lead one to suppose that the Value Line "predictions" are heavily based on past performance i n price changes.  If such i s the case, one might expect that there should be  l i t t l e significance to the c o r r e l a t i o n between "forecasted" and (future) price appreciations.  "observed"  The author finds that i n only three out  of thirteen tests performed were c o r r e l a t i o n c o e f f i c i e n t s between the "predicted" and the "observed" p r i c e appreciations the f i v e percent l e v e l of significance.  found s i g n i f i c a n t at  The r e s u l t s do not d i f f e r greatly  from the results one might expect had predictions been based on past prices alone, where the market i s assumed to follow a random walk.  It  would seem from the present t e s t s , that the Value Line Investment Survey has f a i l e d to prove that i t s "predictions" of future "Twelve Months Market Performance Rank" are superior to "predictions" based solely on past prices.  However, The Value Line Survey's "predictions" do not take into  account solely the price appreciations (the Value Line method i s described  over a s i x months preceding period  i n Chapter I I ) .  This f a c t i s borne  out by the tests made on The Value Line Survey "predictions" f o r Oct.  29,  31  1962.  Although the " p r e d i c t i o n s " are s i g n i f i c a n t l y c o r r e l a t e d w i t h  " a c t u a l performance** f o r the s i x months p r e c e d i n g p u b l i c a t i o n o f t h e survey, and, a l t h o u g h the " a c t u a l performance" f o r the s i x months p r e c e d i n g p u b l i c a t i o n o f t h e survey i s s i g n i f i c a n t l y  c o r r e l a t e d w i t h the  "observed" ( f u t u r e ) market performance, t h e " p r e d i c t i o n s " a r e n o t s i g n i f i c a n t l y c o r r e l a t e d w i t h t h e "observed" ( f u t u r e ) market  performance.  A l s o , i n t h e one case out o f f o u r i n which " a c t u a l p a s t s i x month's performance" i s n o t found t o be s i g n i f i c a n t l y c o r r e l a t e d w i t h " p r e d i c ted"  performance, ""predicted" performance i s found t o be  c o r r e l a t e d w i t h "observed" ( f u t u r e ) market  significantly  performance.  Although t h e method f o r " f o r e c a s t i n g " "Twelve Months Market P e r formance Rank" does not t a k e i n t o account only changes i n p a s t p r i c e s (which, f o r a l l p r a c t i c a l prices), accuracy.  purposes seem t o be independent o f f u t u r e  t h e r e s u l t s o f i t s a p p l i c a t i o n have n o t shown any c o n s i s t e n t The author i s l e d t o c o n c l u d e t h a t t h e a c c u r a c y o f p r e d i c -  t i o n s by t h i s method i s no g r e a t e r than t o be expected by b a s i n g "pred i c t i o n s " o f a "Twelve Months Market Performance Rank" on a random ranking of stocks.  CHAPTER VI  CONCLUSION  The r e s u l t s o f the author's study do n o t r e f u t e t h e "Random Walk H y p o t h e s i s " f o r stock p r i c e s .  However, though adopted i n the p r e s e n t  study, t h e assumption t h a t a s i n g l e d i s t r i b u t i o n u n d e r l i e s a l l s t o c k p r i c e changes f o r a g i v e n p e r i o d may n o t be v a l i d g e n e r a l l y ,  King f i n d s  " t h a t the movement o f a group o f s e c u r i t y p r i c e changes can be broken down i n t o market and i n d u s t r y components." ^  I n t h e p r e s e n t study, the  " a c t u a l p a s t performance" i s n o t s i g n i f i c a n t l y c o r r e l a t e d w i t h "observed" performance, even though b o t h r a n k i n g s i n v o l v e s t o c k s from d i f f e r e n t industries.  I t i s possible that, a t l e a s t f o r the present project,  the assumption o f a s i n g l e d i s t r i b u t i o n u n d e r l y i n g percentage p r i c e changes f o r a l l s t o c k s i s an adequate  assumption.  " P r e d i c t i o n s " i n a market f o l l o w i n g a random walk may be a c c u r a t e where the " p r e d i c t i o n s " a r e based upon an a p p r a i s a l o f new i n f o r m a t i o n which a f f e c t s p r i c e s .  Dependencies i n t h e i n f o r m a t i o n should n o t l e a d  t o dependencies i n p r i c e changes, as s o p h i s t i c a t e d t r a d e r s w i l l t a k e such dependencies i n t o account, and t h e i r a c t i o n s should tend t o e l i m i n a t e t h e dependencies i n p r i c e changes.  Those a n a l y s t s who can  ^B.F. K i n g , "Market and I n d u s t r y F a c t o r s i n Stock P r i c e B e h a v i o r , " p. 163. 32  33  c o n s i s t e n t l y p r e d i c t t h e appearance o f new i n f o r m a t i o n and determine i t s e f f e c t s on stock p r i c e s should show evidence  o f an a b i l i t y  i n making  "predictions.''" The Value L i n e Investment Survey f a i l s t o e v i n c e a c o n s i s t e n t a b i l i t y t o f o r e c a s t "Probable  Twelve Months Market Performance Rank,"  the r a n k i n g o f s t o c k s a c c o r d i n g t o t h e i r p r o b a b l e performance f o r t h e y e a r .  I t seems t h a t r e s u l t s comparable t o those  based on t h e " p r e d i c t i o n s " c o u l d be gained stocks.  r e l a t i v e market p r i c e  by randomly r a n k i n g t h e same  34  SELECTED BIBLIOGRAPHY  Alexander, S. "Price Movements i n Speculative Markets: Trends or Random Walks." Industrial Management Review, 2, no. 2 (May 1961), pp. 7-26. Alexander, S. "Price Movements i n Speculative Markets: Trends or Random Walks, No. 2," i n P.H. Cootner, ed. Random Character of Stock Market P r i c e s . Cambridge, Mass., M.I.T. Press, 1964. Bachelier, L. "Theorie de l a Speculation" (doctoral d i s s e r t a t i o n i n mathematics, University of Paris, March 29, 1900). Annales de l'Ecole Normale Superieure, Ser. 3, XVII (1900), pp. 21-86. An English t r a n s l a t i o n appears as pp. 17-75 i n P.H. Cootner, ed. The Random Character of Stock Market P r i c e s . Cambridge, Mass., M.I.T. Press, 1964. Bernhard, Arnold. The Evaluation of Common Stocks. New York, Simon and Schuster, 1959. Board of Governors of the Federal Reserve System. B u l l e t i n . Washington, 1960-1964.  Federal Reserve  Cootner, P.H. "Stock P r i c e s : Random vs. Systematic Changes." Indust r i a l Management Review, v o l . 3, no. 2 (May 1961), pp. 7-26. Cootner, P.H., ed. The Random Character of Stock Market P r i c e s . Cambridge, Mass., M.I.T. Press, 1964. Cowles, A. "Can Stock Market Forecasters Forecast?" v o l . 1 (July, 1933), pp. 309-324.  Econometrica,  Cowles, A. "Stock Market Forecasting." Econometrica, v o l . 12, nos. 3-4 (July-October, 1944), pp. 206-214. Fama, E.F. "Mandelbrot and the Stable Paretian Hypothesis." Journal of Business, v o l . 36, no. 4 (October, 1963), pp. 420-4297 Fama, Eugene F. "The Behaviour of Stock Market P r i c e s . " Journal of Business, v o l . XXXVIII (January, 1965), pp. 34-105. Fama, E. and Blume, M. " F i l t e r Rules and Stock-Market Trading." Journal of Business, v o l . XXXIX (January, 1966), pp. 226-241. Fredrikson, E.B., ed. Frontiers of Investment Analysis. International Textbook Company, 1965.  Pennsylvania,  35  Friend, I., Brown, F.E., Herman, E. and Vickers, D. "A Study of Mutual Fundsi Investment Policy and Investment Company Performance," i n H, Wu and A.J. Zakon, ed. Elements of Investments. New York, Holt, Rinehart and Winston, Inc., 1965. Freund, J»E. 1962.  Mathematical S t a t i s t i c s .  New Jersey, Prentice-Hall, Inc.,  Graham, B., Dodd, D.L., and Cottle, S. Security Analysis. New York, McGraw-Hill Book Company, Inc., 1962.  4th ed.  Granger, C.W.J, and Morgenstern, 0., "Spectral Analysis of New York Stock Exchange Prices." Kyklos, 16, (1963), pp. 1-27. Kendall, M.G. Rank Correlation Methods. Co. Ltd., 1948.  London, Charles G r i f f i n and  Kendall, M.G. "The Analysis of Economic Time-Series, Part Is P r i c e s . " Journal of the Royal S t a t i s t i c a l Society, v o l . 96, Part I (1953), pp. 11-25. King, B.F. "Market and Industry Factors i n Stock Price Behavior." Journal of Business, v o l . XXXIX (January, 1966), pp. 139-190. Lorie, J . "Some Comments on Recent Quantitative and Formal Research on the Stock Market." Journal of Business, v o l . XXXIX (January, 1966), pp. 107-110. Mandelbrot, B. "The Variation of Certain Speculative P r i c e s . " Journal of Business, v o l . 36, no. 4 (October, 1963), pp. 394-419. Mandelbrot, B. "Forecasts of Future Prices, Unbiased Markets, and 'Martingale' Models." Journal of Business, v o l . XXXIX (January, 1966), pp. 242-255. Moore, A.B. "Some Characteristics of Changes i n Common Stock Prices" i n P.H. Cootner, ed. The Random Character of Stock Market P r i c e s . Cambridge, Mass., M.I.T. Press, 1964. Niederhoffer, V. "A New Look at Clustering of Stock Prices." of Business, v o l . 39, no. 2 ( A p r i l , 1966), pp. 309-313.  Journal  Osborne, M.V.M. "Brownian Motion i n the Stock Market." Operations Research, v o l . 7 (March-April, 1959), pp. 145-173. Roberts, H. "Stock-Market 'Patterns* and F i n a n c i a l Analysis: Methodo l o g i c a l Suggestions" Journal of Finance, v o l . 14, no. 1 (March, 1959), pp. 1-10. Sauvain, H. Investment Management, 2nd ed. Inc., 1960.  New Jersey, Prentice-Hall,  36  The V a l u e L i n e Investment Survey. Inc., 1960-1964.  New  York, A r n o l d Bernhard and  W i l l i a m s , J.B. The Theory o f Investment V a l u e , H o l l a n d P u b l i s h i n g Company, 1956.  Co.,  Amsterdam, N o r t h -  Working, H. "A Random-Difference S e r i e s . " J o u r n a l o f the American S t a t i s t i c a l A s s o c i a t i o n , XXIX (1934), pp. 11-24. Wu,  H. and Zakon, A. Elements o f Investments. h a r t and Winston, I n c . , 1965.  Wu,  H.  New  York, H o l t , R i n e -  " C o r p o r a t e I n s i d e r T r a d i n g P r o f i t s and t h e A b i l i t y t o F o r e c a s t Stock P r i c e s , " i n H. Wu and A . J . Zakon, ed. Elements o f I n v e s t ments. New York, H o l t , R i n e h a r t and Winston, I n c . , 1965.  

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