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Relative price performance : the theory and an empirical test 1970

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RELATIVE PRICE PERFORMANCE: THE THEORY AND AN EMPIRICAL TEST by WILLIAM P. HALLAM B.Comm., University of British Columbia, 19&8 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION in the Department of Commerce and Business Administration We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1970 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th i s thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my wr i t ten permission. WILLIAM P. HALLAM Department of Commerce and Business Administration The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada Date September 29, 1970. ABSTRACT This study has a twofold purpose. The primary purpose is to examine empirically the hypothesis of rela- tive price performance. This hypothesis states that issues in the stock market which have recorded a price performance superior to the market for a period of time w i l l tend to continue to record a superior price performance relative to the market. Conversely, those issues which have re- corded an inferior price performance relative to the mar- ket w i l l tend to maintain an inferior relative performance. The secondary purpose of the study is to develop a theoret- i c a l framework that attempts to explain how complexity in corporations is a constraint on the analysis of those cor- porations and is a determinant of security price behavior. The data consisted of a sample of 1214 companies which constituted those stocks included in the four major indices on the Toronto Stock Exchange as of January 1, 19&5. The data tested were adjusted monthly stock prices cover- ing the period January, 1965 to November, 1969. The me- thodology employed was the estimation of regression equa- tions to determine the relationship between his t o r i c a l measures of relative price performance and subsequent re- lative price performances. i i The r e s u l t s of the empirical te s t i n g provide no support for the hypothesis. In p r a c t i c a l l y every regres- sion equation estimated the significance of the findings was almost n e g l i g i b l e . The findings inferred that the hypothesis should be rejected. The development of a t h e o r e t i c a l framework i n - volving complexity i n corporations and information types demonstrated that trends in security price movement are l o g i c a l l y possible but only in certain cases. As a consequence of the two purposes of the study two conclusions were arrived at. F i r s t l y , the hypothesis as tested here must be rejected due to an absence of any support for i t . Secondly, recognition of the constraining influence of complexity on the security valuation process revealed that c e r t a i n categories of companies would tend to exhibit a consistency i n th e i r s e c u r i t i e s ' r e l a t i v e price performance. Therefore i t was suggested that future research i n the f i e l d of security price behavior should give consideration to disaggregating the sample into cate- gories of complexity. TABLE OP CONTENTS CHAPTER PAGE I INTRODUCTION 1 Purpose of Study 3 Importance of the Study I4 Outline of the Paper . . . . . . . 5 II THE HYPOTHESIS OP RELATIVE STRENGTH . . 7 The General A n a l y t i c a l Process . . 7 Fundamental Analysis 8 Technical Analysis 10 Relative Price Performance . . . . 13 The Importance of Relative Price Performance 18 The Random Walk 19 III NATURE OP THE DATA AND METHODOLOGY EMPLOYED 21 Data 21 Methodology and Approach Taken . . 27 Method of Testing 2 9 Tests Conducted 30 Unranked Relative Price Performance Tests I - II . . . 33 Ranked Relative Price Perform- ance Tests III - XI 3 6 CHAPTER PAGE IV DISCUSSION OP THE FINDINGS 1+6 Results of the Empirical Tests I - XI 1+8 Summary 63 V A CONSTRAINING FRAMEWORK OF COMPLEXITY FOR SECURITY ANALYSIS 65 Complexity and the Analyst 67 Knowledge Structures and Images . . . 69 Framework for Complexity . . . . . . 71+ Information Types and Content . . . . 80 The Valuation Process Related to Complexity and Information Contents 81+ Summary 91+ VI CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH 96 Conclusions from the Empirical Examination of Relative Price Performance 97 Implications of the Constraints of Complexity 98 Suggestions f o r Further Research . . 99 BIBLIOGRAPHY . . . . . . . 101 APPENDIX I 101+ LIST OF TABLES TABLE PAGE 3 - 1 Stock Price Performances Relative to the Market 3 1 3 - 2 Stock Price Performances Ranked Relative to Each Other 3 2 3 - 3 Disaggregated Sample - Five Groups . 3 9 3-1+ Disaggregated Sample - Seven Groups . I4I 3 - 5 Market Trends - Uptrends vs Down- trends kk I4.-I Regression S t a t i s t i c s - Test I . . . U 9 b,-2(a) Regression S t a t i s t i c s . . . 5 0 i[-2(b) Frequency of Moving Averages Con- sidered S i g n i f i c a n t . . . . . . . . 5 1 l[-2 (c ) Frequency of Regression Signs . . . . 5 2 I4—3 Regression S t a t i s t i c s of Ranked Rela- tive Strength . 5 3 li-b, Multiple Regression S t a t i s t i c s . . . 55 l p 5 Multiple Regression S t a t i s t i c s . . . 5 6 I4-6 Regression S t a t i s t i c s 5 7 J4-7 Regression S t a t i s t i c s 5 8 I4-8 Regression S t a t i s t i c s 5 9 i|- 9 Multiple Regression S t a t i s t i c s . . . 6 0 i|-10 Multiple Regression S t a t i s t i c s . . . 6 1 TABLE PAGE I4-II Simple Regression S t a t i s t i c s 62 $-1 Categories of Complexity by Domain and Dynamic Dimensions 76 5-2 Constraints of Complexity and Con- sequent Stock Price Behavior 86 INTRODUCTION There i s nothing as disastrous as a r a t i o n a l investment policy i n an i r r a t i o n a l world. - John Maynard Keynes.^" The above quotation summarizes very n i c e l y a major dilemma that has faced the investment community f o r years - the r a t i o n a l i t y of the stock market. Investors, investment managers and economists have attempted f o r decades to understand the r a t i o n a l i t y of the market's be- havior. Throughout the years a d i v e r s i t y of opinions and explanations have been espoused and employed i n attempting to forecast stock prices. Many of these explanations have been applied and developed into more mature theories while others have been disputed and rejected. In spite of the fact that the stock market has been a subject of enquiry f o r many years the investment community and academics continue to debate the basis of i t s behavior. Ije rome B. Gohen, Edward D. Zinbarg, Investment Analysis and P o r t f o l i o Management. (Homewood, 111.: R.D. Irwin, Inc., 1967), P. 503. 2 Amidst the arguments two schools of investment analysis are predominant. The fundamentalist school proposes that the basics or fundamentals of corporate and economic data can be analyzed to forecast the earnings flow of firms to determine t h e i r present value. The present value i s then compared to the market value and i f greater, the issue is suggested for purchase, i f less then the issue i s suggested to be sold. From the fundamentalist theory numerous.valuation models have evolved hypothesizing the rel a t i o n s h i p of the fundamental variables. While the "technical" school of analysis puts f o r t h the theory that various market indicators are more usefu l i n forecasting stock prices rather than ana- l y z i n g the fundamentals of companies. The technical approach has resulted i n the creation of d i f f e r e n t measures and indices to gauge the sentiment of the market and the demand-supply forces behind i n d i v i d u a l stocks within the market. The technical approach, however, has come under opposition i n recent years from advocates of the random walk theory. The random walk model is based on the premise that successive price changes are independent which is i n contradiction to the tec h n i c a l analyst's view that trends exist between successive price changes and can be detected by c e r t a i n technical indicators. This paper is an analysis of the r e l a t i v e price performance hypothesis or as i t i s more commonly referred to, 3 the r e l a t i v e strength hypothesis. It presents tests of several alternative formulations and spe c i f i c a t i o n s of the hypothesis. PURPOSE OF STUDY There were two purposes to this study. The f i r s t was to test the hypothesis of r e l a t i v e price performance and determine i t s v a l i d i t y . Relative price performance i s a mea- sure of an i n d i v i d u a l security's price performance for a given time period i n the market r e l a t i v e to a l l other issues or a segment of a l l other issues' price performances. It is hypo- thesized that an issue which has recorded for a period of time a price performance superior to other issues w i l l tend to continue to do so. Conversely, an issue which has shown an i n f e r i o r price performance r e l a t i v e to other issues w i l l tend to continue to record an i n f e r i o r price performance. As t h i s study was undertaken i t became clear that the t h e o r e t i c a l underpinnings of technical analysis and that of the random walk model were inadequate. The t h e o r e t i c a l inadequacy appeared to stem from a lack of consideration given to the limitations of uncertainty i n the security valuation process. The neglected problem of uncertainty in the security valuation process prompted questioning of the a n a l y t i c a l process from a general systems viewpoint. ^Refer to Chapter V f o r an explanation of general systems. This i s relevant to the second purpose of the study. This was to develop a t h e o r e t i c a l framework that attempts to explain how complexity i n corporations i s a constraint on the analysis of those corporations and i s mirrored i n t h e i r stock's price movement. In essence, the framework developed i s an attempt to explain the limi t a t i o n s placed on r a t i o n a l decision making i n the market. IMPORTANCE OF THE STUDY The examination of r e l a t i v e price performance (relative strength) i s important as i t may indicate changing supply-demand factors of i n d i v i d u a l issues which can be used as a preselection technique i n conjunction with fundamental analysis. A changing r e l a t i v e strength position f o r an issue and tending towards the same d i r e c t i o n ( i . e . a trend) may be of si g n i f i c a n c e , as the f i r s t i n d i c a t i o n of a substantial change i n that issue's valuation. Relative strength then, although a techn i c a l indicator, may be used as a complement to fundamental analysis by preselecting issues which should be analyzed. The development of a t h e o r e t i c a l framework reveal- ing the constraint of complexity i n the security valuation process i s of value i n i l l u s t r a t i n g the re l a t i o n s h i p of complexity to the degree of accuracy i n analysis and the p r e d i c t a b i l i t y of forecasts. In other words, the measure- ment of complexity may be of value i n measuring the r i s k 5 of inaccurate investment forecasts. Therefore an under- standing of complexity and the p o s s i b i l i t y of i t s measure- ment i s an attempt to enlargen the body of f i n a n c i a l valua- t i o n theory. Also, the development of such a framework i s a demonstration of how f i n a n c i a l theory can be developed i f an i n t e r d i s c i p l i n a r y approach i s taken. This should i n - clude concepts of general systems, information theory and knowledge from f i e l d s of psychology and sociology. OUTLINE OP THE PAPER The theory of r e l a t i v e strength w i l l be expanded i n Chapter II and a hypothesis w i l l be formulated to enable tes t i n g . A more complete discussion of fundamental and technical analysis and the random walk model than was given above w i l l be presented to draw a more complete picture of approaches to security price behavior. Chapter III w i l l present the data col l e c t e d to comprise the sample, the methodology used and the tests conducted on the sample. Chapter IV i s a discussion of the s t a t i s t i c a l findings i n d i c a t i n g e i t h e r acceptance or re j e c t i o n of the hypothesis. Chapter V, which might be viewed as a separate topic, covers the second purpose of the study - the development and explan- ation of complexity, i t s role and constraining influence and the importance of information i n the security valuation 6 process. The l a s t chapter is a conclusion of the findings and the implications f o r further research r e s u l t i n g from the recognition that complexity i n corporations i s a de- terminant of s e c u r i t y price behavior. 7 CHAPTER II THE HYPOTHESIS OP RELATIVE STRENGTH The hypothesis stated in Chapter I shall now be elaborated on. In order to appreciate the value of the theory of relative strength and its reasoning i t is neces- sary to discuss before hand the general process involved in any analytical function and the diverging "fundamental" and "technical" methods of investment analysis. The hypo- thesis of relative strength w i l l be explained within the context of the two schools of investment analysis and how i t is in contradiction to the model of the random walk. The General Analytical Process The function of analyzing anything whether i t be a livin g organism, a social problem, a p o l i t i c a l system, or a corporate entity can be broken down into four facets of study. The f i r s t facet in the analysis involves the scanning of a l l the data available, recognizing which factors might be pertinent and attempting to comprehend them. This part of the study enables the analyst to conceive a l i s t of those 8 variables or facts that should be given further study. The second aspect of the analysis is the attempt to derive or estimate the causal relationships between the perceived fac- tors and to express these relationships i n quantifiable terms. The t h i r d aspect is the summarization of these factors and t h e i r relationships to arrive at a conclusion or valuation of that which i s being studied. The fourth aspect i s the analyst's comparison of his findings and valuations with those of others. The comparison is to determine i f the analyst has discovered something which is s u b s t a n t i a l l y d i f - ferent from other findings and i f so, are his findings im- portant. Fundamental Analysis The analytic process sketched above approximates quite c l o s e l y the i d e a l function of the "fundamental" security analyst. The "fundamentalist" as the name implies analyses the fundamental or the important factors of com- panies that w i l l be r e f l e c t e d i n those companies' potential earnings and future dividends. The fundamentalist w i l l peruse a company's f i n a n c i a l h i s t o r y noting sales growth, rates of p r o f i t a b i l i t y , earnings s t a b i l i t y and all other factors which have had or could possibly have an influence on the company's earnings. Along with various underlying or causal factors including costs, assets, management 9 a b i l i t i e s , product potentials, tax rates, etc., the analyst t r i e s to extrapolate trends and forecast future earnings. He also notes past pay-out r a t i o s and examines possible circumstances that might j u s t i f y a possible change i n d i v i - dend p o l i c y . He then estimates future dividends that would accrue to the s e c u r i t y holder. The analyst i n his summar- i z a t i o n of the firm's value arrives at an appropriate cap- i t a l i z a t i o n rate for the firm's earning power and f i n a l l y places a value on the s e c u r i t i e s available."'" The funda- mentalist i n following the fourth aspect of analysis com- pares his valuation with that i n the market. If a sub- s t a n t i a l difference exists he w i l l recommend to other i n - vestors to either purchase, hold or s e l l the firm's secur- i t i e s . The fundamentalist carries out this process with the additional insight of economic trends, general business conditions and industry potentials. It i s assumed that the fundamentalist armed with his accumulated knowledge and a n a l y t i c a l a b i l i t i e s to deductively forecast p o t e n t i a l re- turns w i l l benefit more so than that part of the market which does not share h i s insight. The above i s based on the prem- ise that the analyst has been accurate and correct in his analysis and also that the market w i l l i n time change i t s valuation of the p a r t i c u l a r security towards that of the ^Benjamin Graham, David L. Dodd, Sidney Cottle, Security Analysis - Principles and Technique. (L;th edition) (New York, N.Y.: McGraw-Hill Book Co., Inc., 1962) pp. U3U - 10 analyst 1s. Technical Analysis Technical stock market analysis is an attempt to study the internal workings of the market activities to gain insight to changing supply and demand forces either for in- dividual issues or for the market as a whole. In contrast to the study of corporate and economic factors technical analysis is a study of past and current market action of stocks as a basis for forecasting stock prices. Technical analysis is based on the premise that a l l the factors affecting stock prices including economic, p o l i t i - cal, emotional and corporate influences in the market enter into the forces behind the supply and demand for stocks and are eventually reflected in the price changes of those stocks. The technical analyst argues that a l l these factors cannot be examined accurately because of their diversity and volume. In addition, he argues that stock price moves are the result of interacting supply and demand factors which are also the p result of the changing flow of funds between the securities. Hence he holds that the changes in the security prices are noted f i r s t by technical indicators rather than by funda- mental analysis of financial and economic data. ^Jerome B. Cohen and Edward D. Zinbarg, Investment Analysis and Portfolio Management. (Homewood, I l l i n o i s : R.D. Irwin, Inc., 1967), pp. 5 0 3 - 53U» 11 Some technicians hold the view that certain p r i - vileged people may obtain pertinent information even before the fundamentalists and that the trading patterns may change before the fundamentalists complete t h e i r analysis.^ Fur- thermore, the technician points out that the fundamentalists are faced with the problems of unavailable and unreliable information and the interpretation of that information. These are only a few of the d i f f i c u l t i e s of fundamental security analysis which are encountered, not to mention the doubtful methods of presenting and reporting of f i n a n c i a l statements. There also i s the problem of the voluminous flow of information which must be analyzed and from the ind i v i d u a l investors point of view i t is impossible to attempt to undertake such a feat as keeping up with the information i n the market. The technical analyst espouses that because of the many problems encountered i n attempting a fundamental analysis of s e c u r i t i e s the forces behind the supply and demand for common stocks do not change rapidly. The reasoning is that the numerous problems and factors involved in a fundamental analysis prevents the pertinent information, which could change the supply-demand forces, from spreading quickly throughout the market. Because information spreads J.B. Gohen and E.D. Zinbarg, loc. c i t . 12 throughout the market slowly there emerges patterns and trends i n price adjustments f o r an appreciable period of time. This is the r e s u l t of the market gathering momen- tum i n recognizing the changed valuation of the stock. As a greater part of the market moves to trade the stock and benefit from an early recognition of the new value the price adjusts slowly and creates a trend i n the price adjustments u n t i l the new valuation has been f u l l y r e a l i z e d by the market and a complete price adjustment has taken place. In contrast to the fundamental a n a l y t i c a l process the technical analyst attempts to interpret the trends of the stock market by using developed indicators to gauge the changes i n the supply-demand forces of the stocks.^ To mention just a few indicators that ;are f a i r l y common to practitioners of technical methods one could include the following: breadth of the market, volume of trading, short s e l l i n g i n t e r e s t s , odd-lot trading, price chart patterns, the well known Dow theory, cre d i t balances i n brokerage houses, rate of change analysis, confidence indexes and r e l a t i v e strength measures.^ There are many other technical indicators that are also widely used but as t h i s study i s UR.D. Edward and J. Magee, Technical Analysis of Stock Trends. (Springfield, Mass., U.S.: John Magee, 1966), p. 277. ^J.B. Cohen and E.D. Zinbarg, loc. c i t . 13 not intended to examine a l l the various indicators but rather just r e l a t i v e strength these other indicators are not d i s - cussed here. Relative Price Performance Keeping i n mind the context of the two d i f f e r i n g methods of investment analysis we can proceed with the ex- planation of r e l a t i v e price performance or as i t is more commonly referred to, as r e l a t i v e strength. As mentioned above, r e l a t i v e strength l i e s within the province of technical analysis and is considered an indicator of price trends for in d i v i d u a l stocks rather than for the market as a whole. The hypothesis of r e l a t i v e strength i n simple terms states that common stocks which have and are outperforming or underperforming r e l a t i v e to the o v e r a l l market for a period of time w i l l tend to continue to do so. They w i l l tend to maintain t h e i r r e l a t i v e positions in the same d i - rect i o n . Relative strength indicates the existence of either a strong demand f o r a stock or an abundant supply of that issue i n the market comparable to other issues. A consist- ent pressure either upward or downward on a stock which i s greater than a commensurate pressure on other stocks is an ex h i b i t i o n of forces that must have a consistent source. If 1 1 + a trend of r e l a t i v e strength i s established f o r a company i t must have a causal factor which i s consistently prevalent i n the market. A company which does not have a continuing source of pressure on i t s stock may exhibit a case of strong r e l a t i v e strength but i t w i l l , i n a l l p r o b a b i l i t y , not be a consistent p o s i t i o n of r e l a t i v e strength over time. There have been many suggestions advanced to ex- pl a i n the possible sources of pressure that may be mani- fested i n a consistent r e l a t i v e strength position for stocks. G a r f i e l d Drew suggests that r e l a t i v e strength could r e s u l t from the actions of company o f f i c e r s and executives who have inside information r e l a t i n g to the company's prospects and 6 earning p o t e n t i a l . While Volkert Whitbeck and Manown Kisor J r . suggest that companies with a high degree of v o l a t i l i t y i n t h e i r earnings w i l l tend to exhibit a greater divergence from the market movement than those companies with a lower degree of v o l a t i l i t y i n t h e i r earnings. During periods of market appreciation the companies with the more v o l a t i l e earnings w i l l appreciate more than the other companies' issues. Moreover, during periods of market decline these companies with the v o l a t i l e earnings w i l l experience greater declines i n t h e i r stocks r e l a t i v e to the other companies' "Ga r f i e l d Drew, New Methods for P r o f i t i n the Stock Market. (Boston, Mass: The Metcalf Press," 195U), PP' 268 - ~2W. 15 stocks.' However G. Drew contrarily suggests that those issues which have demonstrated superior performances in advancing markets w i l l be resistant to downward pressures a in declining markets. Another possible explanation of the cause of relative strength trends is the gradual spread of information throughout the market causing a slow process in recognizing the new value of the stock resulting from changed prospects of the company. The effect could be a gathering of momentum in the market's sentiment towards the issue. Whatever the cause is for a stock to demonstrate a strong or weak relative price performance as long as i t has established a trend in its relative position i t is hypothesized that the stock w i l l tend to maintain its relative position in the market. The relative strength for such a stock from one point in time to another not too distant point in time should not change substantially. S t a t i s t i c a l l y the relationship between the two relative strengths should be a high positive correlation. The 7S. Whitbeck and M. Kisor,, Jr., "A New Tool i n Investment Decision Making". Reprinted i n Frontiers of Investment Analysis (Ed. E.B. Fredrickson) (Scranton, Perm.: International Textbook Co., 1 9 6 5 ) , PP. 3 35 - 3 5 0 . ®Drew, loc. c i t . 16 following equation i l l u s t r a t e s the case. Rt/Rt+1 1.0 where: R-t is a r e l a t i v e strength measure for a stock at time t Rt+1 is "the r e l a t i v e strength measure for the same stock at time t+1 The r e l a t i v e strength i s calculated as the percentage price change of a given stock f o r a given time i n t e r v a l divided by the percentage price change of the entire market or of a re- lated market segment f o r the same time i n t e r v a l . R.A. Levy revealed some int e r e s t i n g findings of r e l a t i v e strength to support the arguments of the technical analysts.^ He found that a s e r i a l c o r r e l a t i o n study of per- formance ranks rather than successive f i r s t differences de- tected the existence of trends over the long term but not over the short term. Basing his work on the b e l i e f that the co-movement of stock prices might conceal e x i s t i n g de- pendencies i n successive price changes he made use of r e l a - t i v e strength ranks to eliminate this co-movement. He con- structed r a t i o s designed to measure h i s t o r i c a l strength and future performance and then employed the h i s t o r i c a l r a t i o s 9R.A. Levy, An Evaluation of Selected Applica- tions of Stock Market Timing Techniques. Trading Tactics and Trend Analysis, (unpublished Ph.D. d i s s e r t a t i o n , American University, I966) pp. 83 - 1 8 5 . 17 to select issues at a point i n time. The selected issues were then compared with th e i r subsequent (future)ratios to measure the investment "success". Levy calculated f i v e price r a t i o s f o r each issue at weekly i n t e r v a l s : the performance over the past 26 week period by di v i d i n g the current price by the average of the 27 prices of the immediately previous weeks i n - cluding the current price. the performance over the past ij. week period by d i v i d i n g the current price by the average of the 5 prices of the immediately previous weeks i n - cluding the current price I the future performance over a 1 week period by d i v i d i n g the current price by the price of the following week. the future performance over a week period by d i v i d i n g the current price into the price 1+ weeks subsequent to the current week. the future performance over a 26 week period by di v i d i n g the current price into the price 26 weeks subsequent to the current week. He then ranked the performances according to r e l a t i v e strength, v o l a t i l i t y of performance, the o v e r a l l market weekly per- formance, a misbehavior performance and the market's diverg- ence of performances. Levy reported that h i s t o r i c a l r e l a t i v e strength tends to continue f o r a period of time. The short term future r a t i o s did not bear th i s out but the long term 18 r a t i o s did substantiate the hypothesis. His hypothetical investment r e s u l t s showed that the 10 percent h i s t o r i c a l l y strong stocks gained an average of 9.6 percent while the 10 percent h i s t o r i c a l l y weak stocks gained only an average of 2.9 percent i n the same period. His c o r r e l a t i o n of h i s t o r i c a l and long term future groupings of performances was found to be s i g n i f i c a n t l y high f o r both the grouped r a t i o s and the grouped ranks. Levy concluded that selec- t i o n of r e l a t i v e l y strong and r e l a t i v e l y v o l a t i l e stocks resulted i n gains greater than those possible by random sel e c t i o n . He also found that superior performances could be achieved by purchasing stocks i n a market which h i s t o r - i c a l l y had been strong. The Importance of Relative Price Performance A change i n the r e l a t i v e p o sition of an issue tending toward the same d i r e c t i o n over a period of time could be considered as an i n d i c a t i o n that the issue's market condition is changing and that a fundamental analy- si s of the company might reveal the cause or causes of the changing conditions. Therefore, although r e l a t i v e strength is a technical indicator i t may be viewed as a valuable t o o l to be used as a preselection method fo r fundamental analysis. The ranking of r e l a t i v e strength f i l t e r s out the co-movement i n the market and can provide the funda- mentalist with the advantage of r e a d i l y noting superior 19 or i n f e r i o r performances of issues. This is a d e f i n i t e ad- vantage over the tech n i c a l analyst who uses i n d i v i d u a l price charts as an indicator of future price changes which are d i f f i c u l t to compare. To keep the concept of r e l a t i v e strength i n proper perspective the contradicting theory of the random walk i s set out below. The Random Walk To obtain a broader perspective of stock price movements i t i s valuable to discuss the theory and rat i o n - ale of the random walk model which is i n opposition to the theory of r e l a t i v e strength. The adherents of the random walk model advocate that successive price changes for com- mon stocks fluctuate randomly around the true i n t r i n s i c value of the issues. The reasoning behind t h i s theory i s based on the premise that the stock market approximates to a large degree that of a perfect economic market. It i s argued that the market allows easy entry and ex i t at a low cost and ensures that the price i s quite free to adjust to minor changes i n expectations r e s u l t i n g from news which en- ters the market randomly i t s e l f . Hence the price adjusts randomly operating as the e q u i l i b r a t i n g mechanism between 20 supply and demand f o r c e s . x u Moreover, i t is argued, that the investment community and the f i n a n c i a l press services are very competitive with e f f i c i e n t methods of r e t r i e v i n g , assembling, in t e r p r e t i n g and disseminating news. The re- s u l t of such a market i s almost instantaneous investor reaction to the random entry of news items and information. The f i n a l r e s u l t is automatic price adjustments i n stocks to t h e i r new value and i n the process of doing so evidence random price behavior. This chapter has explained the facets involved i n the general a n a l y t i c a l process, the differences between fun- damental and technical analysis and f i n a l l y how the theory of r e l a t i v e strength f i t s into technical analysis. Also explained b r i e f l y was the random walk model which purports to refute tec h n i c a l a n a l y t i c a l methods. The next chapter s h a l l explain the methodology and data used i n t e s t i n g the hypothesis of r e l a t i v e strength. - R.A. Brealey. An Introduction to Risk and Return from Common Stocks. (Cambridge, Mass.: The M.I.T. Press, 1969), P. 5. 21 CHAPTER III NATURE OF THE DATA AND METHODOLOGY EMPLOYED This chapter sets out the process which was used i n the c o l l e c t i o n of the data and the methodology used in the tests that were conducted. Data With respect to the assembling of data a major point of concern that arises is the s u i t a b i l i t y of the population to the constraints of the hypothesis. In the discussion of the hypothesis i t was stated that a stock tended to maintain a position of r e l a t i v e strength as a res u l t possibly of information spreading throughout the market. It was also stated that the hypothesis was i n contradiction to that of the theory of the random walk which assumes perfect or near perfect market conditions. Although th i s i s not an attempt to refute the contradic- tory theory the market chosen as the population should 22 approximate as best as possible a perfect economic market as a protection against using data that might have aber- rations i n i t . A d i s t i n c t i o n i s made here between d i f f e r - ent stock exchanges as markets and prospective populations for the following reasons. Conclusions drawn from a study of a p a r t i c u l a r market may not hold true to other markets as stock exchanges have d i f f e r e n t standards, requirements for disclosure and properties which prevent these d i f f e r - ent exchanges from having the same degree of market per- f e c t i o n . Therefore, the conclusions drawn from this study may not be v a l i d f o r other stock exchanges or markets. The market chosen from the possible Canadian stock exchanges to be the universe or population i s the Toronto Stock Exchange. The Toronto Stock Exchange was chosen because i t has been the largest Canadian exchange i n terms of shares traded, d o l l a r value and i n the number of participants including a range of i n s t i t u t i o n a l and ind i v i d u a l traders and investors. In addition, i t s i n - formation services are nationwide and i t maintains the highest standards of disclosure and has always been a leader among exchanges i n the use of automatic quotation systems.^" The Investment Dealers Association of Canada, The Canadian Securities Course. (Montreal, Que., I968) chapter 16. 23 Once the population is chosen the next point of concern is determining a relevant sample which can be tested. Drawing s t a t i s t i c a l inferences from a sample for an entire population requires that the sample be repre- sentative of the population. The question arises of what data are available in a c o l l a t e d form at a reasonable cost or are available to be collated for t e s t i n g . As there were no suitable data available i n a form such as on magnetic tape ready f o r electronic data processing the data con- s i s t i n g of monthly stock prices were col l e c t e d manually from the Toronto Stock Exchange Reviews which are pub- lished monthly by the Exchange. The sample chosen con- si s t e d of those stocks constituting the Toronto Stock Exchange Indices as of January 1, 1965. It was f e l t that since the exchange selects these p a r t i c u l a r stocks to form the major indices to represent the movement of the entire market and that these p a r t i c u l a r stocks are selected im- p a r t i a l l y on the basis of t h e i r trading importance i n the market that such a sample would f u l f i l l the sample require- ments mentioned above. However, i t i s recognized that there i s no documented proof that the Indices are true rep- resentations of a l l the l i s t i n g s on the Toronto Stock Ex- change. Therefore a bias may exist i n the chosen sample. The Toronto Stock Exchange's Indices at that point i n time consisted of 121+ stocks representing a 21+ s t a t i s t i c a l cross-section of the Exchange's active l i s t - ings. The In d u s t r i a l Index being the broadest based and most representative index of the exchange's four indices, was employed i n ca l c u l a t i n g the r e l a t i v e price performances of a l l the stocks i n the sample. The four indices each represent a segment of the exchange's l i s t i n g s and the i n d u s t r i a l index i s made up of 86 stock's c l a s s i f i e d as i n d u s t r i a l companies. The other 38 stocks i n the sample are c l a s s i f i e d as being either a gold, base metal or western o i l producer and make up the three other respect- ive indices. However as no composite index existed to cover the entire sample the Indu s t r i a l Index was Used. If a composite index did exist which included the gold, base metal and western o i l stocks as well as the i n d u s t r i a l stocks then the r e l a t i v e price performances calculated for each stock would be d i r e c t l y related to that stock's prop- o r t i o n a l contribution to the index's movement. The e f f e c t would be an accurate measurement of each stock's r e l a t i v e price performance and an accurate basis for comparison between the stocks. Although the Industrial Index does not include a l l the stocks i n the sample i t does include a majority (69.1+$) of the sample and therefore provides a ^Since that time the indices have been enlarged and adjusted f o r the growth and continual changes that have taken place i n the Toronto Stock Exchange. As of June, 1970 the four basic indices: I n d u s t r i a l , Gold, Base Metal and Western Oils consisted of 211+ stocks. 25 f a i r l y d i r e c t r e l a t i o n s h i p of the sample's stocks contribu- t i o n to the index. The In d u s t r i a l Index does provide an adequate representation of the major facets of Canadian business and permits ready adjustment when changes occur i n outstanding c a p i t a l i z a t i o n and f a c i l i t a t e s the addition, d e l e t i o n and/or s u b s t i t u t i o n of one stock f o r another with- out disturbing the index.3 For each of the stocks i n the sample monthly prices were collected f o r 5 8 consecutive months s t a r t i n g at January 1, 1 9 6 5 . For each stock data were gathered to make the nec- essary adjustments throughout the test period for stock s p l i t s and appropriate adjustments were made dating back to the s t a r t of the time period. This time period, January 1965 - November 1 9&9 , w a s chosen as i t was the most recent data available and covered at least one f u l l market cycle including an upswing, a peak, a downswing and a trough i n the market movement. The complete cycle started at i t s peak, i n January 1 9&5 , a n <* declined to a low i n October, 1966 and then reversed i t s d i r e c t i o n to reach another peak and complete the cycle i n August, 19&7 . It w a s considered important to use such a period including the d i f f e r e n t market phases to determine i f r e l a t i v e strength was v a l i d 3The Investment Dealers Association, op. c i t . . p . 2 5 8 . 26 i n a l l phases of the market or i f i t s v a l i d i t y might vary according to the market phases. The data were collected i n monthly intervals f o r the following reasons. If an adequate size sample was re- quired and a time period that covered a f u l l market cycle was also required then the c o l l e c t i o n of weekly prices manually would e n t a i l a substantial amount of time. There- fore monthly prices were given thought to whether they might produce the hypothesized r e s u l t s . F i r s t , the calcu- l a t i o n of a monthly price performance for a stock is a l - most i d e n t i c a l to the cumulative price performance of weekly or d a i l y price changes. Second, evidence to support the use of monthly prices was found i n R.A. Levy's study of r e l a t i v e strengths.^ Although his data base made use of weekly prices he grouped his data into four and twenty- s i x week periods of r e l a t i v e strengths. Examination of the short term rankings (1+ week period) suggested that there was no discernible pattern i n stock prices. In contrast, examination of the longer term rankings (26 week periods) i l l u s t r a t e d that patterns do exist and support was given to the r e l a t i v e strength theory. In l i g h t of Levy's ^Robert A. Levy. An Evaluation of Selected Applications of Stock Market Timing Techniques. Trading Tactics and Trend Analysis.(Unpublished Ph.d. Disserta- t i o n . ) (Ann Arbor, Michigan: University Microfilms Inc., 1966). 27 findings that r e l a t i v e strength rankings of periods approx- imating 6 months showed discernible patterns and that r e l a - t i v e strength rankings of periods approximating one month did not show any patterns i t was f e l t that monthly data would be adequate. Therefore because of the time element which would be required i n c o l l e c t i o n of the data and be- cause of Levy's results i t was decided that monthly prices could be used. Methodology and Approach Taken The approach taken in tes t i n g the v a l i d i t y of r e l a t i v e price strength was to use electronic data pro- cessing (IBM 36O/67) and to calculate the s t a t i s t i c a l c o r r e l a t i o n between the h i s t o r i c a l and future r e l a t i v e strengths. In this study h i s t o r i c a l is used i n reference to past behavior of price strength up to a point in time and future i s used i n reference to price behavior from that point i n time on. The raw data including unadjusted prices, stock s p l i t s , and the Toronto Industrial Index were placed on magnetic tape f o r computer use. The stock prices were then adjusted to take into account stock s p l i t s that occurred throughout the 58 month time period. 28 Once the appropriate adjustments were made, r e l a - t i v e points were then calculated for each stock for the f u l l period. The r e l a t i v e points equaled the price of the stock divided by the Toronto Stock Exchange Ind u s t r i a l Index at each monthly i n t e r v a l . The equation below i l l u s t r a t e s t h i s . R i j = p i j / * j where: i s the price of stock i at time j Mj is the market index at time j Rj_j i s the r e l a t i v e point of stock i at time j Then the r e l a t i v e price performances were calculated. These measure the positive or negative percentage changes of the r e l a t i v e points between successive months. The following equation sets t h i s out. C i j = ( F i j + l ~ S i j ^ i j where: R i j + i i s the r e l a t i v e point for stock i at time j+1 R J J is the r e l a t i v e point for stock i at time j Cjj i s the r e l a t i v e performance of stock i to the market at time j The development of the above measure of r e l a t i v e price performance formed the necessary foundation upon which a variety of tests were conducted. 29 Method of Testing After the data had been adjusted and the appro- priate calculations of r e l a t i v e strengths were made the out- put was organized f o r t e s t i n g using the TRIP l i b r a r y pro- gram.^ The TRIP program consisting of a c o l l e c t i o n of routines computed either simple, multiple or stepwise mul- t i p l e regression equations of the general form Y^=a+b X^. The dependent variable, Yj., i n the general regression equa- t i o n was the estimated r e l a t i v e price performance (R t) and the independent variable (s), X^, was the h i s t o r i c a l r e l a - tive price performance ( R t _ n ) . The routines i n the program provided c o e f f i c i e n t s of c o r r e l a t i o n and determination which measure the amount of v a r i a t i o n i n estimated r e l a - t i v e price performance that i s explained by h i s t o r i c a l r e l a t i v e strength. The r e l a t i v e price performance hypothesis propos- ing that r e l a t i v e price performance at one point i n time i s determined i n a large part by the re l a t i v e price perform- ance of the immediately p r i o r point in time leads us to the following expectations about the regression r e s u l t s . The ^J.H. Bjerring, J.R.H. Dempster, R.H. H a l l . U.B.C. TRIP (Triangular Regression Package). (U.B.C, Computing Center, January, 19ob./360 Implementation Feb. 1969). It i s assumed here that the reader has a general knowledge of l i n e a r regression techniques. Therefore no fur- ther elaboration of regression equations i s given. 30 c o r r e l a t i o n between the h i s t o r i c a l and subsequent r e l a t i v e price performances should be s i g n i f i c a n t l y high. This would be confirmed i f the c o e f f i c i e n t of determination was greater than +.50 and approaching +1 .0 . We would, also expect that a Q i n the equation w i l l approximate zero and that b i w i l l approach unity from +.50. We would not expect b i to equal unity as th i s would infer that r e l a t i v e price performance is t o t a l l y explainable by h i s t o r i c a l r e l a t i v e price, sug- gesting invariant r e l a t i v e performances f o r a l l issues. This would be suggesting the case of no change i n r e l a t i v e positions for issues rather than suggesting a tendency to maintain r e l a t i v e positions as stated i n the hypothesis. The general form of the regression equation varied from simple to multiple or stepwise multiple regressions de- pending on the p a r t i c u l a r approach taken i n each t e s t . Tests Conducted In t o t a l 11 tests of the hypothesis were ca r r i e d out on the sample. The tests approached the sample from a number of angles to ensure that the hypothesis was tested adequately. The tests conducted can be divided into two groups. The f i r s t group consisting of only two tests ex- amined the relationships between h i s t o r i c a l and future r e l a - t i v e price performances. The second group consisting of the remaining 9 tests examined the relationships between 31 h i s t o r i c a l and future rankings of r e l a t i v e price performances. The f i r s t e s s e n t i a l l y measured whether a stock maintained a consistent price performance r e l a t i v e to the market index. For example, whether a stock which out-performed the market i n one month or over a period of time by a c e r t a i n percen- tage would tend to maintain that r e l a t i v e percentage per- formance. While the second set of tests measured whether a stock's ranked r e l a t i v e price performance i n one month or over a period of time would tend to maintain i t s ranked position i n the l i s t of performers. The ranking of r e l a - t i v e performances was to demonstrate i f stocks had a con- si s t e n t ranking performance. For example, between two given intervals under examination the o v e r a l l market may have a negligible change and the stocks i n the market may not have a consistent performance r e l a t i v e to the market but they could very well be consistent to each other. Table 3»-l and Table 3>-2 below elaborate on thi s point i n a hypo- t h e t i c a l case. TABLE 3>-l STOCK PRICE PERFORMANCES RELATIVE TO THE MARKET PERIOD MARKET STOCK A STOCK B STOCK C STOCK D MARKET PERFORM- ANCE PERFORMANCE SPREAD 1 0 + .25 +.37 - .1+2 -.20 .85 (+.37 to -.1+2) 2 0 +.08 +.09 -.10 -.07 .19 (+.09 to- .10) 3 0 +.02 +.01+ -.01 -.05 .09 (+.01+ to-.05) 32 In this fabricated case the market performance was held i n variant which i n r e a l i t y would be a r a r i t y but was done here merely f o r i l l u s t r a t i v e purposes. The market's invar iance here is in d e n t i c a l to the s i t u a t i o n where the t o t a l market influence i n a stock's movement has been subtracted to leave the stock's independent movement. As can be seen each stock's price performance i s not consistent from one period to another and the inconsistency is explained by the varying spread between the performances exhibited i n the l a s t column. However, by ranking the performances of the stocks as done i n Table 3-2 below, patterns may emerge i n the rankings. TABLE 3-2 STOCK PRICE PERFORMANCES RANKED RELATIVE TO EACH OTHER PERIOD STOCK A STOCK B STOCK C STOCK D 1 2 1 3 4 2 2 1 3 1+ 3 2 1 3 1+ It may be that during times of o v e r a l l market enthusiasm h i s t o r i c a l l y strong performers reveal greater strength than do h i s t o r i c a l l y weaker performers and during times of pessimism i n the market the h i s t o r i c a l l y stronger stocks are re s i s t e n t to downward movement and maintain t h e i r 33 positions i n the l i s t i n g s . The above case of such a con- sis t e n t pattern i s highly u n l i k e l y , i f not impossible, but was created as such to exaggerate the possible value of ranking the performances. R.A. Levy suspected that the ranking of performances might reveal greater consistencies i n patterns and his study bore t h i s out.^ Therefore i n l i g h t of his findings the ranking of r e l a t i v e strengths appears to us to be of greater importance i n revealing trends than the study of unranked r e l a t i v e strengths. Unranked Relative Price Performance Tests Test I The f i r s t test consisted of estimating regression equations of the general form: R^t = a Q + b ^ R i ^ . i where: Rj^ = r e l a t i v e price performance & r stock i at month t R_.t-i = r e l a t i v e price performance for stock i at month t - 1 Equations were estimated f o r each of the 121+ stocks i n the sample r e s u l t i n g i n 121+ regression equations. There were 57 monthly observations. As pointed out i n the foregoing ?R.A. Levy, op. c i t . t pp. 115 - 180. 3U discussion the hypothesis leads one to expect ag to approxi- mate zero and to approximate unity. It is also expected that the c o e f f i c i e n t of determination calculated by the TRIP routine w i l l approach unity. Test II The second test involved estimating regression equations with more than one independent variable i n a stepwise manner. The equation had the form: R i t = 8Q + b]M2 + b2M3 + h^M^ + b̂ Mfcj + bt̂ Mfc where: R ^ = r e l a t i v e price performance f o r stock i at month t M£ ^ a two month moving average of r e l a t i v e price performances from month t-1 to month t-2 = a three month moving average of r e l a - t i v e price performance from month t-1 to t-3 = a four month moving average of r e l a - t i v e price performance from month t-1 to t-k M£ = a f i v e month moving average of r e l a - tive price performance from month t-1 to t -5 35 = a six month moving average of r e l a t i v e price performance from month t - 1 to t - 6 . A l l f i v e of the moving averages were taken as independent variables. The equations were estimated f o r the entire sample of 121+ stocks and included 51 observations in each equation. The stepwise multiple regression routine allowed the entrance of the independent variables into the equation one at a time, i n order of decreasing contribution to the reduction of variance of the dependent r e l a t i v e price per- formance. The independent variables already included i n the regression were tested for significance and i f any f e l l be- low the s p e c i f i e d significance l e v e l of .05 the least s i g n i - f i c a n t was eliminated from the regression analysis. If no variable needed to be eliminated, the designated independent variables not yet included i n the regression were tested f o r significance of the contribution each would make i f included next. If any were above the significance l e v e l , the most s i g n i f i c a n t was included i n the regression. The rationale f o r employing multiple regression was to determine i f the variance of future r e l a t i v e strengths °J. Dempster, Gagon, and Hogan. Triangular Regression Package. (U.B.C. Computing Center. A p r i l , 1965), P. 5. 36 is explainable i n part by the r e l a t i v e strengths whose h i s - tory i s greater than one month. This reasoning was supported by Levy's findings that longer duration r e l a t i v e strengths had greater predictive v a l i d i t y than short duration measures of r e l a t i v e strengths. The stepwise technique was used to gain further insight i n the question by helping to determine which period of h i s t o r i c a l r e l a t i v e strength had the greatest s i g n i f i c a n c e . In other words, whether a l\ month h i s t o r y of r e l a t i v e strength had more or less significance than a 6 or 3 month h i s t o r y would be revealed with stepwise regression by displaying which independent variable was considered most frequently. Ranked Relative Price Performance Tests Test III equations of ranked r e l a t i v e price performances. The equa The t h i r d test consisted of estimating regression tions took the form: where: i t ranked r e l a t i v e strength for stock i at time t R i t - 1 ranked r e l a t i v e strength for stock i at time t-1 37 Unlike the previous two tests t h i s one approached the sample by examining a l l the ranked r e l a t i v e strengths of the stocks one month at a time. Hence, there were 56 equations e s t i - mated i n t o t a l each with 121+ observations. The reasoning for taking a cross sectional approach i s that r e l a t i v e strength may possibly have more v a l i d i t y at d i f f e r e n t times i n the market than at others and sequential t e s t i n g of i n d i - vidual stocks' rankings would not necessarily bear any such evidence. Test IV In this fourth test a cross sectional approach was taken again but the number of independent variables was in*- creased from one to four. The estimated regression equation was of the form: 12k k_ R i t = a + b x £ t R i t-n i= l n=l where : = the ranked r e l a t i v e strength for stock i at month t Rit-n = the ranked r e l a t i v e strength for stock i at month t-n where n i n - creases from one to four. There were 53 estimated regression equations each with 121+ observations. This increase of independent variables was done to take into consideration the p o s s i b i l i t y of a lagged e f f e c t 38 from the rankings. The reasoning for considering a lagged e f f e c t was the same as stated i n Test II. The routine c a l l e d f o r i n the TRIP program was f o r computation of a multiple l i n e a r regression equation. As t h i s routine had been deleted from the program, the program defaulted auto- ma t i c a l l y to c a l l i n g a stepwise multiple regression but one with unspecified significance levels which i n eff e c t i s i d e n t i c a l to a multiple regression. The multiple regression unlike that of the stepwise regression used i n Test II i n - cluded a l l the independent variables regardless of t h e i r significance to compute the t o t a l explainable variances. The equations were developed through months 5 to 57 to produce a t o t a l of 53 equations each with 121+ observations. Test V This f i f t h test was a duplication of Test IV ex- cept that the number of independent variables was extended from 1+ to 6 variables. The estimated regression equation had the i d e n t i c a l form of Test IV: 121+ 6 R i t = 8 + b l £ R i t - n i = l n=l However i n t h i s test n went from one to six. There were a t o t a l of 51 regression equations each with 121+ observations. 39 Test VI The cross se c t i o n a l approach was maintained i n t h i s test however the sample was disaggregated into fi v e groupings approximating 20 percentiles for the following reasons. As the entire sample was not d i v i s i b l e into f i v e equal groups the sample was divided i n the following groups. TABLE 3;-3 DISAGGREGATED SAMPLE - FIVE GROUPS Group Sample Size Rankings 1 21+ 1-21+ 2 21+ 25 - 1+8 3 28 1+9 - 76 1 + 2 1 + 77 -100 5 21+ 101 -121+ The groups are i n descending order of the dependent month's rankings. The data were reorganized to test the correla- tions of the corresponding stocks of the immediately prior h i s t o r i c a l month's rankings. It was suspected that those stocks which have the most extreme r e l a t i v e price perform- ances might tend to maintain t h e i r positions more so than those stocks which have a less extreme r e l a t i v e price per- formance. For example, those stocks with rankings i n the ko top 20% of the l i s t i n g s may be more consistent performers than those stocks with rankings i n the middle 20% of the l i s t . If the above suspicion could be proved true then the former tests on the aggregate sample would have con- fused the f i n d i n g of any r e l a t i v e strength value. For example, the average r e l a t i v e performers, middle 20% may exhibit no consistency of r e l a t i v e performance, thus re- ducing any consistency that might be present i n the res t of the data. This test used the simple regression routine and regressed the h i s t o r i c a l month's rankings of the f i r s t group on the future month's rankings for the same group. This process was repeated for the other L\. groups. Five equations were estimated for each of the 56 months f o r a t o t a l of 280 equations. Test VII This test continued the logic of Test VI but the sample was further disaggregated into seven groupings. The rearrangement of the groupings was e s s e n t i a l l y a further re- finement of the extreme performers from the 20 percentiles into groups approximating.the top two 10 percentiles (1 - 10$ and 11 - 20%) and the bottom two 10 percentiles (81 - 90$ and 91 - 100%) while the rest of the sample was l e f t l+i unchanged. The table below exhibits the disaggregation more clearly. TABLE 3-1+ DISAGGREGATED SAMPLE - SEVEN GROUPS Group Sample Size Rankings 1 12 1 - 12 2 12 13 - 21+ 3 21+ 25 - 1+8 k 28 1+9 - 76 5 21+ 77 - 100 6 12 101 - 112 7 12 113 " 121+ 1 It was thought that i f the validity of relative strength varied with the degree of relative strength then the refinement of the degree of relative strength may re- veal greater valid i t y of the technical indicator. Essen- t i a l l y this was testing i f the validity of ranked relative strength was a function of the extreme rankings of rela- tive strength. Test VIII This eighth test consisted of estimating regres- sion equations of ranked relative performance in a similar form to that i n Test I where the data was examined s e r i a l l y one stock at a time. The equation i s as follows: R i t = a + b R l t . i where: R^t = ranked r e l a t i v e strength for stock i at month t RjLt_]_ = ranked r e l a t i v e strength for stock i at month t-1 A t o t a l of 12l\ equations were estimated each with 56 obser- vations. Test IX Test nine involved an extension of Test VIII by increasing the number of ranked r e l a t i v e performances from one to s i x . The equation had the form as follows: 6 R i t = a + b Z. H i ( t _ n ) n — l where: R^ = ranked r e l a t i v e strength f o r stock i at month t 5~ Rjrt.j^) = ranked h i s t o r i c a l r e l a t i v e strength n=l for stock i at month t-n where n goes from one to s i x . There were 121+ multiple regression equations e s t i - mated with 51 observations i n each. U3 Test X This tenth test was an extension of Test VIII and Test IX but the number of monthly ranked h i s t o r i c a l performances was increased to ten. The form of the equa- t i o n i s i d e n t i c a l to that i n Test IX excepting that n went from one to ten 10 (i.e . 2Z R i ( t - n ) . n=l Again 121+ multiple regression equations were estimated but with the number of observations reduced to 1+6 i n each equa- t i o n . Test XI This l a s t test examined the v a l i d i t y of r e l a t i v e strength rankings when the market was i n either an uptrend or a downtrend. It appeared reasonable to suspect that r e l a t i v e strength may very well not hold as true i n a "Bear" market as i t might i n a " B u l l " market, or vice versa. At any rate i t was f e l t that the time period under study should be divided into basic uptrends and downtrends. The c r i t e r i o n f o r the d i v i s i o n of the trends was the perform- ance of the Toronto I n d u s t r i a l Index. If the market i n - dex continued to increase.from one month to the next i t was viewed as an uptrend u n t i l the index decreased by more than an a r b i t r a r i l y decided 5 percent. Then the market kk was viewed as being i n a downtrend u n t i l the index increased by an amount greater than 5%. Although i t i s recognized that four phases exist i n the market cycle the exercise of defin- ing these four phases with the use of monthly price data would be of l i t t l e p r a c t i c a l value. Such an exercise would define the four d i f f e r e n t phases i n the market but they would not necessarily be coincidental with the monthly data base because a market phase could reverse i t s d i r e c t i o n more than once within a monthly i n t e r v a l which would not be revealed i n the data base. Therefore the market cycle was kept to the basic trends of being eit h e r a " B u l l " or a "Bear" phase. Table 3-5 below displays the series of market phases used i n the t e s t . TABLE 3-5 MARKET TRENDS - UPTRENDS vs DOWNTRENDS DOWNTRENDS UPTRENDS Feb. 1965 - Nov. 1965 Nov. 1965 - Feb. 1966 Feb. I966 - Oct. 1966 Oct. I966 - Aug. I967 Aug. 1967 - Mar. I968 Mar. I968 - Apr. 1969 Apr. 1969 - Aug. I969 Aug. 1969 - Nov. I969 This test examined the sample of stocks i n d i v i d - u a l l y during periods of market uptrends- and then downtrends. A t o t a l of 2I4.8 regression equations were estimated. 1+5 The following chapter w i l l discuss the r e s u l t s from the tests explained above and w i l l point out the s i g - nificance of unranked and ranked r e l a t i v e strength measures. 1+6 CHAPTER IV DISCUSSION OP THE FINDINGS t The results and interpretation of the series of tests conducted and outlined i n Chapter III w i l l be d i s - cussed here. Because each test generated a number of re- gression equations, the l i s t i n g of a l l the equations and th e i r s t a t i s t i c a l measures would create a voluminous number of tables that have l i t t l e i l l u s t r a t i v e value. Instead, summaries of the tests w i l l be given and w i l l include the means and ranges of the relevant s t a t i s t i c a l measures i n - dic a t i n g the extent of correlations and predictive value of r e l a t i v e strength. Included i n the discussion of each test i s the c o e f f i c i e n t of determination (R 2) which i s that portion of the t o t a l v a r i a t i o n in the estimated Y value (either the predicted r e l a t i v e strength or the predicted ranking of r e l a t i v e strength) that is explained by the s i g n i f i c a n t h i s t o r i c a l r e l a t i v e strengths. The c o e f f i c i e n t of determ- ination i s expressed as either a percentage or a r e a l 1+7 number between 0 and 1. If t h i s c o e f f i c i e n t of determin- ation is closer to 1, ( i . e . , R^^+.^O), then the regres- sion l i n e is a good approximation of the observed data. With a good approximation of the data, the regression equation w i l l have a high predictive value. Conversely, a c o e f f i c i e n t of determination close to 0.0, ( i . e . R2<T+ .50), w i l l indicate a poor or i n s i g n i f i c a n t approx- imation of the observed data by the calculated regression l i n e . The r e l a t i v e strength as measured by the regression equation would be a poor or i n s i g n i f i c a n t predictive t o o l . In addition to the c o e f f i c i e n t of determination the discussions w i l l include the F - p r o b a b i l i t y s t a t i s t i c which measures the significance of the regression c o e f f i c - ient (b^) i n the general equation of Y^ = SQ + b^ X. An F - value i s calculated by the TRIP routine and the p r o b a b i l i t y of obtaining a value greater than this F - value i s determined assuming £ ^ = 0 i n the assumed true regression equation of y = <X + 3j[x« If the p r o b a b i l i t y i s less than .05 i t is usually concluded that b^ is s i g n i f i - cantly d i f f e r e n t than zero. If the F- p r o b a b i l i t y is greater than .05 then the regression c o e f f i c i e n t b^ is not s i g n i f i c a n t l y d i f f e r e n t than zero i n the computed equa' t i o n . 1 As pointed out i n Chapter III the b - value i n the -J.H. Bjerring, J.R.H. Dempster and R.H. H a l l , U B C TRIP (Triangular Regression Package). (The University of B r i t i s h Columbia, January, 19&8), p. 1+9. U8 regression equation should approximate unity i f the hypothe- s i s i s v a l i d . That i s , i f future r e l a t i v e strength i s de- termined i n large part by h i s t o r i c a l r e l a t i v e strength then the regression c o e f f i c i e n t , b, should be close to one. If the P - pr o b a b i l i t y s t a t i s t i c indicates that the b - value i s not s i g n i f i c a n t l y d i f f e r e n t from zero then the hypothesis has no s i g n i f i c a n t v a l i d i t y . The hypothesis leads to the expectation of a con- sistency of r e l a t i v e strengths between h i s t o r i c a l and sub- sequent months. Therefore a positive r e l a t i o n s h i p is ex- pected between the h i s t o r i c a l and subsequent r e l a t i v e strengths. In those tests where i t was considered import- ant to note the sign of the regression c o e f f i c i e n t i t was done so and w i l l be discussed with the other relevant sta- t i s t i c s . For those tests which purposely made use of the stepwise routine f o r multiple correlations the order of entry of the s i g n i f i c a n t variables w i l l also be discussed. Results of the Empirical Test The summarized findings are covered i n the same order i n which the tests were conducted and outlined i n Chapter I I I . 1+9 Teat I The estimated regression equation for this f i r s t t est as discussed i n Chapter III had the general form: R i t = a + b Rit.-L where : R^t = the r e l a t i v e strength of stock i at month t R i t _ l = the r e l a t i v e strength of stock 1 at month t-1. The relevant s t a t i s t i c s f or this test are exhibited in Table 1+-1 below. TABLE 1+-1 REGRESSION STATISTICS - TEST I Coefficient of P - Probability Standard Error Determination of the E s t i - mated Y value Mean . 0 3 6 6 .1*313 5 1 . 8 2 7 6 Range . 7 5 9 8 - . 0 0 0 0 .91+37 - . 0 0 0 0 Range . 1 7 8 7 - . 0 0 0 0 .91+37 - . 0 013 (revised) The mean c o e f f i c i e n t of determination derived from the sequential t e s t i n g of the 121+ company sample was . 0 3 6 6 and ranged from . 7 5 9 8 to . 0 0 0 0 . The upper range l i m i t i n th i s test was considered an unexplainable abnormality be- cause i f the p a r t i c u l a r equation with t h i s high c o r r e l a t i o n 5 0 was eliminated from the sample the upper range l i m i t would drop to . 1 7 8 7 . Also, although t h i s p a r t i c u l a r equation re- ported a very s i g n i f i c a n t c o r r e l a t i o n the standard error of i t s estimated Y value was 2 2 7 8 . 0 which i s completely use- less for predictive purposes as an estimate based on the regression equation could not be made with accuracy. The mean of the P - prob a b i l i t y s t a t i s t i c was . U 3 1 3 indicating that the regression c o e f f i c i e n t (b) is not su b s t a n t i a l l y d i f f e r e n t from zero. With a low c o r r e l a t i o n c o e f f i c i e n t and a high P - pro b a b i l i t y as i n this test the regression l i n e calculated i s a poor or i n s i g n i f i c a n t approximation of the data. Interpreted this means that r e l a t i v e strength as tested here has no s i g n i f i c a n t v a l i d i t y . ing averages as possible independent variables i n a step wise multiple regression are exhibited i n Table l|-2(a). Test II The results of th i s test which examined f i v e mov- TABLE 4 - 2 (a) REGRESSION STATISTICS Coefficient of P - Pro b a b i l i t y Determination Standard Error of the Estimated Y value Mean .01+1*8 . 2 8 5 8 .61+11* - . 0 0 2 U . 7 8 2 5 - . 0 0 0 0 . 9 8 7 6 Range Range . 1 8 2 1 - .0021+ (revised) 5 1 The mean of the c o e f f i c i e n t of determination i n - creased from the previous test but only minutely. Its range was from .61+11+ to .0021+. The upper l i m i t i n the range, l i k e the previous test, was exaggerated due to one equation which included more than 1 variable i n explaining the t o t a l v a r i a t i o n . The elimination of t h i s equation would reduce the c o r r e l a t i o n range to .1821 - .0021+ which i s almost equivalent to Test I. The P - pro b a b i l i t y dropped but only to .2858 which reveals that the regression c o e f f i c - ient is not s i g n i f i c a n t . Although the test used stepwise regression to de- termine the order of entry and the number of s i g n i f i c a n t variables at a significance l e v e l of .05, i n a l l the equa- tions except one the number of variables taken into consid- eration was only one. The singular case of exception i n - cluded three independent variables. The frequency of the variables considered s i g n i f i c a n t and which were the f i r s t entrants to the equations are exhibited below in Table l+-2(b). TABLE l+"2(b) FREQUENCY OF MOVING AVERAGES CONSIDERED SIGNIFICANT Moving Average No. of Times Included i n Percentage of Total the Regression Equation S i g n i f i c a n t Variables 2 months 1+2 33.9$ 3 " 26 20.9 1+ " 17 13.7 5 " 11+ i i . 3 6 " _25 20.2 121+ 100.0$ 52 As can be seen the 2 month moving average was considered the most s i g n i f i c a n t duration of h i s t o r i c a l r e l a t i v e strength while the other moving averages appear to be somewhat equal but of less significance i n t h e i r con- t r i b u t i o n to explaining the v a r i a t i o n in the estimated rela- t i v e strengths. A point of note is the sign of the regression co- e f f i c i e n t , b, i n r e l a t i o n to the d i f f e r e n t moving averages. Table l+-2(c) displays the signs associated with each v a r i - able and the t o t a l frequency of the signs. TABLE U"2(c) FREQUENCY OF REGRESSION SIGNS Moving Average No. of Posi- Percent No. of Nega- Percent t i v e Signs of Total tiv e Signs of Total Found Found 2 months 10 23.8$ 32 76.2$ 3 " 6 23.1 20 76.9 k " U 23.5 13 76.5 5 " 7 50.0 7 50.0 6 " 10 UO.O }$ 60.0 37 297B$ "87 70.2$ A point of interest i s that for the entire test 70.2$ of the variables had negative signs and 29.8$ had positive signs. The hypothesis inferred that the r e l a t i o n - ship between h i s t o r i c a l and subsequent r e l a t i v e strengths would be po s i t i v e . But this test reported a predominantly 53 negative re l a t i o n s h i p . Also of interest is that the shorter h i s t o r i c a l moving averages were more negative than were the longer h i s t o r i c a l moving averages. This i s evident from the f a i r l y consistent negative correlations in the two, three and four month moving averages and the s h i f t to a more equal weighting of positive and negative correlations i n the f i v e and six month moving averages. The ov e r a l l negative corre- l a t i o n f o r the test disputes any positive c o r r e l a t i o n be- tween h i s t o r i c a l and subsequent r e l a t i v e strength measures. In view of the low correlation c o e f f i c i e n t , the high F - pro b a b i l i t y and the negative correlations t h i s test can o f f e r no support for the hypothesis of r e l a t i v e strength. Test III The summarized results for th i s f i r s t test of ranked r e l a t i v e strengths are presented below i n Table I+-3. TABLE k'3 REGRESSION STATISTICS OF RANKED RELATIVE STRENGTH Coefficient of Standard Error of Frequency of the Determination the Estimated Y Sign Value Positive - Negative Mean .0253 3U-9U 1U (25 )̂ 1*2(75$) Range .1535 - .0000 36.09 - 33.20 The c o e f f i c i e n t of determination as i l l u s t r a t e d with a mean of .02$3 and an upper range l i m i t of only . 1 5 3 5 i s quite i n s i g n i f i c a n t . The mean standard error of the estimated Y value at 3U.9U i s too large to have any predictive v a l i d i t y . The frequency of the sign of the regression c o e f f i c i e n t is quite heavily weighted nega- t i v e l y i n d i c a t i n g a f a i r l y consistent negative c o r r e l a t i o n . The frequency of the sign here demonstrates that i f a high c o r r e l a t i o n was found the regression line would be nega- t i v e l y sloped and that a high ranking of r e l a t i v e strength i n one month would be followed by a low ranking of r e l a - t i v e strength i n the next month. However because the c o r r e l a t i o n i s not s i g n i f i c a n t the negative sign i s not r e a l l y of great importance. The results found here i n this test provide no substantiation of the hypothesis. Test IV The pertinent s t a t i s t i c s from t h i s test of ranked r e l a t i v e strength using multiple l i n e a r regression tech- niques are presented i n Table I4.— 1+ • 55 TABLE k~k MULTIPLE REGRESSION STATISTICS Coefficient of Determination P - Probability S t a t i s t i c Standard Error of the Estimated Y Value Mean .0698 .2112 35.23 Range .1886 - .0157 .8105 - .0001 36.30 - 32.91 In this test the c o e f f i c i e n t of determination i n - creased somewhat due to the inclusion of more h i s t o r i c a l rank ings from the point of tes t i n g . Included were h i s t o r i c a l ranks up to 1+ months past. But the c o e f f i c i e n t of determ- ination reported i s s t i l l not s i g n i f i c a n t as i t explains only 6.98$ of the v a r i a t i o n i n the estimated rankings of re l a t i v e strength. The range of the c o e f f i c i e n t points out that the highest c o r r e l a t i o n explained only 18.86$ of the var i a t i o n . The P - pro b a b i l i t y s t a t i s t i c at .2112 reveals that the regression c o e f f i c i e n t is not s i g n i f i c a n t l y d i f - ferent from zero. The large standard error of estimated Y value points out that the equations have l i t t l e predictive value. The signs of the regression c o e f f i c i e n t s , as i n the previous test, indicate that the more distant ranks of r e l a - t i v e strength have a more positive c o r r e l a t i o n than do the short term h i s t o r i c a l ranks. A l l in a l l this test gave no s i g n i f i c a n t support to the hypothesis. 56 Test V The results from this test which extended the length of h i s t o r i c a l ranks to include ranks s i x months past in the equations are presented in Table 1+-5. TABLE 1+-5 MULTIPLE REGRESSION STATISTICS Coefficient of P - Probability Standard Error of Determination S t a t i s t i c the Estimated Y Value Mean .1013 .1516 31+.92 Range .2365 - .0288 .71+91 - .0000 36.32 - 32.20 The c o e f f i c i e n t of determination increased once again but s t i l l the mean explainable v a r i a t i o n reached only 10.13$. The range of the c o e f f i c i e n t also increased s l i g h t l y from the two previous tests to 23.65$ - 2.88$. The F - pro b a b i l i t y s t a t i s t i c although improved from the previous test by dropping to .1516 i s s t i l l not low enough to con- sider that the regression c o e f f i c i e n t i s s i g n i f i c a n t . The standard error of the estimated Y value improved as well but again only very s l i g h t l y as i t dropped to 31+.92. This size of error for the estimate creates a range of 69.81+ within which the ranking of r e l a t i v e strength can be predicted. With such a large range f o r error the u t i l i t y of such a prediction is quite meaningless. 57 Although improvements were found i n the s t a t i s - t i c s by extending the multiple regression equation to i n - clude 6 months of h i s t o r i c a l ranks from the previous test of including 1* month h i s t o r i c a l ranks the improvements were too s l i g h t to warrant support f o r the hypothesis. Test VI The results of this test which disaggregated the sample into f i v e groups approximating 20 percentiles are given below i n Table 1+-6. TABLE 1*"6 REGRESSION STATISTICS Group Coefficient of P - Probability Standard Error Determination S t a t i s t i c of the E s t i - mated Y Value 1 .01*17 .5228 7.08 2 .01*19 .1*912 7.08 3 .0379 .1*822 8.22 1* .0566 .1*689 7.01 5 .0381 .1*852 7.O9 The c o e f f i c i e n t of determination f o r any one group is no more than .0566 and no less than .0379 i n d i c a t i n g that the consistency of r e l a t i v e strength is not related to super- i o r , mediocre or i n f e r i o r price performance i n the market. The P - p r o b a b i l i t y s t a t i s t i c indicates that the regression c o e f f i c i e n t is not s i g n i f i c a n t l y d i f f e r e n t from zero for any 58 one group of rankings. The standard error of the estimated Y value f o r a l l the groups ranges from 7.01 to 8.22 which i s too large to have any predictive value. This test gave no support to the hypothesis. Test VII into those stocks which were the strongest 10 percent and those that were the weakest 10 percent to examine the more extreme performers. The groups of ranks are arranged in the same manner as the previous test and the respective re- sult s are set out i n Table 1+-7. TABLE 1+-7 REGRESSION STATISTICS Group Coefficient of P - Probability Standard Error Determination S t a t i s t i c of the E s t i - mated Y Value This test refined the disaggregation of the sample 1 2 3 6 7 .0787 .0878 . 01+23 .0383 .0567 .0609 .0570 .1+907 • 531+U .1+992 .5665 .5911 3.63 3.60 7.07 8.22 7.02 3.66 3.67 The groups to note are 1 - 2 and 6 - 7 as groups 3 - 5 were not modified i n any way from the previous t e s t . The d i s s e c t i o n of the former group 1 into two groups of 59 ranks (groups 1 and 2) increased the c o e f f i c i e n t of determ- ination but only by a very small amount. Likewise, the dissecti o n of the former group 5 into two groups of ranks (now groups 6 and 7) also increased the c o e f f i c i e n t of de- termination but only by a minute amount. The P - proba- b i l i t y f o r the groups indicates that the regression coe- f f i c i e n t s are not s i g n i f i c a n t . The results produced lead to the same inference made i n the immediately above test that there is no sub- s t a n t i a t i o n of the hypothesis evident here. Test VIII The regression s t a t i s t i c s generated from this test which took each stock separately and sequentially examined the c o r r e l a t i o n between a one month h i s t o r i c a l rank and the subsequent rank are displayed i n Table 1+-8. TABLE 1+-8 REGRESSION STATISTICS Coefficient of P - Probability Standard Error Determination S t a t i s t i c of the E s t i - mated Y Value Mean .0276 .1+268 36.21 Range .1569 - .0000 .91+1+3 - .0026 1+7.18 - 23.21+ 60 The c o e f f i c i e n t of determination with a mean of .0276 and a range of .1569 to .0000 is f a r too low to have any significance as i t explains only a negligible amount of the v a r i a t i o n i n the rankings of a stock's r e l a t i v e strength. The mean F - pr o b a b i l i t y s t a t i s t i c at .1+268 is too high and reveals that the regression c o e f f i c i e n t (b) is not s i g n i f i c a n t . The standard error of the estimated Y value is also too large to predict accurately a stock's ranking of r e l a t i v e strength from past ranks. The findings of this test have not given the r e l a t i v e strength theory any foundation of support. Test IX This test which was an extension of the immediately prior test to include six months of h i s t o r i c a l ranks i n a sequential examination of each stock's rankings report the findings i n the following Table I*-9. TABLE U-9 MULTIPLE REGRESSION STATISTICS Coefficient of F - Probability Standard Error Determination S t a t i s t i c of the E s t i - mated Y Value Mean .1237 .1*899 35.38 Range .3272 - .0100 .9975 - .0068 52.36 - 23.53 61 The c o e f f i c i e n t of determination increased with the i n c l u s i o n of more distant h i s t o r i c a l ranks but the amount of v a r i a t i o n explained by the regression equation s t i l l amounts to only 12.37$ and the range of the explainable v a r i a t i o n i s from 1.0$ to only a maximum of 32.72$. The P - pr o b a b i l i t y at .1+899 i s an increase from the previous test i n d i c a t i n g no improvement in the significance of the regression c o e f f i c i e n t which was expected. The standard error of the estimated rank remained overly large for pre- d i c t i v e purposes. Test X This test followed the method of the two previous tests but again extended the h i s t o r i c a l ranks included i n the multiple regression equation to 10 months from 6 months. The findings are presented i n Table 1+-10 below. TABLE 1+-10 MULTIPLE REGRESSION STATISTICS Coefficient of Determination P - Probability S t a t i s t i c Standard Error of the E s t i - mated Y Value Mean .2122 .5178 35.50 Range .1+005 - .051+8 .9907 - .0310 53-06 - 21.13 62 The c o e f f i c i e n t of determination increased once again from e a r l i e r tests but at the expense of the s i g n i f i - cance of the regression c o e f f i c i e n t . The c o e f f i c i e n t of determination increased to explain 21.22$ of the subsequent months' rankings i n comparison to the former test's 12.37$ but the P - pr o b a b i l i t y s t a t i s t i c increased as well to .5178 from .1+899 indi c a t i n g no improvement i n the s i g n i f i - cance of the regression c o e f f i c i e n t . The standard error of the estimated Y value increased n e g l i g i b l y to 35.50 i n f e r - r i n g no improvement i n the predictive u t i l i t y of the com- puted equations. The extension of the multiple regression equation to include more distant h i s t o r i c a l ranks proved of no value to substantiating the hypothesis. Test XI This last test examined each stock's rankings separately i n a sequential manner when the market was i n eith e r a basic uptrend or downtrend. The findings are exhibited f o r both basic trends i n Table 1+-11. TABLE U - l l SIMPLE REGRESSION STATISTICS Coefficient of P - Probability Standard Error of Determination S t a t i s t i c the Estimated Y Value Downtrend .01+50 .1+560 3U-99 Uptrend .0531 .3717 35.01+ 63 Perusal of the findings reveals that there i s no substantial difference i n the c o r r e l a t i o n of ranked r e l a t i v e strengths between uptrends or downtrends in the market. This is evidenced from the c o e f f i c i e n t of determination: downtrend .01+50; uptrend. .0531. Both P - p r o b a b i l i t i e s of the two trends i l l u s t r a t e that the regression c o e f f i c i e n t i s not s i g n i f i c a n t l y d i f f e r e n t from zero. The inference drawn here i n t h i s test i s that ranking of r e l a t i v e strength has no more s i g n i f i c a n t v a l i d i t y when the market is i n an uptrend or a downtrend. Summary The findings of the tests, as reported i n t h i s chapter, on the hypothesis of r e l a t i v e strength indicate quite strongly that r e l a t i v e strength, ranked or unranked, has l i t t l e s i g n i f i c a n c e . This is c l e a r l y seen i n the low c o e f f i c i e n t s of determination which reveal the amount of the estimated r e l a t i v e strengths that are accounted for by the h i s t o r i c a l r e l a t i v e strengths. The lack of significance is also demonstrated by the P - p r o b a b i l i t y s t a t i s t i c whose mean is above .05 i n a l l the tests pointing out that the regression c o e f f i c i e n t (b) i s c l e a r l y not s i g n i f i c a n t l y d i f f e r e n t from zero. Hence the regression l i n e s c a l c u l a - ted do not have s i g n i f i c a n t positive or negative slopes. 6U If the hypothesis is to be accepted the computed regression equations and lines must have s i g n i f i c a n t regression coef- f i c i e n t s to indicate a positive r e l a t i o n s h i p between h i s - t o r i c a l and subsequent r e l a t i v e strengths. In addition, the standard errors of the estimated Y value f o r the tests were too large to have any predictive value. In summary, the s t a t i s t i c a l t e s t i n g of the hypo- thesis from a number of d i f f e r e n t angles resulted in an absence of any support for the theory of r e l a t i v e strength. 65 CHAPTER V A CONSTRAINING FRAMEWORK OF COMPLEXITY FOR SECURITY ANALYSIS The findings reported i n Chapter IV provide l i t t l e substantiation for the hypothesis of r e l a t i v e price performance and i t would appear adequate to conclude that the hypothesis has no s i g n i f i c a n t v a l i d i t y and should be rejected. This chapter w i l l attempt to demonstrate how the hypothesis may s t i l l be considered v a l i d and how the "opposing" theory of random walk is also v a l i d and com- patible with the r e l a t i v e strength model i n the same market i f recognition i s given to the constraints within which security valuation operates. The approach taken here is to study valuation and security price movements from a general systems viewpoint which i s a higher, more general l e v e l than the narrow u t i l - i t a r i a n f i n a n c i a l models. This approach creates the oppor- tunity to f i l l i n the gaps between the more s p e c i f i c "con- t r a d i c t o r y " empirically based security price movement 66 models. A short discourse explaining the systems concept, what general systems theory i s and of what value i t may be to the study of f i n a n c i a l analysis i s required here. F i r s t , a system is a whole which functions as a wholy body by v i r - tue of the interdependence of i t s parts.- General systems theory attempts to c l a s s i f y systems, i n t h i s case corpora- tions, by the way t h e i r components are organized or int e r - related and to derive the patterns of behavior for the 2 d i f f e r e n t classes of systems singled out by the typology. The value of t h i s approach is to point out how corporations may be c l a s s i f i e d according to t h e i r complexity and the consequent problems a r i s i n g i n t h e i r analysis. Starting from the general systems viewpoint a th e o r e t i c a l framework is constructed revealing the con- st r a i n t s of complexity. The recognized constraint of com- pl e x i t y i n analysis i s then related to the market's problem of b u i l d i n g "knowledge structures" and resorting to the fab- r i c a t i o n of "images" f o r the purpose of attaining a required l e v e l of cert a i n t y i n valuation. By viewing companies as systems and using two of three possible dimensions, which w i l l be explained l a t e r on in the chapter, as yardsticks ^Anatol Rapoport, "Foreward" Modern Systems Re- search for The Behavioral S c i e n t i s t . Ed. W. Buckley. ( Chicago, 111.: Aldine Publishing Company, I968J p . x v i i . Loc. c i t . 67 to measure complexity, companies can then be c l a s s i f i e d according to t h e i r degree of complexity. Information and i t s content is then introduced and the difference between a p o s t e r i o r i and a f o r t i o r i information is explained. These two types of information are then related to the categories of complexity to i l l u s t r a t e t h e i r resultant significance in the a n a l y t i c a l process. An o v e r a l l t h e o r e t i c a l framework can then be constructed to provide the foundation f o r the rationale of conditions under which security price changes exhibit either trends or randomness. The thread of l o g i c at this point may appear rather loose i n r e l a t i n g these sys- tems concepts and types of information to security valuation and stock price movement but i f the reader keeps i n mind that the role of information and i t s receipt i s both a v i t a l point of contention and a basic tenet of both trendists and advocates of the random walk this chapter w i l l attempt to explain how complexity constrains the function of informa- t i o n . In spite of i t s importance i n valuation processes and stock price movements information has yet to be properly elucidated by either school of price behavior. Complexity and the Analyst Complexity denotes something which has many varied i n t e r r e l a t e d parts, elements and patterns which are 6 8 consequently d i f f i c u l t to analyze. ̂  Complexity i s a r e l a - t i v e term likened to a continuum where at one extreme pole there exists t o t a l s i m p l i c i t y and movement i n degrees to- wards the other pole produces increasing complexity to the point of t o t a l obscurity and confusion. For a given system, here the corporation, the s i m p l i s t i c pole would apply to a company where a l l the elements and variables are recogniz- able and t h e i r relationships known to the mechanical degree where the attributes of importance are quantifiable and the outcomes are t o t a l l y predictable. This is the case of com- plete determinism and certainty. The opposing case i s at the extreme complex pole where the system is completely obscure allowing no p o s s i b i l i t y f o r q u a n t i f i c a t i o n of the variables and t h e i r r e l a t i o n s h i p s . Here the behavior of the system is t o t a l l y indeterminate and unpredictable. This is the case of complete uncertainty. The degree of complexity within the parameters of a corporation therefore i s of importance to the analyst who wishes to determine the value of a company. In the simplis- t i c case the analyst, assuming a given l e v e l of i n t e l l i g e n c e and competence, can obtain a c l e a r l y definable understanding of the company and can predict with certainty the e f f e c t of ^Webster's Third New International Dictionary (of the English Language Unabridged). (Springfield, Mass., U.S.: G. & C. Merriam Company, Publishers), p. U6£. 69 changing or new attributes i n the system. Automatically he can adjust his valuation of the company based on a c a l c u l a - ted return and r i s k . In the t h e o r e t i c a l l y opposite case of t o t a l complexity the analyst can obtain only a vague obscure understanding of the company and must operate i n t o t a l uncer- t a i n t y unable to predict outcomes with any degree of accuracy. Hence the degree of accuracy and certainty i n analysis i s an inverse function of complexity within the company. Knowledge Structures and Images Remaining for the moment with the idea of a one dimensional measure of complexity the concept of creating a knowledge structure or image f a b r i c a t i o n should be i n t r o - duced here. The human being is the only animal known to be capable of v i s u a l i z i n g abstracts and i n understanding the relationships of abstract variables.^ A person performing an a n a l y t i c a l function hopefully exercises t h i s capacity of comprehending f a c t s , constructs between facts and the valuation of these rela t i o n s h i p s . This summation can be viewed as the process of obtaining a structure of informa- t i o n or of knowledge. In short, this is a learning process for the i n d i v i d u a l . How, the a b i l i t y to obtain such a UK .E. Boulding, The Image. (Knowledge i n L i f e and Society) (Ann Arbor, Michigan, U.S. 1968) pp. 19 - 31. 70 knowledge structure is dependent on the complexity of that which i s being analyzed. In the case where there i s a paucity of information, or where the sal i e n t attributes and t h e i r r e l a - tionships cannot be comprehended c l e a r l y then the i n d i v i d u a l w i l l not be able to develop a knowledge structure. Instead he w i l l r e l y upon stereotyped images which e s s e n t i a l l y have an emotive basis. This resorting to an image i s depicted f a i r l y c l e a r l y with the analogy of an ignorant person who is incapable of comprehending certain events and w i l l ex- p l a i n such events i n terms of perhaps r i t u a l , t r a d i t i o n , dogmatic slogans or an unconsciously memorized ideology. In a f i n a n c i a l example, an i n d i v i d u a l unaware or ignorant of opportunities and the associated risks i s assumed to be less l i k e l y to make a r a t i o n a l decision than what would appear to a more knowledgeable person. A r a t i o n a l decision is used here i n the sense of an i n d i v i d u a l choosing among a l l known alternatives of opportunities which would maxi- mize his u t i l i t y function. Why should an i n d i v i d u a l r e l y upon a stereotyped image when he is unable to obtain a clear understanding of something? The rationale is that man t r i e s to reduce the l e v e l of uncertainty in the world i n which he resides. This is done i n the hope of attaining greater security. To accomplish this he t r i e s to understand the world around 7 1 himself. However, i n the s i t u a t i o n where he i s unable to acquire an understanding he w i l l invoke a sense of c e r t a i n t y through the adoption of an image based on other than fact and concrete knowledge. In other words an i n d i v i d u a l i n th i s s i t u a t i o n would exercise a preference to accept any explanation of his world rather than acknowledge t o t a l i g - norance and be l e f t with uncertainty. Connecting this d i s - cussion to security analysts and investors i t i s possible to hypothesize that i n the situations where to t a l informa- t i o n i s not available the i n d i v i d u a l w i l l resort to making estimations and projections based on the knowledge that he does have plus a fabricated image created by a concensus of the investment community. Security analysts and the market are d i f f e r e n t i a t e d in terms of t h e i r a n a l y t i c a l a b i l i t i e s and understanding of security values. Security analysts are assumed to be more knowledgeable because of the vast flow of information i n the market which has resulted i n development of s p e c i a l i s t s to interpret this information. Just as i n any other f i e l d the study, analysis and a c q u i s i t i o n of facts and information whether i t be finance, medicine, law, or physics, w i l l tend to create discrepancies of understanding throughout the population connected to that f i e l d of a c t i v i t y . The r e s u l t 5 l b i d . . pp. 19 - 3 1 . 72 is the development of "experts" whose function i s to main- t a i n a superior expertise i n th e i r f i e l d and to advise those persons less knowledgeable. This d i f f e r e n t i a t i o n of analysts and others i n the market i s to point out that participants i n the market are not uniform in t h e i r a b i l i t y to comprehend opportunities and r i s k s . This d i f f e r e n t i a t i o n of c a p a b i l i - t i e s w i l l be elaborated on la t e r in the discussion of c l a s s i - f i c a t i o n of complex companies. As established e a r l i e r the l e v e l of certainty or degree of accuracy i n the analysis of a system is a function of complexity. As complexity increases i n a system the l e v e l of c e r t a i n t y decreases - an inverse function. Now, the se- cu r i t y analyst, as previously pointed out, encounters i n - creasing d i f f i c u l t y i n examining f a c t s , i n determining t h e i r relationships and i n a r r i v i n g at a t o t a l value of the par- t i c u l a r corporate system and i t s respective common share value as the degree of complexity increases. The analysts' and the market's understanding of the company becomes more d i f f u s e . E f f e c t i v e l y the company's potentials becomes less amenable to analysis and a discrepancy of opinions as to the value of the common shares w i l l a r i s e . If a "true" i n t r i n s i c value could be determined and compared with the market's concept of an i n t r i n s i c value we could expect the following diagram to i l l u s t r a t e the divergence of opinion as companies are measured along a line of complexity. To 73 understand the rel a t i o n s h i p more c l e a r l y one could think i n terms of companies such as Balco Forest Products or maybe B.C. Telephone Ltd., as being at point A, EDP Indus- t r i e s Ltd., one of the large chartered banks, or B.C. Forest Products Ltd., as being at point B and G.P.R., Neonex International or Noranda as being at point C i n the diagram. FIGURE I Simple Company ^ Complex Company ) Range of marke ' " - ' " , r t r u e " i n t r i n s i c value } i n t r i n s i c valu. B. i r k e t 1 s ilue As one moves along t h i s l i n e of complexity from the state of s i m p l i c i t y to complexity the market would be forced to replace i t s knowledge of the companies with an image. The understood value of the companies would become more diffuse and so would the assumed i n t r i n s i c value of the companies. Because of the diffuseness or obscurity and a reliance on an image fabricated and perpetuated by the investment com- munity the valuation of the common shares for more complex companies are more dependent on the emotions of the invest- ment community. The r e s u l t , at any point i n time, can be a larger deviation of the market valuation from the "true" i n t r i n s i c value f o r complex companies than f o r more simple companies. 71+ Framework for Complexity If the environment of a corporation i s analogous to a system and that a system is taken as the set of a l l ob- jects a change i n whose attributes affect the system and also those objects whose attributes are changed by the behavior of the system^ then the complexity of the environment of a cor- poration can be measured along the same three dimensions used i n general systems. The f i r s t of these three basic d i - mensions i s the domain which i s the constituent parts of the system or organization. This could include the management, personnel, assets of the firm, i t s products, geographical locations, and a l l other attributes of the fi r m which have a functional value contributing to the organization. The second dimension i s the dynamics of the organization which i s the rate of change of a l l the functional parts making up the domain. This could be looked upon as the speed at which the parts develop, are replaced or improved and af f e c t the behavior of the organization or system. For example, this could include the rate at which the f i r m i s expanding, d i - ve r s i f y i n g , changing i t s product mix, or developing either i t s c a p i t a l or human resources. The l a s t dimension i s the ec o l o g i c a l which is the relat i o n s h i p of the system's domain ^A.D. H a l l and R.E. Fagen, " D e f i n i t i o n of System". Modern Systems Research For The Behavioral S c i e n t i s t . ( e d . W. Buckley) (Chicago, 111.: Aldine Publishing Co., 1968) pp. 81-93. 75 to the outside environment. An example of thi s dimension is competitive pressures, global or national supply and demand factors, governmental influences on the fir m or any other relationships beyond the immediate control of the organization. By employing the above dimensions i t i s possible to construct a set of c l a s s i f i c a t i o n s to discern companies as to t h e i r degree of complexity. This c l a s s i - f i c a t i o n of companies is an attempt to refine the d i f f e r - ences of the s a l i e n t factors analyzed by noting t h e i r contributions to the complexity of the firm. The employment of the dimensions of complexity can provide insight to understanding the e f f e c t that i n - formation or news w i l l have on the current knowledge structures or images held by the market and i n turn how the market w i l l react to the news. If each dimension measured complexity i n the extreme terms of being either simple or complex i t would be possible to obtain eight permutations or c l a s s i f i c a t i o n s . However, these eight c l a s s i f i c a t i o n s can be reduced to four. The eco l o g i c a l dimension measuring the corporate r e l a t i o n s h i p to the politico-economic environment may be removed i n a rather f a c i l e manner. Because part of t h i s dimension i s common to most companies and part is common to companies i n the same industries i t is possible to remove a substantial part of t h i s dimension. This can be accomplished by 76 subtracting a broad market index and the relevant indus- t r i a l indices from the company's stock price movement. This is not perhaps the most acceptable way to reduce the number of c l a s s i f i c a t i o n s but i s f e l t to be adequate as i t i s recognized that the framework which i s being devel- oped i s being done so at a rather crude l e v e l . Recogni- t i o n must be given to the crudeness of a t h e o r e t i c a l con- st r u c t i o n when i t i s i n i t s infant stage. The ec o l o g i c a l dimension should be reintroduced at a l a t e r time when i t is considered that the t h e o r e t i c a l framework i s at a more mature stage. Making use of the two remaining domain and dynamic dimensions to measure complexity i t is possible to arrive at four categorizations of companies. Table 5-1 below displays these categories and how they are arrived at. TABLE 5-1 DIMENSION CATEGORIES OF COMPLEXITY BY DOMAIN AND DYNAMIC DIMENSIONS Ci c 2 c 3 C^ simple simple complex complex simple complex simple complex Domain Dynamic 77 The f i r s t case, C^, would be a company with a simple domain and a simple dynamic dimension. This could very well be a company which produces or handles one pro- duct, i s established within a single geographical l o c a l i t y and has a rather mediocre growth rate. An example of t h i s case could be B.C. Telephone Co. Ltd. This i s not necessar- i l y a stagnant company but one with an o v e r a l l simple cor- porate structure that is amenable to analysis and to the development of a knowledge structure of the company's factors and potentials. Here the analyst and the investor w i l l have a good understanding of the company and can pre- d i c t i t s potentials with a high degree of accuracy and certainty. The second case, C2, could represent a company that has a narrow tangible corporate base of products, management q u a l i t i e s , and location but i s r a p i d l y chang- ing that base. An example could be EDP Industries Ltd. It could be expanding i t s product base, developing and introducing new management, or perhaps changing i t s organ- i z a t i o n a l functions. This rate of change i n the corporate structure of t h i s f i r m may be rather small i n r e l a t i o n to other firms rate of growth but the functional change is i n r e l a t i o n to the p a r t i c u l a r firm's domain or organizational base. It i s possible to analyze the company and develop 78 a knowledge structure but i t is d i f f i c u l t to forecast with accuracy the outcome and the potentials that w i l l r e s u l t from the changes which i t is currently undergoing. The res u l t i s a f a i r l y high degree of uncertainty in any pre- dictions made. The t h i r d case, C^, would be a company with a complex domain but which is undergoing l i t t l e f unctional change and may be perceived as a staid or a mediocre con- glomerate. An example here could be International Nickel Ltd. Such a company may be one that has a large multi- product base and a diverse organizational structure oper- ating in and serving many markets. Because of the divers- i t y of functions the company, although amenable to analysis, would require a highly competent analyst who could afford the time and expenditure of the analysis to arrive at an i n t r i n s i c value. The knowledge structure necessary for a r r i v i n g at the valuation could be developed by such an analyst but due to i t s abstractness the market would tend to r e l y on a t r a d i t i o n a l image of the company. The market would r e l y on an image presented to i t in the past because of i t s i n a b i l i t y to obtain a complete understanding of the v i t a l components of the domain. In addition, the ana- l y s t (s) would have d i f f i c u l t y conveying the eff e c t of new information on the firm's earnings prospects. This would re s u l t as a consequence of the market t r y i n g to perpetuate 79 i t s perceived t r a d i t i o n a l image and invoking a greater sense of certainty. However, with analysts influencing the market i n the face of d i f f i c u l t y the market over time would slowly change i t s image of the firm's value. The l a s t case, C^, would be a company that has both a complex domain dimension and a complex dynamic dimen- sion. A company of t h i s type could very well be one that has a vast, diverse corporate structure, likened to a large conglomerate, but one that i s undertaking or about to under- take a program of expansion that would have substantial ramifications on the earnings prospects of the Company. A case i n point would be L i t t o n Industries Ltd. Because of i t s conglomerate mix and the fa c t that i t i s changing i t s organizational structure the company would not be amen- able to analysis and any forecasts of projected earnings would be highly uncertain and inaccurate guesses. Analysts as well as the remainder of the market would r e l y heavily on a fabricated image that appeared acceptable. The se- c u r i t y analysts would have no better understanding of the firm's potentials than would the market because he would not be able to analyze the s a l i e n t factors and therefore would not be able to develop any knowledge structure. The entire market then i n i t s attempt to determine i t s value would r e l y upon an acceptable image. Any i n d i v i d u a l i n the market t r y i n g to analyze such a company would soon 80 realize) his i n a b i l i t y to do so and would be extremely reluctant to suggest a value s u b s t a n t i a l l y d i f f e r e n t from that presented i n the market. The image would tend to per- petuate i t s e l f as everyone i n the market r e a l i z i n g his own inaccuracy would, seek and accept that type of information that enhanced his perception of the imagined value and would conversely d i s c r e d i t that information which sug- gested a negation of the image. The market i n i t s r e s i s t - ance to change would continue "believing" the current value u n t i l i t could c l e a r l y be disproven. The constructed categories of complexity and t h e i r associated amenabilities for analysis w i l l be discussed fur- ther on i n r e l a t i o n to information types. Information Types and Content Remembering that information i n the market is a point of contention and a basic tenet of trendists and ad- vocates of the random walk i t i s necessary to d i s t i n g u i s h d i f f e r e n t types of information and explain the conditions required f o r information to be s i g n i f i c a n t . The point of contention between the two schools of price behavior is found i n their arguments of how i n - formation i s received and in how i t i s dissipated through- out the market. Proponents of the random walk argue that 81 information enters the market randomly and i s dissected by the market quickly and adjustments i n price of common shares are made with incredible speed as i f instantaneously. The subsequent conclusion from almost automatic responses to random information can only be random price adjustments. While trendists contend that information is dissected much slower and dissipates throughout the market, perhaps gather- ing momentum but at least creating dependencies i n succes- sive price changes and creating trends i n price changes. Both schools neglect to make any d i s t i n c t i o n between types of information, information content, and the type of ana- l y t i c a l reasoning associated with the d i f f e r i n g types of information. The above facets of information w i l l be elu- cidated and related to complexity to outline the possible compatibility of both theories of r e l a t i v e strength and random walk. The content or significance of a piece of in f o r - mation i s the amount of change i t generates f o r the receiv- er (s) of the information i n his e x i s t i n g knowledge structure or image that he has of a system. Upon the receipt of i n - formation, one of three alternatives may be generated. 7 The f i r s t alternative is the s i t u a t i o n where there i s very low K.E. Boulding, op. c i t . . pp. 3 - 18. 82 or n i l content i n a piece of information and does not gen- erate any perceivable change i n the receiver's knowledge structure. The second alternative is the s i t u a t i o n where the content is meaningful and produces a change i n the knowledge structure i n some regular or well defined manner. The l a s t alternative is the s i t u a t i o n where the information content i s highly potent and generates a revolutionary change i n the receiver's knowledge structure or image. Information content i s not s o l e l y dependent on the amount or type of information i n the "news" item but i s more dependent on i t s r e l a t i v e e f f e c t on the knowledge struc- ture. The e f f e c t of a "news" item on a knowledge structure can be very dependent on the complexity of that which i t is providing information about. For example, two d i f f e r e n t news items containing i d e n t i c a l types and amounts of i n - formation f o r d i f f e r e n t companies can i n a l l p r o b a b i l i t y have quite d i f f e r e n t effects on the known state of each company.® One piece of information could generate no change whatsoever i n the knowledge structure of the company. While the other piece of information could generate a vio- lent change i n the knowledge structure of the company upon which i t i s reporting. Thus, the respective contents of °A case i n point could be the reporting by two com- panies of each adding new product l i n e s . One could be a l o g i c a l complement to the firm's products and p r o f i t s could be forecast whereas the other f i r m may be introducing a product quite d i f f e r e n t from i t s other lines and costs and p r o f i t s are unpredictable. 83 the two pieces of information w i l l d i f f e r i n the extent to which they may expand or reorganize the comprehended struc- ture of knowledge of the companies. The next l o g i c a l question to follow such an asser- t i o n is how can one determine the content of a piece of information and the eff e c t that i t may generate. To answer t h i s question, information can be broken down into either a p o s t e r i o r i or a f o r t r i o r i information. The general c r i t e r - ion for the d i s t i n c t i o n being whether deductive or induc- tive reasoning i s used i n the application of the p a r t i c u l a r piece of information. For the purposes of t h i s study a p o s t e r i o r i information is information that provides the receiver with facts upon which he may deduce outcomes which should l o g i c a l l y follow.^ A r e a l i s t i c case i n point would be a news item or piece of information revealing that a nation's currency i s being revalued. One who i s f a m i l i a r with the economics of that nation can deductively conclude that exporting companies w i l l be under greater competitive pressure and that the earnings potential of those companies w i l l be reduced. While a f o r t i o r i information reveals to the receiver information marked by a certainty inferred from and taken to be even more conclusive than another reasoned conclusion of f a c t . ^ Continuing with the same case i n ^Webster's Third New International Dictionary, op. c i t . , p. 1 2 5 . - Ibid., p. 37. point, a news item of th i s type would report that p a r t i c u l a r exporting companies f o r a f i s c a l period had a decline i n sales and net income. A p o s t e r i o r i information has a s i g - n i f i c a n t content only when the receiver can make use of that information i n changing his knowledge structure. If the receiver has only a vague knowledge structure or image of a company then he w i l l not be able to make use of the information and i t s content or significance w i l l be very low or n i l to him. If on the other hand, the receiver has a very clear understanding of a company and has developed a good knowledge structure then a p o s t e r i o r i information would have a very high or meaningful content and s i g n i f i - cance to him. In the above cited s i t u a t i o n where the receiver does not have a good knowledge structure and a p o s t e r i o r i information has l i t t l e s i g n i f i c a n c e , a f o r t i o r i w i l l have a greater content i n revealing after the fact information which can be used inductively. The Valuation Process Related to Complexity and Information Contents Gathering the loose conceptual threads of com- pl e x i t y , knowledge structures, information contents and the capacities f o r analysis into a l o g i c a l framework for f i n a n c i a l valuation i t is possible to gain insight into the market as a socio-economic phenomena. Table 5-2 85 below displays t h i s constructed t h e o r e t i c a l framework and the resultant constraints on " r a t i o n a l " security valuation which i n turn i s r e f l e c t e d in stock price movements. The table i s set up according to the varying de- gree of complexity for corporations and types of informa- ti o n and t h e i r respective contents. The constraints on the reasoning used i n the valuation processes leads to a d i f f e r e n t i a t i o n of the market's reactions to the receipt of information. The end r e s u l t of the d i f f e r e n t i a t i o n of market reactions i s the e x h i b i t i o n of either randomness or dependencies i n price changes. The degree of complexity should not necessarily be taken as an increasing function from to C^. Although i t can be taken for granted that is less complex than either C2, C3, or Cĵ  and that G 2 and C3 are less complex than C^, i t i s not clear i f C 2 i s less complex than C3. This judgment would depend on the greater importance of either the domain or the dynamic dimension. 86 TABLE 5-2 CONSTRAINTS OP COMPLEXITY AND CONSEQUENT STOCK PRICE BEHAVIOR X p © rH* £ © 0 > p 1 a •r l - P O «H G H p, g - p a a • H P a © a © o rH - r l <4-l O o > © 43 C< G 3 © © © •r l 3 • r l ' r l > +J a r H ' © O N - P > G «o <M P •r l bO 3 rH • r l r"» pi «rl © QO <D © • H O © • P G -O > a •r l XJ 3 G 3 3 CO © (—1 © g 4-| CD O O 03 CO H bOTJ H> H pi 3 p rH o •r l a G s S G o CO •r l C CO © P O 3 42 o X) CO 3 © •»"* •r l G > CO «rl > Pi CO O 43 © © 1 o co © 1 1 g - r l H • P G I aO p • P 1 o u a co U CO •r l a C CO r l O CO 1 • H g P — ' © Pi © © g CO ©. 1 CO «rl 4H ••H a o Pi r H ' CL O oO PH TH P o G O * d r l © 43 <s O \ W 3 © X <M 3 II o a o •r l »rl *0 CD > P CO © «H <D O H O © P P O CO co 43 P %H r*» © P •r l M © P r̂ > Pi H < •r l — rH • O © - P 0'- © © «rl rH<-p CO + 5 G - H © rH © © <M H p © 3 3 rls! •r l © ^ +» G - P G O © © r-H ? P P g <4H CO CO 0) O r< Pi + 3 <M o O U • H M n 3 ft r H ! P, a Pi O fX © O •r l G t l ' i H G +S CO O - H H a co 3 *rl O O © p a , a H © o o T3 CO rH P M n s > G G CO « g o 1 co g o co Pi m co E n O G- X i G © I 1^5-P © rH- © aO rH G ' H © 1 Pi P . i-tr-i' r"» © © TH CO i Pi CO CO r l - P © g 43 © - P © 60 Pi co - P •a 3. •r i O O CO H ' P ^ ! qj \ CO > G r H i ' O 3 G CO o CO ' r l © -r l Pi O 3 r H . CO \ ° N © - r l «H (D p t » co © © G S H CO Pi 3 > 43 © © a, r -s rH ' CO +> rH l o a o • r l 3 © O £ MH g rH +3 CO IS 3 U 'ri CO - H O G © P O © © r H . • H CO |S p r—If O Pi •r l <M P p CO QU O CO CO Pi H > g O . G O G o © o G - P CO ' r l 3 O CO r H l i H © O C O - H o a CO rH i O > £4 © S-( G 43 - P rH CO CO 43 CWri S P T3 © P 1 1 • r l P 1 Pi ^ ! © © rH G 1 1 •a g G P G 03 O H i © rH r H ' © © © CO O CO O G o a 1 © . r l 43 - r l Q rH'. a 43 > p W) rt o 3 CO o o •r l © G O T3 Pi > 4 3 CO © C "O 3 •H -O © aO a o •r l «rl 'O © © N r l ' i H t © - P (>s ffl "O H i t ) <M © Pi p G o S-4 t>5 © - P g O <D \ M •r l T J to © © © O ' H H P CO O -r l r-ti H f l + > O IS 3 G © G ^ 43 © P C P G O • d r H ' a CO 00 fi O O fi 60 r l > •r l r l © *n o • H oO CO 3 G G a g G - r l © OO G p •r l O •r l G co r l G G 3 «H O O © a. • H © 43 0 = 4*! «0 ra <M p o 6 a CO CO o* co S o © Pi a C O CO G •r l P o Pi © G •r l O • r l o •r l P • r l Pi • r l Pi Q © © Pi O Pi o Pi g a © •r l a •r l • P Pi >. P +3 > m O p © Pi © G •tl O O o 43 O G o © o H a a St  87 By constraining the market's a b i l i t y to develop the knowledge structure which i s necessary as the founda- t i o n for a n a l y t i c a l reasoning and the extrapolation of po- t e n t i a l earnings, each category of complexity determines the amenability for analysis. The c l a r i t y of a company's knowledge structure w i l l i n turn derive the l e v e l at which analysts can forecast outcomes within a tolerated degree of uncertainty. The significance or content of a p o s t e r i o r i and a f o r t i o r i information w i l l vary with each category of complexity. Also, the r e l a t i v e significance and r e l a t i o n - ship between the two types of information and the speed at which they are received, decoded, interpreted, disseminated and acted upon varies with the constraints of complexity. The type of information related to the constraints of com- pl e x i t y can illuminate the e f f e c t over time of the entrance of information in the market, i t s impact upon the valuation of common shares and the subsequent price adjustments. In short, the summarization of the attributes of complexity related to a p o s t e r i o r i and a f o r t i o r i information can de- termine whether successive dependencies w i l l exist i n price adjustments. A company i n the f i r s t category of complexity, C^, with both the domain and dynamic dimensions being simple would be amenable to analysis. A knowledge structure could 88 be c l e a r l y defined and there would be a low l e v e l of uncer- t a i n t y or a high l e v e l of ce r t a i n t y associated with reasoned forecasts. Because the analyst could comprehend the company c l e a r l y and develop a knowledge structure as a basis f o r reasoning, a p o s t e r i o r i information would be highly s i g n i - f i c a n t to deductively forecast potential outcomes. The en- trance of a p o s t e r i o r i information i n the market would be received, decoded, interpreted and disseminated throughout the market at a f a i r l y quick pace i f not almost instantan- eously. With the high l e v e l of certainty associated with forecasts, predicted outcomes would be discounted well i n advance of the occurrence and reporting of those outcomes. A f o r t i o r i information would therefore have l i t t l e s i g n i f i - cance as t h i s would merely be the reporting of outcomes already discounted and adjusted i n the stock's price. As a p o s t e r i o r i information i s s i g n i f i c a n t i n deducing valua- t i o n changes and i n adjusting the knowledge structure and as i t enters the market randomly the ef f e c t i s rapid, a l - most automatic reactions i n adjusting the price of a com- pany's stock. The end res u l t is the creation of price changes that exhibit randomness. Hence a company i n this category of complexity, the weakest constraining case, would give support to the theory of the random walk. 89 In the second category of complexity, C2, the domain dimension is simple but the dynamic dimension is complex. With a simple domain a company i n t h i s category would s t i l l be amenable to analysis f o r i t s valuation as a knowledge structure could be developed. However, because the dynamic dimension i s complex a very low l e v e l of cer- t a i n t y would be associated with any predictions of poten- t i a l s . A p o s t e r i o r i information would be f a i r l y s i g n i f i - cant i n revealing possible outcomes but i n conjunction with a high l e v e l of uncertainty i n t r y i n g to forecast the possi- b i l i t y of the suggested outcomes being r e a l i z e d the market would demonstrate quickly changing expectations. A case i n point would be a company that is rapi d l y changing i t s cor- porate base or is undergoing a reorganization which the market has some pertinent information about but which cannot be forecast with accuracy. Such a company becomes succeptible to speculative expectations and quickly chang- ing opinions as d i f f e r e n t segments of the market attempt to out reason other segments. A f o r t i o r i information would be s i g n i f i c a n t i n revealing actual outcomes as they unfold because the inaccuracy associated with forecasts derived from a p o s t e r i o r i information may have been misleading or confusing. Both a p o s t e r i o r i and a f o r t i o r i information may have a substantial effect on the price valuation of the company and could produce a great v o l a t i l i t y i n the 90 stock's price behavior. This i s the resu l t of inaccurate forecasts y i e l d i n g divergent expectations i n the market and the reporting of a f o r t i o r i outcomes which could be unexpected. The end re s u l t is the creation of v o l a t i l e price changes and a randomness i n these changes. This case could then also provide support for the theory of random walk. The t h i r d category of complexity, C^, has a com- plex domain but a simple dynamic dimension. An example of such a company i s a conglomerate that has a vast organiza- t i o n but which is rather slow i n changing i t s organization- a l base. This type of company i s d i f f i c u l t to analyze for the purpose of developing a knowledge structure. The know- ledge structure would be characterized by a lack of c l a r i t y . E s s e n t i a l l y i t would be rather abstract. Highly competent analysts could discern the relevant data and factors f o r valuation but due to the company's abstractness the remain- der of the market would resort to an image of the company's value based on previously understood value. The simple dy- namic dimension prevents the o v e r a l l valuation of the com- pany from changing r a p i d l y and produces the s i t u a t i o n where forecasts can be made by the competent analysts with a f a i r degree of accuracy. A p o s t e r i o r i information would be received, decoded, and interpreted at a f a i r l y slow pace 91 because of the abstractness of the underlying knowledge structure. Also, because of the company's abstractness the cost of analysis would be r e l a t i v e l y higher i n com- parison to the analysis of more simple companies yet the benefit would be only one investment opportunity. There- fore the cost-benefit factors would be an additional de- terrent to analyze a p o s t e r i o r i information f o r such a company and would slow down further the pace at which the information i s spread throughout the market. There- fore, although the p o s t e r i o r i information can be used deductively to forecast pot e n t i a l outcomes the number of analysts concentrating on this company i s reduced and then they are faced with the problem of dissuading others of the adjusted value. The reason being f o r t h i s l a t t e r problem i s that the market i n i t s r e l a t i v e lack of under- standing of the company tends to be emotionally defensive over i t s current image of the stock's value. This defensiveness stems from the attempt to maintain an acceptable l e v e l of certainty for something which i s not f u l l y comprehended and a method of maintain- ing a sense of certainty i s to accept an image espoused by a concensus of the investment community which i s con- t i n u a l l y being reinforced. As explained previously, a person who has accepted a b e l i e f i n something f o r which 92 no clear explanation exists tends to accept r e a d i l y i n f o r - mation that reinforces his b e l i e f and tends to d i s c r e d i t information which c r i t i c i z e s or opposes his b e l i e f . If superior analysts are capable of r e a l i z i n g variation adjustments upon the receipt of pertinent pos- t e r i o r i information and i f they attempt to spread t h e i r recommendations throughout the market, the acceptance by the market w i l l be slow because of i t s defensiveness to- wards i t s current image of value. A f o r t i o r i information on the other hand w i l l be mostly discounted by the time of i t s announcement. The slow movement of the newly recom- mended value w i l l create a gathering momentum of buying or s e l l i n g f o r the company's stock. The re s u l t w i l l be the development of a trend i n i t s price changes. For such companies r e l a t i v e strength would be discernible and would prove to be s t a t i s t i c a l l y v a l i d i f the sample tested gave recognition to the categorization of varying complexities i n corporations. The l a s t category of complexity, C^, i s the se- verest case of complexity and has both a complex domain and a dynamic dimension. An example of t h i s case i s a company that has a vast, d i v e r s i f i e d organizational base which is undergoing a change i n organization that is com- mensurate with i t s corporate base. This type of company 93 is very d i f f i c u l t i f not impossible to analyze because of i t s abstractness. Any forecast attempts would be done so with a high degree of uncertainty and would have very l i t t l e predictive value. Because the knowledge structure would be impossible to develop the market, including a l l analysts, would resort to an image of the company's value. The image in t h i s case would be much more fi x e d and emotionally based than i n the previous case of C3. A p o s t e r i o r i information is i n s i g n i f i c a n t as no one can determine the importance of the news item or information on the p o t e n t i a l earning power of the company. No deductive reasoning can be applied here. However, a f o r t i o r i information may be of significance i f the information i s v i t a l enough to e f f e c t questioning doubts as to the foundations of the image. If the f o r t i o r i i n f o r - mation i s concerned only with a minor aspect of the image then the market w i l l tend to maintain the current image by r e j e c t i n g information negating the image. Negative i n f o r - mation of minor significance repeatedly entering the market w i l l a l t e r the image but the process could be slow. It should be kept i n mind that negative information i s merely information which opposes the current image and is not necessarily pessimistic news. This category of complexity should y i e l d patterns i n price changes because of the image factor and the r e s u l t 9U should be a trend i n the stock's price movement. This above statement must be q u a l i f i e d with the understanding that i f the image of a stock's value as expressed i n the traded price has deviated excessively from i t s "true" value the price i s vulnerable to a f o r t i o r i information entering the market, generating a substantial emotive change to bring about a sudden large price change. In this category r e l a t i v e strength may be v a l i d but is vu l - nerable to experiencing a violent price change i n the stock. Summary This chapter has been included with the purport of advancing the theory of common share price behavior and explaining the possible v a l i d i t y and compatibility of the theories of r e l a t i v e price performance and random walk. The t h e o r e t i c a l framework has been developed from a general systems approach examining corporations as systems with d i f f e r i n g degrees of complexity. Complexity measured along two of three possible dimensions has been related to the problems of analysis, understanding the r e l a t i o n a l components and factors f o r valuation and the development of knowledge structures of companies. Information, a necessary key to any a n a l y t i c a l process, has been broken 95 down into two types depending on whether the information can be used deductively or inductively. F i n a l l y , the two types of information were applied to the categories of com- pl e x i t y to reveal the market valuation and price adjustment process. The end r e s u l t demonstrated how the random walk model would be vulnerable to large price changes i n v a l i - dating the use of r e l a t i v e strength techniques. It i s hoped that t h i s t h e o r e t i c a l development w i l l be given a c r i t i c a l appraisal and w i l l be considered as a furthering of understanding the market place as a socio-economic phenomena. 96 CHAPTER VI CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH This paper, as explained i n the Introduction, has had two purposes. The f i r s t was ah empirical exam- ination of the hypothesis of r e l a t i v e price performance to determine i t s v a l i d i t y and possible use to supplement fundamental analysis by preselecting which issues to analyze. The second puirpose was to develop a theoreti- c a l framework which attempts to explain the constraint of complexity encountered i n security valuation. The conclusions drawn from both purposes are presented here in the respective order i n which the two enquiries were covered i n the paper. Although t h i s dichotomy of pur- pose exists the conclusions reached are not t o t a l l y i n - dependent. The recognition of the constraint of complex- i t y and i t s rela t i o n s h i p to information receipt q u a l i f i e s the findings of the empirical examination by i l l u s t r a t - ing some of the necessary conditions for r e l a t i v e price performance to operate. 97 Conclusions from the Empirical Examination of Relative Price Performance The 11 tests conducted on the data which examined the v a l i d i t y of the hypothesis that r e l a t i v e price perform- ance of common stocks is dependent on recent h i s t o r i c a l re- la t i v e price performance provided no s i g n i f i c a n t support for the hypothesis. Correlations of h i s t o r i c a l and sub- sequent r e l a t i v e price performance, as measured here i n the co e f f i c i e n t of determination, were i n s i g n i f i c a n t . Also, in many cases the estimated regression equations were s l i g h t l y negative when a positive r e l a t i o n s h i p was hypo- thesized to exi s t . The tests of the hypothesis varied i n approaches from examining the entire sample of stocks one month at a time to examining each stock i n d i v i d u a l l y for the f u l l time period under review. The approaches taken also varied from including only one month's h i s t o r i c a l r e l a t i v e performance as the independent variable i n the regression equation to including up to ten months of h i s t o r i c a l r e l a t i v e perform- ance. The results from the variations of approach were n e g l i g i b l y d i f f e r e n t in most cases. In those other cases where the c o r r e l a t i o n improved due to an inc l u s i o n of more independent variables the improvement was s l i g h t and was achieved at the expense of the error of estimate. 98 The findings i n this study lead to the conclusion that h i s t o r i c a l r e l a t i v e price performance has no s i g n i f i - cant v a l i d i t y i n predicting future r e l a t i v e price perform- ance of common share prices and that the hypothesis as stated i n this paper cannot be rejected. Implications of the Constraints of Complexity The t h e o r e t i c a l framework of complexity developed i n t h i s paper revealed the constraining e f f e c t of complex- i t y encountered i n security valuation. It was shown that as the degree of complexity i n corporations increases i t becomes more d i f f i c u l t to analyze these companies and to arrive at an accurate valuation. It was then demonstrated that the degree of complexity can be measured i n corpora- tions by using the three dimensions of systems: domain, dynamic and e c o l o g i c a l . However, by eliminating industry and general market movement from i n d i v i d u a l stock price movement the ecological dimension could be subtracted. Complexity i n companies forces the market i n an attempt to maintain a sense of certainty to r e l y on an image of value which i s perpetuated by a concensus of the investment com- munity. It was then shown that the reliance on an image stemming from an emotive basis creates a defensiveness as to news and information which might be negative to the image. 99 Complexity was related to types of information and revealed the constraining e f f e c t on understanding i n - formation that might be used deductively (a p o s t e r i o r i ) and information that would be used inductively (a f o r t i o r i ) . The r e l a t i o n s h i p of categories of complexity to information types presented a framework of variations i n security valu- ation and hypothesized security price movements that would r e s u l t . The rather crude framework of four categories of complexity for corporations i l l u s t r a t e d that two categories would exhibit random security price movement, one would exhibit trends i n security price movement and the last category should also exhibit trends but which could be vulnerable to dramatic price changes. Recognizing the possible variations of security price behavior caused by differences of complexity leads to the inference that the findings of the empirical tests of r e l a t i v e price performance may have been more s i g n i f i - cant i f the sample consisted of only those companies whose degree of complexity was conducive to trends i n security price trends as revealed by the framework. Suggestions fo r Further Research Further research should be directed towards ex- panding and r e f i n i n g the framework of complexity. More 100 thought should be given to applying knowledge from psychol- ogy* sociology and other related d i s c i p l i n e s to the frame- work to attempt to expand the understanding of behavior and decision making process of individuals i n the market place. Thought should also be given to developing refined methods of measuring complexity and the related r i s k of inaccurate investment forecasts. Further research on r e l a t i v e price performance could be conducted on "selected" samples of corporations that are t h e o r e t i c a l l y conducive to trends i n security price movements. F i n a l l y , future research could be directed towards attempts to measure investment r i s k i n cases of uncertainty through improved techniques of measur- ing complexity of investment opportunities. The application of general systems concepts and information theory should be considered as an aid to comprehending complexity and the li m i t a t i o n s on " r a t i o n a l " investment decisions. 101 SELECTED BIBLIOGRAPHY BOOKS Boulding, K.E. The Image (Knowledge i n L i f e and Society). Ann Arbor, Michigan, i 9 6 0 . Brealey, Richard A. Risk and Return from Common Stocks. Cambridge, Mass., The M.I.T. Press, 1969. Brown, J.A.C. Techniques of Persuasion from Propaganda to Brainwashing. London, Eng., Cox & Lyman Ltd., 1963. Baumol, W.J. The Stock Market and Economic E f f i c i e n c y . New York, Fordham University Press, 1965. Cohen, J.B. and Zinbarg, E.D. Investment Analysis and P o r t f o l i o Management. Homewood, 1 1 1 . , R.D. Irwin Inc., 1 9 6 7 . Cootner, P.H., ed. The Random Character of Stock Market Prices. Cambridge, Mass., The M.I.T. Press, 1961*. Drew, G.A. New Methods f o r P r o f i t i n the Stock Market. 1+th e d i t i o n . Wells, Vt., Fraser Publishing Co., 1966. Edwards, R.D. and Magee, J. J r . Technical Analysis of Stock Trends, l+th e d i t i o n . S p r i n g f i e l d , Mass., Stock Trend Service, 1958. Fredrikson, E. Bruce, Editor. Frontiers of Investment Analysis. Scranton, Penn., Wharton School of Finance and Commerce, University of Pennsylvania. International Textbook Co., 1 9 6 5 . Freund, J.E. and Williams, F.J. Modern Business S t a t i s t i c s . Englewood C l i f f s , N.J., Prentice-Hall Inc., 1 9 5 8 . Graham, B., Dodd, D.L., Cottle, S. In collaboration with Tatham, C. Security Analysis: Principles and Techniques, l+th e d i t i o n . McGraw H i l l Book Co. Inc., 1962. 102 Granville, J.E. A Strategy of Daily Stock Market Timing for Maximum P r o f i t . Englewood C l i f f s , N.J., Prentice-Hall, I960. Harper, H.H. The Psychology of Speculation: The Human Element i n Stock Market Transactions. Wells, Vermont, Praser Publishing Co., 1966. Hayes, D.A. Investments: Analysis and Management. New York, The MacMillan Co., 1966. Investment Dealers Association of Canada. The Canadian Securities Course. Montreal, Que., 1968. UNPUBLISHED WORKS Bjerring, J.H., Dempster, J.R.H. and H a l l , R.H. U.B.C. TRIP (Triangular Regression Package). Uni- v e r s i t y of B.C. Computing Center, January, 1968/360 Implementation February, I969. Dempster, J., Gagon, Hogan. Triangular Regression Package. University of B.C. Computing Center, A p r i l , 1965. Levy, R.A. An Evaluation of Selected Applications of Stock Market Timing Techniques. Trading Tactics and Trend Analysis. Ph.D. Disserta- t i o n , Ann Arbor, Mich., University Microfilms, Inc. Nye, D.J. Relative Value Analysis. M.B.A. Thesis. University of B r i t i s h Columbia, I968. 103 ARTICLES Bauman and Scott. " S c i e n t i f i c Investment Analysis: Science or F i c t i o n . " F i n a n c i a l Analysts Journal. 1967. Fama, E.F. ' "Random Walks i n Stock Market Prices." F i n a n c i a l Analysts Journal, v o l . XXI No. 5 (September-October, 1965), p. 57. King, B.F. "Market and Industry Factors i n Stock Price Behavior." Journal of Business, v o l . XXXIX, No. 1, Part II (January, 1966), pp. 139 - 170. Kourday, M. "Relative Values - A Method of Outperform- ing the Market." F i n a n c i a l Analysts Journal, v o l . 19, No. 6 (November-December, I963) PP. 35 - UU« Levy, R.A. "Relative Strength As A C r i t e r i o n for Investment Selection." Journal of Finance, v o l . XXII, No. I4 (December, 1967), pp. 595 - 610. Mao, J.C.T. "The Valuation of Growth Stocks." Journal of Finance, v o l . XXI (March, I966) ?T95 APPENDIX I INDUSTRIALS BANK Bank of Montreal Bank of Nova Scotia Canadian Imperial Bank of Commer Royal Bank of Canada Toronto-Dominion Bank BEVERAGE Canadian Breweries D i s t i l l e r s Corporation Seagrams John Labatt MoIson Breweries 'A' Hiram Walker-Gooderham CHEMICAL AND TEXTILE Canadian Industries Chemcell Dominion Textile DuPont of Canada Harding Carpets 'A' CONSTRUCTION AND MATERIALS Canadian Cement Dominion Bridge Standard Paving FINANCIAL Argus Corporation Canada Permanent Mortgage Imperial L i f e Assurance Industrial Acceptance 105 FINANCIAL (continued) Investors Group 'A' Laurentide Finance National Trust Power Corporation of Canada Traders Finance ,!A' FOOD AND RETAIL At l a n t i c Sugar Beaver Lumber Canada Packers 'B' Dominion Stores Hudson's Bay Company Lbbrlaw Company 'B' Oshawa Wholesale Salads Foods Simpson's Limited George Weston 'A' Woodward Stores INDUSTRIAL MINE Aluminium Ltd. Cominco Falconbridge Hoilinger International Nickel Noranda METAL WORKING Anthes Imperial 'A' Dominion Electrohome Ford Company of Canada General Motors Hawker Siddeley Hayes S t e e l Levy Industries Massey-Ferguson Slater Steel OIL REFINING B.A. O i l Canadian Petrofina Imperial O i l Sh e l l Canada Texaco PAPER AND FOREST PRODUCTS A b i t i b i B.C. Forest Products Consolidated Paper Domtar Fraser Company Great Lakes Paper MacMillan, Bloedel Price Brothers PIPELINE Alberta Gas 'A' Interprovincial Pipe Line Pembina Pipe Line Trans-Canada Pipe Line Trans-Mountain Pipe Line Westcoast Transmission STEEL Algoma Steel Dominion Foundries Dominion Steel & Coal Steel Company of Canada UTILITY B e l l Telephone B.C. Telephone Galgary Power Consumers' Gas Northern & Central Gas Union Gas of Canada MISCELLANEOUS Canada Steamship Canadian P a c i f i c Railway Dominion Glass Moore Corporation Southam Press Famous Players White Pass & Yukon GOLD Aunor Gold Bralorne Campbe11 Bad Lake Cochenour Willans Dickenson Dome Mines Giant Yellowknife Kerr-Addison Macassa Madsen Red Lake Sigma Upper Canada BASE METAL Campbell Chibougama Cassiar Asbestos Craigmont Mines Denison Mines East S u l l i v a n Hudson Bay Mining & Smelting Mattagami Lake Normetal Opemiska Quemont Rio Algom S h e r r i t t Gordon Steep Rock United Keno WESTERN OIL Canadian Superior O i l Central Del Rio Dome Petroleum Great Plains Development Home O i l 'A' Hudson's Bay O i l Husky O i l P a c i f i c Petroleum Scurry Rainbow

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