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An Empirical Test of the Theory of Random Walks In AN EMPIRICAL TEST OF THE THEORY OF RANDOM WALKS IN STOCK MARKET PRICES: THE MOVING AVERAGE STRATEGY by GARRY CRAIG YIP B.Com., University of British Columbia, 1970 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF BUSINESS ADMINISTRATION in the Faculty of Commerce and Business Administration We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1971 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of UCWUMU- ftjntl BwiJUv\U& ftcliwinjqJj^YU The University of British Columbia Vancouver 8, Canada Date fliuxuit • ABSTRACT This study investigates the independence assumption of the theory of random walks in stock market prices through the simulation of the moving average strategy. In the process of doing so, three related questions are examined: (1) Does the past relative volatility of a stock furnish a useful indication of its future behavior? (2) Is the performance of the decision rule improved by applying it to those securities which are likely to be highly volatile? (3) Does positive dependence in successive monthly price changes exist? The purpose of Test No. 1 was to gauge the tendency for a stock's relative volatility to remain constant over two adjacent intervals of time. As measured by the coefficient of variation, the volatility of each of the 200 securities was computed over the 1936 to 19^5 and 1946 to 1955 decades. In order to evaluate the strength of the relationship between these paired observations, a rank correlation analysis was performed. The results indicated a substantial difference in relative volatility for each security over the two ten-year periods. In Test No. 2 a different experimental design was employed to determine whether the relative volatility of a stock tended to remain within a definite range over time. According to their volatility in the 1936 to 1945 period, the 200 securities were divided into ten groups. i i i Portfolio No. 1 contained the twenty most volatile securities while Portfolio No. 2 consisted of the next twenty most volatile, etc. An average coefficient of variation was calculated for each group over the periods, 1936 to 19^5 and 19^6 to 1955. The rank correlation analysis on these ten paired observations revealed that the most volatile securities, as a group, tended to remain the most volatile. Test No. 3 consisted of the application of the moving average strategy (for long positions only) to forty series of month-end prices covering the interval, 1956 to 1966. These securities had demonstrated a high relative volatility over the previous decade and, on the basis of the findings reported in Test No. 2, it was forecasted that they would be the most volatile of the sample of 200 in the period under investi• gation. Four different moving averages ranging from three to six months, and thirteen different thresholds ranging from 2 to 50 per cent were simulated. The results of the simulation showed the moving average strategy to be much inferior to the two buy-and-hold models. Every threshold regardless of the length of the moving average yielded a nega• tive return. In addition, the losses per threshold were spread throughout the majority of stocks. Altogether, therefore, considerable evidence was found in favour of the random walk theory of stock price behav i or. TABLE OF CONTENTS PAGE CHAPTER I. THE THEORY OF RANDOM WALKS AND ITS IMPLICATIONS FOR FUNDAMENTAL AND TECHNICAL ANALYSIS ... 1 CHAPTER I I. FILTER RULES 12 CHAPTER III. THE MOVING AVERAGE STRATEGY APPLIED TO HIGHLY VOLATILE SECURITIES lh Selected Techniques for Improving the Performance of the Filter Rule and Moving Average Strategy 2k The Data 29 Test No. 1: The Experimental Procedure and the Resul ts 30 Test No. 2: The Experimental Procedure and the Results 31 Test No. 3: The Experimental Procedure and the Results 32 CHAPTER IV. CONCLUSIONS AND FUTURE RESEARCH 37 Summary 37 Suggested Research Topics kO BIBLIOGRAPHY 50 Page TABLE I. Subsequent Volatility of Portfolios of Stocks Selected on the Basis of Prior Volatil ity 42 TABLE II. Selected Sample of Forty Securities .... 43 > TABLE III. Three Month Moving Average Results 44 TABLE IV. Four Month Moving Average Results 45 TABLE V. Five Month Moving Average Results 46 TABLE VI. Six Month Moving Average Results 47 Hypothetical Chart of a Stock Price Subject to Random Movement Within Fixed Limits Hypothetical Chart of a Stock Price Subject to Random Movement Within Periodically Changing Limits ACKNOWLEDGMENT I would like to express my gratitude to Dr. William Wood for his valuable guidance in the preparation of this thesis. I am also indebted to Mr. Vincent S. Manis for his programming assistance and Miss Susan Lew for typing both the rough and completed drafts. r THE THEORY OF RANDOM WALKS AND ITS IMPLICATIONS FOR FUNDAMENTAL AND TECHNICAL ANALYSIS For decades the dynamics of price formation in the stock market has been a subject of study for a sizeable segment of the investing public. The reason for such overwhelming interest in this capital market is attributable to several factors, most of them interrelated. To begin with, it is recognized that this market is among the best organized of the multitude and almost always ranks as the largest in terms of value of sales. Also, it is widely known that speculative prices are extremely sensitive to all events, both real and imagined, providing an insight into the future. As one might expect, these elements operate in conjunction with one another to cause a considerable total of gains and losses to be experienced each trading day. Needless to say, fluctuations such as these may present the opportunity for large profits to be realized within a very short time horizon. This has undoubtedly provided a constant attraction to men with dreams of instant wealth. With numerous participants in the equities market it would be natural to find a vast array of "magic" formulas for predicting stock prices and indeed, such is the case. Investors have correlated the movement of share prices to every conceivable phenomenon for forecasting purposes. While an infinite number of formulas exist, there are only two basic approaches to investing, fundamental analysis and technical analysis. Under the fundamental philosophy the analyst, in searching for bargains, bases his valuation of a security upon those factors which he believes other rational investors use to assess value. In general terms these factors consist of the expanse of information contained in economic and financial statistics. More specifically they include earnings, dividends and assets of the firm represented by the security under observation. All such data, past or present, is taken into account to appraise the value of the share or as it is commonly referred to, the intrinsic value of the share. The belief of the fundamentalist that undervalued securities exist, implies an imperfect market. He attempts to capitalize on the asset price disequilibrium situation by purchasing a bargain and expects the market later to adjust to an equilibrium state. Implicitly the fundamentalist is assuming that imperfect knowledge characterizes the market place and that trends will develop from the gradual spread of awareness of the relevant facts. Unlike the fundamental approach, technical analysis is con• cerned with predicting share prices solely on the basis of past information. A direct result is that rational investment behavior is not a critical assumption for the technician. The market continually and automatically weighs all factors including not only those relevant to the fundamentalist but also opinions, moods, and guesses. In one important respect a parallel can be drawn between fundamental and technical analysis. They both infer that the market is not perfect by assuming that facts at one moment of time will govern prices at some future date. For the technician this is in the form of a belief that stock prices tend to move in trends which persist for an appreciable length of time and that these trends can be uncovered by studying price movements of the immediate past. While numerous professional practitioners endorse the technical approach to investing, academics have not followed suit. Rather, they suggest that stock prices behave as a random walk and that future movements of prices could just as well be determined by tossing a coin as by any sophisticated analysis of past price changes. This serious threat to the technician's livelihood has engendered a commensurate degree of controversy between the respective parties. "The theory of random walks in stock prices is based on two hypotheses: (1) successive price changes in an individual security are independent, and (2) the price changes conform to some probability distribution."^ Of the two, the first is more important. If dependence in successive increments of prices exists then the theory is not valid. The second hypothesis is not nearly as definitive because the form or shape of the distribution need not be specified. Consequently, any distribution which satisfies the condition of correctly characterizing the process generating the price movements is consistent with the theory. Eugene F. Fama, 'The Behaviour of Stock Market Prices," Journal of Business, 38 (January, 1965), P- ^0». In statistical terms independence means that the probability distribution for the price change during time period t is independent of the sequence of price changes during previous time periods.
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