THE ODD-LO? STOCK TRADSNG THEORY ThosEs fat the Degree of D‘ B. A. MiCH£GAN STATE UWVERSWY Danaié Joseph Kiaén $95543 1 W 3 1293 10232 7289 ‘ LIBRARY ' Michigan State University This is to certify that the thesis entitled THE ODD-LOT TRADING THEORY presented by DONALD JOSEPH KLEIN has Pflfl ceept ed t osward fulfillment the reirequ remensotfr d6 3669" Gin LW )j/Mu, (5: ”dew/L Majorroesspf Date 6427/44 {7% /75% ROOM L333 ONLY, W Wales l'i'i ABSTRACT THE ODD-LOT STOCK TRADING THEORY by Donald J. Klein The main purpose of this study was to test the validity of the odd-lot stock trading theory by means of an empirical investigationo The theory states that, "Odd- lotters tend to buy the majority of their stocks at the wrong time (near the tOp of a market trend) and sell at the wrong time (when the market is at a low point)." In addition to the lack of supporting empirical evi- dence there has been no written history of the theory thus far. After outlining the history of the theory, the vali- dity of using the Dow—Jones Industrial Average (DJIA) as the norm to which the odd-lot trading activity is compared was questioned and a new method of comparison devised. A list of those stocks which are considered "most active" on the New York Stock Exchange (NYSE) was thought to be more representative of the action of the stock market and, there— fore, a more acceptable basis of comparison than the thirty stocks which comprise the DJIA. Since odd—lot transactions do not require the match of a buyer and a seller, as round-lot transactions do, two dis- tinct groups of odd-lotters were investigated: odd—lot Donald J. Klein sellers and odd-lot buyers. To these two groups was added the round—lotters. A sample of stocks, consisting of the twenty most active stocks by volume, for each group, was taken monthly from the NYSE for the years 1955 through 1961. In addition, the DJIA and the Standard & Poor's Composite 500 Stock Index (S&P) were used to test the current concept of the theory, as well as to see if their performance paral- leled that of the round—lot sample. The profitability of these samples, along with the DJIA and S&P, were tested to determine which one had the greatest amount of price appre- ciation and dividend yield. To test the price appreciation aspect of the study, the initial dollar portfolio value of each monthly sample was compared with its portfolio value six months, one year and two years later. This resulted in the monthly price appre— ciation of each group for each month. Then the arithmetic average of these monthly appreciation figures was determined. This represented the average profitability of each group at the designated periods of comparison. The dividend yields of each group were determined in a similar manner for all three periods of comparison. This was accomplished by dividing the total dividends received by each monthly sample during the twelve months preceding the periods of comparison by its respective portfolio value, as determined above. Donald J. Klein Finally, the results of the price appreciation test and the dividend yield test were combined to give an average pro— fitability (accounting profit) for each group at the desig— nated periods of comparison. These average profitability figures for each group were then compared to see which one showed the greatest profit or, from the sales aspect of the theory, which one had the largest opportunity cost. If the odd—lot buyers had the greatest profit, the purchase phase of the theory would be incorrect, for the odd—lotters could not buy at the "wrong" time and still make more profit than any other group of investors. The theory would be substan— tiated, however, if the odd-lot sellers had the largest opportunity cost (measured in terms of price appreciation). Their portfolio of stocks would have forfeited the highest profit of any group of stocks sold. The results indicated that the complete theory was invalid, The sales aspect of the theory was supported while the purchase side was challenged. Copyright by Donald Joseph Klein 1965 THE ODD—LOT STOCK TRADING THEORY By Donald Joseph Klein A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF BUSINESS ADMINISTRATION Department of Accounting and Financial Administration 1964 ACKNOWLEDGMENTS I wish to express my gratitude to the members of my committee--Professor Stuart B. Mead, Chairman; Professor Floyd W. Windal and Professor Leonard H. Rall-—for their unlimited assistance and encouragement, and to Professor Robert W. Johnson who suggested the topic of this study and offered numerous helpful comments. I am also indebted to Michigan State University and its faculty for the phase of my graduate academic prepara- tion leading to this dissertation. The completion of this research would not have been possible without the generous assistance and COOperation of Carlisle & Jacquelin and DeCoppet & Dorremus, the two largest odd-lot dealers on Wall Street. Finally, I deeply appreciate the assistance of my wife, Julie, whose work, forebearance and sacrifice are invisibly transcribed on each page. 11 TABLE OF CONTENTS Page ACKNOWLEDGMENTS . . . . . . . . . . . . . . 11 LIST OF TABLES. . . . . . . . . . . . . . . v LIST OF CHARTS. . . . . . . . . . . . . . . vii LIST OF APPENDICES . . . . . . . . . . . . . viii Chapter I. INTRODUCTION. 1 Purposes of the Study 2 Methodology . . . . . . . . 3 Order of Presentation . . . . . . . 5 II. HISTORY OF THEORY . . . . . . . . . . 7 Early Connotations . . . . 7 Humphrey B. Neill' 3 Interpretation. . . 9 Brookings Institute Study. . . . .' . 15 Garfield A. Drew's Interpretation . . . . 17 Current Theory . . . . . . . . 37 Summary. . . . . . . . . . . . . Al III. METHOD OF INVESTIGATION . . . . . . . . . A6 The Past . . . . . . . . . . A6 The Wrong Approach . . . . . . . . . 50 A New Approach . . . . . . . ., . . 52 Other Considerations . . . . . . . . 67 Summary . . . . . . . . . . . . 74 IV. STATISTICAL RESULTS OF PRICE APPRECIATION AND/OR DEPRECIATION . . . . . . . . . . . 78 The Sample. . . . . . . . . . . . 78 Portfolio Values. . . . . . . . . . 87 Summary. . . . . . . '. . . . . . 100 V. STATISTICAL RESULTS OF THE DIVIDEND YIELDS AND COMPLETE TESTING OF THE THEORY . . . . . 104 iii Dividend Yield Computations Actual Dividend Findings Overall Testing . Summary. . VI. CONCLUSION APPENDICES BIBLIOGRAPHY Price Appreciation Test Dividend Test. . Combined Test. Implications iv Page IDA 107 110 120 125 128 131 133 137 1143 198 'Table LIST OF TABLES Percentage of Respective Universes that the Various Samples Represent for the Years 1955 through 1961. Dollar and Percentage Breakdown of Volume for the Odd-Lot and Round-Lot Samples by Ten Dollar Ranges from 1955 to 1962 The Monthly Average Price Appreciation or Depreciation in Portfolio Value for the Round-Lotters, Odd—Lotters, Dow-Jones Industrial Averages and Standard & Poor's Composite Averages for all Three Periods of Comparison: Six Months, One Year and Two Years After Initial Purchase or Sale Estimated Standard Error of the Means Used in the Study (Table 3) for Each Group for all Three Periods of Comparison: Six Months, One Year and Two Years After Initial Purchase or Sale Yearly Dividend Rates‘of the Portfolio Values Found for the Round-Lots, Odd-Lots, Dow-Jones Industrial Averages and Standard & Poor's Composite Averages at all Three Periods of Comparison: Six Months, One Year and Two Years Later. . . . . . . . . Estimated Standard Error of the Dividend Yields Used in the Study (Table 5) for Each of the Groups for all Three Periods of Comparison: Six Months, One Year and Two Years Later . Total Relative Profitability of the Portfolio for Each Group Six Months After the Initial Portfolio was Purchased or Sold . Page 82 85 9O 93 107 110 Ill Table Page 8. Total Relative Profitability of the Portfolio for Each Group One Year After the Initial Portfolio was Purchased or Sold . . . . . 113 9. Total Relative Profitability of the Portfolio for Each Group Two Years After the Initial Purchase or Sale of the Stock Portfolio . . llA vi Chart LIST OF CHARTS Comparison of the Dow-Jones Industrial Averages With Drew's Indexes l9A8-1962. Customers' Odd—Lot Balances Related to the Dow- Jones Industrial Average, 1950-1960. Six Month Moving Average Comparison of Relative Increases and Decreases in Portfolio Values of the Round-Lots, Odd-Lot Sales, Odd-Lot Purchases Six Months after the Initial Port- folio was Purchased/Sold, 1955 through 1961 Six Month Moving Average Comparison of Relative Increases and Decreases in Portfolio Values of the Dow-Jones Industrial Average and Standard & Poor's Composite Averages Six Months after the Initial Portfolio was Purchased/Sold, 1955 through 1961 Six Month Moving Average Comparison of Relative Increases and Decreases in Portfolio Values of the Round—Lots Odd—Lot Sales, Odd-Lot Purchases One Year After the Initial Port— folio was Purchased/Sold, 1955 through 1961 Six Month Moving Average Comparison of Relative Increases and Decreases in Portfolio Values of the Dow—Jones Industrial Average and Standard & Poor's Composite Averages One Year after the Initial Portfolio was Pur— chased/Sold, 1955 through 1961 Six Month Moving Average Comparison of Relative Increases and Decreases in Portfolio Values of the Round-Lots, Odd-Lot Sales, Odd-Lot Purchases Two Years after the Initial Port- folio was Purchased/Sold, 1955 through 1961 Six Month Moving Average Comparison of Relative Increases and Decreases in Portfolio Values of the Dow-Jones Industrial Average and Standard & Poor's Composite Averages Two Years After the Initial Portfolio was Purchased/Sold, 1955 through 1961. . . . . . vii Page 35 A8 9A 95 96 97 98 ‘99 Appendix A. LIST OF APPENDICES List of the Actual Stock Selections Used in Each Monthly Group for the Seven Period 1955 through 1961. . Sample Work Sheet Used to Record All the Data Used in this Analysis . . . . . Computation of the Arithmetic Mean and the Standard Error for the Means . Computation of the "T-Test" for Large Samples and the "T" Values . . . The Monthly Percentage Value of the Original Dollar Portfolio Values for all Groups Studied: Six Months, One Year and Two Years Later . . . . . . . . . The Monthly Dividend Yields for all Groups: Six Months, One Year and Two Years After Initial Purchase or Sale of the Portfolio viii Page 1AA 172 177 179 183 192 CHAPTER I INTRODUCTION "Buy cheap and sell dear," the motif of all Wall Street wisdom, is every investor's ambition. But if the principle is simple enough, the practice is not, or every man would be a Croesus. For price, after all, is a relative theory and success lies in knowing Just when stocks are cheap and getting dearer and when they are dear and getting cheaper. Out of this simple wisdom and the hard lesson arising from it has grown up over the years a Rube Goldberg maze of schemes to "beat the market"--mechanical oscillators and timers, cycle and sunspot theories of market tides, formula buying plans and contrary opinion theses galore.l It is a history studded with a few temporary successes and many ultimate failures. And yet the search goes on end- lessly. One such device much in evidence these days is one that has become known as the "odd-lot theory," based on the daily reports of odd-lot transactions on the New York Stock Exchange (NYSE). Its essence is simply that Wall Street "pros" believe the collective sentiment of odd-lot l"Are Market Turns Predictable?", FOTEEEA July 15’ 1958, p- 13. buyers and sellers is often wrong and most particularly at crucial turning points in market trends. It borrows heavily from the hoary belief of professional traders that they could make profits whenever they could correctly sensereversed.points in the market and do exactly the op— posite of what the odd-lot traders were doing. Everyone would like to be a "professional" in this sense. How- ever, only a few of the people who make their living on Wall Street really are and even their record is far from perfect. There have been many different versions of the odd— lot theory since a group of twenty-four New York business- men started meeting daily under a buttonwood tree on Wall Street in 1792 for the purpose of buying and selling securities.1 The odd-lot theories printed today in many leading financial periodicals and newspapers are outgrowths of the history of the small investor in the "street," known as the public. Purposes of the Study One individual wrote to the editors of the Stock Exchange Magazine (September, 1957) and asked, "What avail— able evidence exists to support the claim of the odd—lot theory?" The editors replied, "None at all, so far as we know." Since this time, a review of the literature has lOdd-Lot Manual, A Guide Prepared by Carlisle & Jacquelin, Odd-Lot Dealers (New York: Carlisle & Jacque- lin, 1961), p. 9. not shown any confirming or repudiating empirical evidence of the current idea of the odd-lot stock trading theory. There have been many interpretations of the odd-lot theory since the 1870's but no thorough study has given empiri- cal evidence of the current notion of the theory by look- ing at individual stock selections. While reviewing the literature it also became evi- dent that there is no one source that gives a history of the different theories. Consequently, there are many fragmentary pieces of this or that odd-lot theory here and there. The purpose of this thesis is twofold: 1. It will provide a history of the different odd- lot theories from the 1870's to 196A and 2.' It will be the first empirical study either to add support to the current odd-lot stock trading theory or to challenge its validity by means of investigating individual stock issues in relationship to this theory. Methodology This thesis is based on the principle that the only way one can gauge the success of the odd-lot inves- tors as a group is by determining whether or not they make less profit or have greater losses than the profes- sionals or the so-called round-lot investors. Therefore, a comparison of the profitability of these two groups of investors by means of samples will be utilized. A stratified sample of the oddwlotters and roundv letters will be determined by compiling a list of the twenty most active stocks each month for the years 1955 to 1962 from NYSE. Since each sample of stocks to ‘be used in the thesis has a high probability of having extreme price ranges within respective samples, a weight- ing,factor will be used to alleviate this problem. After the samples are determined, the profitability of each sample considered will be determined on the basis of stock appreciation or depreciation and dividend yield. at three different time intervals. The time intervals are six months, one year and two years after the initial purchase or sale of stock. The extent of profitability will be determined by both the timing of purchases and sales of odd-letters as well as by the indicated indi- vidual stock selections. Since an odd-lot transaction does not require a "match" of a seller and buyer as does a round—lot transaction, it is necessary to consider both odd~lot groups as separate entities in the analysis. The two are classified as odd-lot purchases and odd-lot sales. Consequently, the analysis of profitability will be made among three groups: the two already classified and the third, being the round-letters. After the profitability of each group has been con- sidered each group's results by months will be compared with one another, the Standard & Poor's Composite 500 Stock Index (S&P) and the Dow-Jones Industrial Average (DJIA) for the respective time intervals. This will pre— sent a picture as to how well the groups compared to each other as well as to the so-called "blue-chips" in the indexes. It will also give further evidence as to the validity or lack of validity of the current-day odd-lot stock theory. The entire statistical analysis of this thesis has been submitted to a computer analysis for the sake of accuracy and more involved tests so as to provide more reliable conclusions from the gathered data. Order of Presentation In Chapter I the lack of proof for the current odd-lot stock trading theory is discussed. The fact that there apparently is no written account of the dif- ferent interpretations of the theory since its beginning also is presented. In concluding Chapter I the purpose and the methodology as well as an organization of the thesis are indicated. Chapter II traces the history of the odd-lot stock trading theory from the 1870's to 196A. In Chapter III the methodology of the study is unfolded. This chapter also presents a discussion of the possible distorting effects of mutual funds, the monthly investment plan and stock-insurance programs upon the odd-lot statistics. Chapters IV and V are data chapters in which the statistical results of the study are presented. Chapter IV deals with the price appreciation/depreciation test of each sample. It also includes a discussion of the size of the samples as well as the element of extreme price ranges that can be found therein. The statistical findings, using price appreciation as the sole criterion, are used to test the validity of the theory. In Chapter V dividend yields are evaluated and the theory is once again tested, using dividend yield as the sole criterion. Finally, the combined results of the price appreciation/depreciation test and the dividend yield test are analyzed. After a critical observation of the results it is concluded that the theory is not accurate. The conclusions and implications of this study are presented in Chapter VI. In summary, the findings contradict one aspect of the theory but affirm another aspect. Therefore, the complete theory is rejected. CHAPTER II HISTORY-OF.THEMTHEORY Early Connotations As far as can be determined, the first theory to deal with individuals trading fewer than 100 (or multiples of 100) shares in order to help predict market turning points was formulated in the late 1870's. In 1871, the New York Stock Exchange was established using essentially the same procedures that prevail today on Wall Street. In 187A, John H. Jacquelin & Company, predecessor of Carlisle & Jacquelin, was established. Although not originally an odd- lot dealer, the Jacquelin firm began to make a market in odd- lots on the Floor of the Exchange itself. The experiment was a success and gradually.led to the establishment of the present odd-lot dealer system which guarantees for the small investor (a person who trades from 1 through 99 shares in securities listed on the New York'Stock Exchange) the same reliability, fairness, and accuracy as that received by the individual or institutional investor who deals only in round-lots (multiples of 100 shares). In the late 1870's, some professional brokers on Wall Street realized that when the volume of odd-lot purchases and sales indicated heavy trading, they could make substantial profits by buying and selling to this non- professional sector. At this time there were no actual 7 records kept of odd-lot transactions. Even the Securities & Exchange Commission (SEC) had not yet been established. Thus, this hoary belief was practiced only by the brokers and their friends on Wall Street who knew which securities were traded by this sector of the market as well as pre- cisely when the transactions occurred. Many of these brokers followed this belief all their brokerage days. Even on Wall Street today, some of the professional execu- tives will relate this same story. While gathering data for this study, on Wall Street, the above version of how the odd-lot theory began was revealed by two executives of two different professional brokerage firms. This same story was repeated in at least one financialpublication.1 The professional sector is defined as institutions such as insurance companies, pension funds, and foundations; financial intermediaries such as commercial banks, trust companies, and brokers who are not members of the New York Stock Exchange; and individuals who are members of the New York Exchange or partners (stockholders) in a member organization of the Stock Exchange.2 The non-professional sector of the market consists of all the individual members of the public who are not associated with a member . l"Are Market Turns Predictable?", Forbes, July 15, 1958, p. 13. 2These definitions are the same as those used by the Department of Research and Statistics of the New York Stock Exchange and are discussed in detail in the Ex- ihgnge's Eleventh Public Transaction Study, September 13, ‘ 9 l. ‘ organization of the New York Stock Exchange. This non- professional group, which accounts for about half.of the activity on the New York Stock Exchange, is composed of individuals who deal in round-lots as well as odd-lots. In 1959 and 1960 about 3A per cent of the non-professional 1 Because share volume consisted of odd-lot transactions. of the odd-lot price differential which results in slightly higher per share stock prices than round-lots and the smaller amounts of capital involved in odd-lot transactions, it is assumed that virtually none of the odd-lot trading is initiated by the professional sector of the market. It is recognized that the above definitions were not entirely applicable in the late 1870's. Pension funds, insurance companies, foundations, trust companies, etc.,-were not as predominant in the financial realm then 2 as they are today. However, these definitions will be appropriate for the rest of this study. Humphrey B. Neill's Interpretation The evolution of the odd-lot stock theory was further traced back to the 1930's when Humphrey B. Neill wrote his "Letters of Contrary Opinion" under the newspaper name of "The Ruminator." Neill's letters were not an advisory ser- vice but a bi-weekly letter of contrary comment on current 1Share volume computed from data given in New York Stock Exchan e Book 1 61 (New York: New York Stock Ex- changeI, pp. 55-55. 10 economic trends. In simple form he merely sought to point out what prevalent market opinions may be and then investigate the reasons for believing they were wrong. In his book, Tape Readingand Market Tactics,1 Neill stresses his underlying current of rationale. He istrongly.suspected that the study of human nature and mass psychology were elements of primary importance in market determination. He elaborated when he wrote: Price is determined by average human opinion.. If something changes opinion, there will be change in price, regardless of whether the cause of the change was rational, irrational, political, economic, military or even entirely obscure. It is of little importance over the near term, at least, whether the change of mind turns out to be well founded or not. . Even the composite curve of business activity fundamentally is a curve of mass peychology_which goes to even greater extremes in the stock market. There was never any statistical Justification, for example, for the record high prices of 1929 or the lows of-l932., After all, "The Market" is not a >mysterious entity in itself, rising and falling alone. Its price fluctuations result from the actions of-a great many human beings, motivated in buying and selling by their own personal.know; ledge, emotions and opinions. If it was known Just-how the public would-react toany given market situation, how professional traders would behave, what investment trusts would do, etc., "beating the market" would be comparatively easy. As a matter of fact, all so called technical study is really directed at discovering this very thing only it is usually called "determining supply and demand." But Just as financial commentators talk about "The Market" doing something or other, so does the technical field obscure the real issue‘ 1Saxtons River, Vermont: Neill Letters of Con- trary Opinion, 1960. (Special Reprint Edition). 11 with its Jargon of resistance levels, triangles, oscillators, etc. Actually, it is Just an attempt to analyze the changes that are taking place on the activities of the thousands of individuals whose collective action makes all the price move- ments of the market. Neill's underlying reasoning can be summed up by saying that, all other things being equal, a good psy- chologist comes out better than an economist in trading activities at least, by applying his training to the determination of the probable reaction of other groups. Facts Behind Contrary Qpinion The public usually pays the profit of the professional, because in stock speculation no one can make a profit in the and except at the expense of someone else, whether ‘that expense is direct or indirect. If Smith buys a stock at 80 and sells it to Pro at A0, only to buy it back from Pro at 80 again, Pro has obviously profited directly at Smith's expense. But suppose Smith has bought at 20 and sells to Pro at A0 who then sells to Jones at 80 and Jones later sells the stock back to Smith at 20. In that case, Smith and Pro have profited at the expense of Jones. But in addition, Pro also profited at the ex- pense of Smith, because Smith could have sold directly to Jones at 80. Only Pro was "right;" although Smith made a profit. lIbid., p. 32. 12 Although the public does outnumber the professional segment, the professionals can usually exert more influ- ence on the market because all their funds and energies are devoted to this purpose. Moreover, they possess ample working capital and so can afford taking losses as must happen occasionally. Or, in ”testing” the market, they can afford to buy large blocks of stock to find out whether purchase is difficult or easy, thereby learning how the public feels in order that they may do the appo- site. The basic principle of the professional operations is to act contrary to the majority. They assume that the market will-seldom do the obvious or take the course gener- ally expected. This is why the theory is usually found to work. The point is that the professionals can make a pro- fit by buying or selling at the same time as the public. It is not always the case but ordinarily they anticipate the problem and do the opposite. The entire theory is based upon a few elementary observations in crowd psychology, amounting to the fact that the public is usually "wrong." Thus, the public is: 1. Always bullish, 2 Little interested when markets are low and dull but become more so as they advance, 3. Attracted by market activity, A. More easily "shaken out" by inactivity than by reactions, 5. Willing to buy on good news and sell on bad news, and 6. Willing to absorb an amazing amount of stock on the decline following the culmination of an important advance. l3 Neill tried to analyze these circumstances as they appeared to the professionals and decide how they would act, either in response to certain prospective conditions or to the public's action. From this network of assump- tions and psychological observations (as above) he formu- lated his own opinion. His opinion was heavily weighted with the action of the public segment of the market and their influence upon the professionals. He made use of the daily odd-lot purchases and sales figures released by the Securities and Exchange Commission after March, 1936, Primarily, however, he relied on analyzing the factors affecting all parts of the market, whether they were economic, military, political, or of another nature. Writing as "The Ruminator," he felt that the public al- ways was late in recognizing new trends. Neill's Summary As Neill expressed it, "The theory of Contrary Opinion is based upon getting cause and effect in their correct channels. Which is to say that the horse must be hitched in front of the cart, not behind. When we recog- nize that pessimism is a result of poor business and falling security prices and that optimism thrives on ac— tive business and rising prices, we then perceive the logic of 'crossing' sentiment, of being contrary."l There lIbid., p. 58. 1A is nothing new in this. It is simply following the copy- book maxims that it is always darkest before dawn and that trees do not grow to reach the sky.1 "The Ruminator" is quick to admit that such questions as "How long will the darkness last?” and "How high do trees grow?" confuse interpretation of the contrary theory. As Garfield A. Drew expresses it, "The timing element is elusive. However, all economic forecasting contains a large amount-of intelligent guessing. The use of the con- trary theory requires intelligent guessing, too."2 Even today there is more of a conscious effort to assess opinion than there was in the years past. A tribute, perhaps, to the theory of Contrary Opinion. Neill is one of the first men to cast wide attention upon "the man in the street" as a possible clue to future market behavior. Also, he laid the groundwork for many studies and concepts of how to interpret odd-lot stock purchases and sales Statistics. Although Neill did not develop a_sophisticated, detailed timing technique based somehow on the action of "the man in the street," people did study this possibility shortly after his book was. published. Because the Securities and Exchange Commission for the first time was divulging odd-lot purchases and sales data, it provoked more similar studies in pursuit of a timing device based on the action cf the public. 1Garfield A. Drew, New Methods for Profit in the Stock Market (Boston, Mass.: The Metcalf Press, 1955). 2Ibid., p. 330. l5 Brookings Institute Study One of the first studies to utilize odd—lot stock statistics was made by the Brookings Institute in 1939. 1 This The author of this research was Charles 0. Hardy. 'exhaustive study of odd-lot trading (for a purpose other than forecasting) covered an eighteen-year period (1920 to 1938). The data was collected on a monthly basis for these years. Although Hardy was not seeking a timing -device, he did hasten the search for one. In the study Hardy said, "Public net sales are generally followed by price advances and public net purchases by price decreases. This phenomenon has been observed frequently enough to give rise to a tradition that the public is always wrong, or is wrong so often that movements of the odd-lot balance furnish a serviceable forecaster of stock prices."2 In Hardy's Judgment, however, the correlations have little or no real forecasting value because a forecast based on the behavior of the odd-lot public would be substantially the same as one based on the movements of the market itself. Hardy pointed out that his conclusion was similar to that of Dr..Kemper Simpson and Willis Ballinger3 in their critique of odd-lot dealers' policy of inventory management Odd Lot Trading on the New York Stock Exchange 1 (Washington, DIE}: The Brookings Institution, 1939). 2Ibid., p. 61. 3"The Feasibility and Advisability of the Complete Separation of the Functions of Dealer and Broker," A Re- port published by the Securities & Exchange Commission, 1936. 16 in 1936. Simpson and Ballinger found that the behavior of the odd-lot trading public was contrary to that of the round-lot trading public which dominated the price move- ments. Hence, the trades of the odd-lot public were "against the trend" and tended to stabilize the market, in so far as they were translated into round-lot trans- actions. Ballinger and Simpson's work was done before odd-lot statistics were made available to the public on a daily basis by the SEC. Of course, their book preceded the publication of Hardy's study. Because of the above hypotheses of both Hardy and Simpson and Ballinger, and the recent innovation of making daily odd-lot statistics available to the public, a further impetus was given to the search for some more definite and precise timing technique. It might be stated that Hardy's observation, "that the public is always wrong," is the same concept used today in the interpretation of the odd-lot stock trading theory found in many financial publications. Hardy's study also pointed out that the widely held assumption that the odd-lot trade is much less speculative in character than the round-lot trade is not completely true. He said this may not be valid because the close relationship between the volume of odd-lot trading and round-lot trading suggests that a large pro- 4’ portion of the odd-lot trading is speculative in character l7- and is controlled by the same factors that determine the volume of round-lottrades.1 Hardy states that, The preponderance of speculation in odd-lot trading is confirmed by a strong tendency of the volume of purchases and that of sales of odd-lots to go up and down together, the net balance of stock bought or sold by the odd-lot public always Being a small per- centage of the amount turned over. Garfield A. Drew's Interpretation After Hardy's contribution to the odd—lot theory, Garfield Albee Drew in l9ho followed with his book en- titled, New Methods for Profit in the Stock Market. Drew seems to be the first writer to actually utilise published odd-lot statistics in an attempt to time the market turns. Drew relied upon Hardy's study as well as the odd-lot statistics newly issued by the SEC each business day." When Drew first published his book he used four indexes (one major and three confirming indexes) to identify the phase of the stock market and to determine-turning points in the direction of market trends. In the last decade or so he has reduced these odd-lot indexes to two. A The rationale of Drew's theory pertaining to odd-lot statistics is that the public simply cannot compete with the trusts and other professional investors who operate 1Hardy, op. cit., p. 3. 2Ibid.,.p. u. 18 with more knowledge and less emotion.1 Many brokers, however, believe that Drew does not do the odd-lotter Justice. Even Drew himself admits that, while odd- lotters may be slow to recognize« short term trends, he has done well over the long run if he has held his stocks. Since 1920 the odd-lotter has generally bought more on balance than he has sold. Drew concedes that, "It should not be supposed that the public is always wrong and the professionals right."2 Wall Street and Drew often disagree about the nature of the little man but there is no doubt that he is impor- tant: in the past odd-lotters usually have accounted for approximately twenty per cent of the market's total volume. Drew's own record at calling the turns of the market (he does not predict trends, only charts them) has been mixed. He claims that his odd-lot index called the exact bottom of the market in the l9u8-9 and 1953-" recessions. But his critics charge that on at least one occasion, in the summer of 1958, when odd-lot purchases were high, Drew's theory indicated that it was time to sell. Those who did were sorry: the market then started to rise. Wall Street also charges that Drew places too much empha— sis on the odd-lot figures, though even Drew recognizes 6 1"Small Investor's Boswell," Time, March 31, 1951: p. 9. 2Drew, ;op. cit., p. 196. 19 their limitations by supplementing them with several other sources--economic,. political, military, etc. cli- mates and events. Market Characterization Drew described the stock market as being made up of Professional and non-professional elements, the"former being Wall Street brokers and speculators and certain institutional traders. The non-professional element constitutes the balance of the market and is termed "the public." Drew contends that the odd-lot trading ordinarily represents a fair sample of what the public is doing on 1 Drew further indicates: the New York Stock Exchange. It is also clear that, to a considerable extent, odd-lot transactions represent the buying and selling of those with insufficient capital to deal habitually in 100 share units, since odd-lot trading is more expensive because of the odd-lot dealer's extra com- mission. If, in the course of a week, there is a marked preponderance of the number of shares pur- chased in odd-lots over those sold, it is a reason- able inference that tse public thinks stocks are cheap and vice versa. In discussing the nature of the public reaction to the stock market, Drew states that: It has been remarked that a good psychologist might well be a better speculator than an economist. He would, for instance, try to analyze the stimuli professionals receive and decide how they would act, either in response to certain prospective conditions lIbid., p. 19A. 2Ibid., p. 195. 20 or to the public's action. Public reaction is more simply analyzed in that, broadly speaking, the public will buy on good neWs and sell on bad news. Drew was a close friend of Humphrey Neill and paral- lels Neill's method of analyzing the market but, unlike Neill's approach to the "Contrary Opinion" theory without data, has recourse to statistics. By the term "without data," it is meant that Neill used no odd-lot stock statistics in the process of arriving at an Opinion. According to Drew, the odd-lotter is captivated by market movements rather than by the intrinsic value of the stock. Business prospects, earnings, and dividends mean little in comparison with a 10 point rally or a decline, and it is in this largely futile attempt to "catch" these moves perfectly that the public is "wrong."2 Drew's entire odd-lot theory is constructed upon the assumption that it is not the number of shares bought or sold on balance that is important, but the proportions of buying or selling to each other. This is the main dif- ference between the current concept of the odd-lot theory and Drew's version. Drew has been accused of changing his concepts of the theory to comply with current notions but he has emphatically and repeatedly denied the charge that his prophecies are based on the absolute figure of net balance purchases or sales. In short, Drew would say that 11bid., pp. 192-93. 21bid., p. 197. 21 the trend of sentiment as indicated by the odd—lot balance of trading is more important than the side on which the balance lies. To illustrate this point Drew said, Odd—lot trading will be well on the buying side at the bottom of a drastic decline, but it will be proportionately less so than it was on the way down. Also, the weekly balances never show a preponderance of selling around important bottoms, although on a few individual days there may be such a balance. Primarily, it is always just a matter of less buying. The converse is true with respect to odd-lot selling on a top, although here there wi 1 be more times when an actual buying balance exists. He goes on to explain that, although the public is never "wrong" in the sense it buys around every bottom, it is almost invariably "wrong” in that it buys proportion- ately less at the bottom than it did on the way down. Further, a change of sentiment on the part of the public after any market trend has been well established is almost always just the opposite of what it should be.2 With all these underlying assumptions Drew devised his indexes. Drew's Indexes The use of ratios is the most logical way to approach the problems of interpreting the actions of odd—lotters because the volume of odd-lot transactions is always geared lIbid., p. 198. 21bid., pp. 198—200. 22 very closely to the total volume of trading. Its propor— tion, a somewhat relative constant, for the past decades has averaged ten per cent of all trading.1 Drew refers to the total trading in a different manner than usually appears in many publications. He doubles the round-lot volume because each share traded represents a share bought and a share sold. He claims that this gives a better picture of the actual number of people involved in the market. He also indicates that the conclusions are just as valid without this feature. After doubling the reported round-lot volume he naturally adds to it the odd-lot purchases and sales figures for the same time interval to determine total volume. In the ‘literature it is often mentioned that the odd-lotters are responsible for approximately twenty per cent of the total volume traded. This is the same estimate Drew uses based on his system of doubling the round—lot volume. Although ten per cent (according to Drew's method of interpretation) is the average figure, there are some minor variations. On Monday of almost every week odd—lot volume is usually relatively high-—apparently due to the fact that many small share holders arrive at investment decisions over the week—end. Drew points out that, while 1 Garfield A. Drew, ”Misunderstood Odd-Lotter,” Barron's,'XLII (June 25, 1962), 19, ’ 23 short term variations have little significance, the wider changes that may occur over a period of a year or so do have some meaning. Moreover, Drew states that when the ratio of odd-lot trading to total trading is low, public interest is rela- tively small and the price trend is being set by the more dominant segments of the round—lot market. Invariably, he says, such periods have coincided with the early up— swings in stock prices. Conversely, high percentages of odd-lot volume have appeared when stocks were selling around what proved to be minor or major tops.1 The Major Balance Index.-—The ratio of odd—lot selling to buying, which Drew considers the more important relation- ship, is actually his so-called ”Balance Ratio." In de— riving this ratio, he divided the number of shares sold by the number of shares purchased (S/P). Thus, if sales hap- pen to exceed purchases, the resulting "Balance Ratio" would be above 100.0. If purchases exceed sales, this ratio is below 100.0. This ratio (or index) rises when the odd-lot trading either tends toward the selling side or the amount of selling increases. The reverse, pur- chases divided by the sales (P/S) would also give as use- ful a ratio (or index), but the other relationship (S/P) is used. This is done because the market should go up lIbid., p. 19. 2U ordinarily, when there is a tendency on the part of the odd-lot public to become more bearish, and it is easier to think of a rising line as having bullish connotations.l The long term average of odd—lot purchases and sales shows that purchases normally exceed sales at a rate of ten to nine, a relationship which may otherwise be expressed by a "Balance Ratio" of 90.0.2 Drew points out that in this respect the records are most advantageously kept by computing the ratios on both a daily and a monthly basis. He said that the monthly figures are significant because the changes they show are extremely valuable in identifying a true "selling climax" at the end of a sharp downward price movement. Such oc- currences are not frequent, but are important when they do arise. The immediate response to some unexpected news development also may yield a valuable clue. Drew formulates his first and major index by com- puting a ten-day moving average of the frequently erratic changes in the Daily Balance Ratios. This is done in order to clarify the trend. Each of the other indexes is also computed as a moving average because of the same possible daily fluctuations in the market. This ten-day moving average Drew called a "Balance Index"-—a term which he proudly indicates has since crept into the jargon of Wall lDrew, New Methods for Profit . . ., op. cit., p. 202. 2Drew, "The Misunderstood Odd—Lotter," 02- Cit-, p- 19- 25 Street. Thus, when the Index line rises, it means that the trend in odd—lot trading is toward the selling side, and that such trading is actually on the selling side if the figure is above 100.0. Similarly, a declining Index means that odd-lot buying is either increasing or is taking the place of selling. For all practical purposes, however, the level can be ignored. Drew stresses that change is the all important factor.1 According to Drew such shifts as above, however, are important only as they relate to changes in the trend of stock prices. The trend of stock prices is identified by the movement of the Dow—Jones Industrial Average. Contrary to pOpular belief, Drew points out, the public's first impulse is not to buy on strength and sell on weak- ness, but just the opposite. Consequently, he said, "When this initial response changes while the price trend con— tinues in the same direction, it is highly probable that the end of the movement is at hand."2 The Short—Sales Index.--Although the behavior of the Balance Index (which reflects all odd-lot purchases and sales) is the more important factor under such circumstances, Drew complements it by using minor Indexes. As indicated earlier, he now utilizes only two indexes where previously lIbid., p. 20. 21bid. 26 he used four. After years of experience with his charting of odd—lot statistics he claims that only the amount of odd-lot short selling is significant enough to consider in timing the market turns. For his purpose Drew uses a "Short-Sales Index," a five-day moving average of daily Short—Sales Ratios i.e., odd-lot short-sales divided by all odd—lot sales. He indicates that the odd—lot short- sales in general tend to increase on declines and de- crease on rallies.l Drew states that, The odd—lot short seller is a completely different breed of cat than odd-lotters in the mass. Not only is he very much in the minority, but also he responds quite differently to circumstances. This is not sur— prising. Very few people have the requisite turn of mind to be interested in short selling. In any event, the major difference to Drew appears to be: the mass behavior revealed by odd—lot trading shows that points of maximum selling are always reached on the way up, and in the early stages of bullish trends which the public regards with great skepticism. However, the odd-lot seller never sells with consistency or increasing intensity in a rising market. In stock trading language, the odd—lot short seller never tries to "feel for a tOp."3 He is only prodded into exceptional activity by the lDrew, New Methods for Profit . . ., op cit., p. 205. 2Drew, "The Misunderstood Odd—Lotter,"op cit., p. 20. 3Ibid. 27 spectacle of sharply declining prices, at which time he proceeds to pattern his action after the majority. In— variably, however, the more prices decline, the greater his willingness to sell, with the result that odd-lot short sellers reach a maximum close to the exact bottom reached by the market. To be sure, Drew says, maximums are not apparent until they are past, and they may reach different heights at different times. Nonetheless, odd—lot short selling will rise sharply during a market decline of any magni— tude. When such a rise coincides with a shift in odd-lot trading as a whole from relatively heavy buying to lighter buying or even to selling, Drew points out, it is a vir- tually foolproof indication that the bottom has been reached. Drew emphasizes that the Short—Sales Index is less useful at tOps. True, it will always be very low at such a time, but it may have been just as low for some time while the market was on its way up. Thus, there is no indicated absolute correlation as in the case of short selling maximums always coinciding with market low points. Consequently, by using the Short—Sales Index to confirm the Major Balance Index and by the necessary evaluation of these two indexes in light of an unexpected news develop- ment caused by economic, political, military or other fac- tors, Drew completes his case. lIbid. l 28 The other two minor indexes that Drew previously used were the "Volume Index" and the "Order Index.” The Volume Index.——There is a strong tendency for the volume of purchases and sales in odd—lots to go up and down together. The net balance of the stock bought or sold by the odd-lot public always is a small percentage of the total volume during any period of time. The actual Volume Index is constructed by compiling a five day moving average of the Daily Volume Ratios. The Daily Volume Ratio is found by adding the odd-lot purchases and sales for each day and dividing the result by twice the total reported daily volume of trading. The Volume Index is ordinarily high around market bottoms and low near tops (percentage—wise). One would assume the opposite but such is not the case, according to Drew. He bases this conclusion on a combination of two factors. First, the greater and often mistaken con- fidence which may be engendered by an advance leads the person who ordinarily trades in odd—lots to go in for round-lots of low priced stocks, thus reducing the usual proportion of odd—lot trading. Secondly, in market breaks, the ranks of odd—lot traders are temporarily swelled by the addition of the bargain-hunter class. This factor would also eXplain why there is usually a preponderance of odd- lot buying around bottoms. Drew also indicates that his experience shows that a decline in the ratio of odd-lot 29 trading to total trading during a market advance is a bearish indication, and vice versa. The Order Index.-—The third subsidiary index used by Drew to help confirm the direction of this Balance Index was his Order Index. His is also known as the Index of Variation. The Order Index is obtained by compiling a five—day moving average of the Daily Order Ratio. To form the Daily Order Index, Drew divides the number of shares sold in odd—lots by the number of orders to sell. The result is the size of the average selling order. The size of the average buying order is similarly computed. Then the ratio is determined by dividing the average sell order by the average buy order. As in the case of the other two subsidiary indexes (Volume and Short-Sales) the Order Index also tends to rise on declines and fall on rallies. This simply means that around bottoms the number of shares in the average sell order tends to exceed the number of shares in the average buy order, and the opposite is the case around tops. The explanation for this phenomenon, says Drew, is perfectly logical./ A decline in stock prices brings about a certain amount of fear and caution among the oddmlot public. Consequently, they are likely to be selling the lower priced speculative stocks (bought when they had 30 greater confidence) and buying only in the higher priced and less volatile brackets. Since they will naturally have had more shares of the lower priced stocks, the average odd-lot selling order is, therefore, likely to be for more shares than the average buy order, the latter reflecting the acquisition of fewer shares of higher priced stocks. Just the reverse, Drew points out, is true on advances when public sentiment becomes emboldened. One minor reason why Drew decided to drop this index was that the available data (the number of orders placed daily) has not been made public by the Securities & Exchange Commission since Febru— ary, 1954. This is a secondary reason, but one worth men- tioning. The real reason Drew said that he decided to elimi- nate the Volume Index and Order Index after years of usage was not that they proved misleading, but that they did not add any support to the valuable indications of the Balance Index and the Short—Sales Index.l Principles of Interpretation.—-If all four Index lines show a rising trend against a market decline, the implica— tions for the market are bullish. The reverse is true in case of a market rise when the Indexes fall. More impor— tance should be attached to the Balance and Short—Sales In- dexes than to the indications of the Volume and Order Indexes. lDrew, New Methods for Profit . . L, op, cit., p. 3A3. 31 When the Balance Index line goes down while prices are rising, the odd—lot public is becoming more bullish on the advance than it has been previously. It makes no difference whether the Index declines because purchases are exceeding sales by a widening margin or sales are exceeding purchases by a narrowing margin. It is the fact of the trend and not the level at which it appears that is important, says Drew. Such a picture has a bearish effect on the market, since the change of senti- ment thus portrayed is probably mistaken. Similarily, if the Short-Sales Index rises while the market is going down, it is a bullish indication because it means that the more market prices are declining, the more bearish odd-lot short sellers are becoming, and they are also likely to be wrong. When the odd—lot group becomes ”abnormal” in its behavior the Indexes diverge from the market trend, in— dicating a change of sentiment which almost invariably proves wrong.1 When the group moves parallel to the trend, it means that the odd—lot public is exhibiting its normal reactions. That is, it sells on increases and buys on declines. No particular significance can be drawn from this situation. lIbid., pp. 209—210. 32 If Drew's whole hypothesis is correct it is evident that the trends shown by the Balance Index should repre— sent in reverse an index of the rise and fall of profes— sional sentiment, since it is assumed that the professionals habitually COpper the public.1 Drew constructed his moving average Indexes on a weekly and monthly basis and he found that with rare exceptions the trends are exactly Opposite to those in a comparable Balance Index of round-lot trading. Drew points out that diverging trends for a period of six to twelve days, depending upon the speed and decisive- ness of the trends in both the market and the Balance In- dex, should provide a valid buying indication. On the other hand, in the case of a tOp formation a valid sell order is indicated after ten to fifteen days of a definite divergence between the Balance Index and the market trend.2 Since even so-called buying climaxes are never as sharp and swift as selling climaxes, there are rarely comparably sharp reversals in the Index at such a time. Consequently, the divergent trends are likely to last longer. In the majority of instances the amount of time needed to gauge 3 a top formation is twelve days. Parallel trends between the Balance Index and the market may continue for long periods, in which case the last decisive indication lIbid., p. 212. 21bid., pp. 225-226. 3Ibid., p. 229. 33 of divergence remains in force unless definitely dis— proved.l A Secondary Advantage.--One of the minor advan- tabes of Drew's Odd-Lot Indexes is that by their very nature they can only indicate buying on weakness and sel- ling on strength. Thus, they are not subject to the whip— saws which tend to plague approaches that rely directly or indirectly upon the breaking of so—called resistance levels. According to Drew, there must be a price decline before the indexes specify that stocks should be bought, and an advance previous to their sell indication. The necessary information is always immediately available, as the record of odd-lot trading for any one day appears early the next morning. Most of the time this is not important, but Drew claims that it can be vital when the market is approaching a climactic bottom. He adds that, coming after what has gone before, one day's behavior may tip the scales at such a time. It is always, however, an interpretive affair and there is nothing about Odd—Lot Indexes, he emphasizes, that smacks of a mechani- cal system for beating the stock market. They are merely a means of determining the changes in public psychology which often have an important bearing on stock prices.2 lIbid., p. 232. 2Drew, "The Misunderstood Odd-Lotter," op cit. p. 23. 34 On the whole, the imperfection of the Odd-Lot Indexes lies in the fact that not every intermediate top or bottom is preceded by a divergence between the market trend and the Balance Index. The parallel course may con- tinue throughout, thus producing not a wrong signal, but simply no signal at all. When they do "talk," however, it is seldom safe to ignore the message, insists Drew. When such decisive divergencies have appeared they have never been wrong in the sense that the market failed to reverse its trend in the indicated direction. In other words, the errors of the Odd—Lot Indexes are errors of omission rather than positive errors of commission.1 The same principles of behavior as one may observe on short—term price movements have always shown up on the longer term trends of stock prices, according to Drew. For dealing with the latter term Balance Ratios, a Balance Index, and a Short-Sales Index are also used, but the base figures employed arerMNNHfiuIinstead of daily totals. These Indexes are three—month moving averages of the Ratios. The accompanying illustration (Chart 1) of the long- term Odd—Lot Indexes covers a period of approximately 13 years. This gives an idea as to the actual picture that Drew attempts to chart from odd-lot statistics. The mass behavior shown in this period is no different from that lDrew, New Methods for Profit . . ., 0p. cit., p. 231. 35 650 Dow-Jones Industrial Average W Monthly Mean Pric. 550 (Scale Left) M/ / w v Balance Index Trend of Buying Sentiment m wx/f (5.... m...) ,0, A (W) M A M": ‘\ . \« F . I ... . W W W *:: .110 Short Sales Index 30- Trend of Selling Sentiment - 7° Scal Left 20 ( . ) M 65 "(W W 1940*[19493[3§so [1951,11952 [1953 [1954‘Il955’11956411957 [1958 [1959 [1960 [l96141é2 Chart l.——Comparison of the Dow-Jones Industrial Averages With Drew's Indexes 1948—1962. 36 which appears in the entire record available, as far back as 1920. Drew attempts to analyze all the significant turning points and phases of the market from 1920 to the date of his publication. Because it is difficult to do justice to the whole analysis for this time span in a brief space and since it does not contribute any more to the basic understanding of Drew's Odd-Lot theory, it has been omitted. Drew's Conclusions Drew points out very clearly in his book that the interpretation of the Odd-Lot Indexes in the light of current circumstances is necessary for any pronouncement as to the phasing of the market. He also stresses that no rigid mathematical formula can be applied to every situation to produce an answer. According to Drew there is not and probably never will be any such thing as a perfect system to call the turns in the market. He just attempts to chart the trends and identify them as turning points. He does not actually attempt to pinpoint the day of the turning point but within a range of days he hOpes to determine a new phase of the market. In this sense he attempts to calculate the turning points of the market from odd—lot statistics. He points out that his method is not a perfect yardstick but the best available to gauge the changes in public sentiment. As a rule, Drew says, the indexes have been more decisive in their 37 indication of the bottom than they have been at the tops. Drew relies on the records to prove that during the course of violent and straightaway declines, they have always prevented premature buying and have come very close later to indicating the exact bottom. It is a virtue of any method, says Drew, if it characteristically can indicate a purchase on weakness and a sale on strength, rather than after the new market trend has started. According to Drew, no decisive divergence has ever proven him wrong as far as a temporary reversal of trend was concerned. He empha- sizes the necessity of a decisive trend existing before taking action. Current Theory Drew, as was pointed out earlier, was one of the first to utilize odd—lot statistics to analyze the market trends. After Drew comes the current theory. The current theory cannot be traced to any specific time or individual. According to the literature reviewed, it did not appear in some of our leading financial periodicals and newspapers until after Drew's book. Since no one individual can be given credit for the current interpretation of the odd—lot theory it will be attributed to Wall Street in general. Wall Street has for many years cherished a caricature of the "man on the street" as a sheep ready for shearing; indeed, the notion that he is generally wrong about the market underlies the current 38 odd-lot stock trading theory. The general belief is that the odd-lot public becomes progressively more bullish as prices rise and does most of its buying at the tOp, only to end up so discouraged by the ensuing decline as to sell out at the bottom. This being the case, the theory indi- cates that, in order to be right, one must buy when the odd—lotters are selling and sell when they are buying. However, there have always been two schools of thought on Wall Street about the perspicacity of the public. One, called the "lamb and wolf theory," holds that the small investor or speculator is always wrong, and that if he is buying it is a danger signal. The other school is represented by those who have observed that in panics many small investors are buying stocks being dumped on the market.1 Actually, both are right or at least partially . correct. It is a danger sign when the "little fellow" begins to buy after a long rise but not when he or at least some of his confreres also buys at the later bot- tom. Broadly speaking, what happens is that the public is skeptical of any major bull market rise for a long time and is inclined to sell or to buy less as it pro- gresses. As the end of the move approaches, however, the public finally becomes convinced of its lasting lDrew, New Methods for Profit . . ., op. cit., p. 213. 39 qualities and begins to buy confidently and in greater prOportion. Then when prices soon after embark upon the downgrade, the buying increases for some time although when the final bottom is reached the purchasing is pro- portionately less than it was on the way down. However, this does not work exactly in reverse because odd-lotters never actually shift to the selling side at the end of a bear market. It is simply a matter of less buying. This is confirmed by the stockholders lists of large corporations. There is a definite tendency for the number of stockholders to increase in a falling market and decrease in the next rising phase. Thus, the small investor buys too soon and sells too soon, even though his inclination is is to buy on weakness and sell on strength. Although right in this general principle, of buying on weakness and selling on strength, the odd—lotters' ill—timed application makes him wrong in practice.1 In short, the followers of the theory believe odd— lotters always buy more stock as prices decline from a high, instead of buying near the bottom of the market. Supporters of the theory are also convinced that odd-lotters sell more stock at the bottom of the market instead of selling while the stock is near its high. Consequently, in order to maxi- mize profits, one should do the Opposite of the odd-lotters. lIbid., p. 21A. NO The current theory, rather than Drew's version, was chosen as the basis of this study because it is better known. Since both theories maintain that the odd-lotter is usually "wrong,” however, both Drew's version and to- day's version will be tested. Most Recent Theory In April, 1962, The New York Times ran an article about Wright Investors' Service of Bridgeport, Connecti— cut.l John Wright has improvised upon Drew's usage of odd—lot statistics, using somewhat the same formulas, but in reverse, and establishing parity points to indicate buy and sell orders. Mr. Wright says that technical studies are useful only because they show investment attitudes and judgments of investors in general and of certain types of investors—— at a given time. This is identical to Drew's theme. Mr. Wright states that: Any technical analysis of these attitudes is of temporary value and is, therefore, useful es— sentially only as an aid to investment timing. Mr. Wright enjoyed approximately two years of suc- cess but the tremendous net balance of odd—lot sales for lBurton Crane, "Small Investor is Often Right Unless He Sells Short," The New York Times (April 29,1962), Sec— tion F, p. 7. 2Ibid. 91 most of 1963 and the first half of 1969 has evidently brought about the end of the success of his statistical indicators. Other financial publications were searched for additional information concerning Mr. Wright but none was found. Mr. Wright was contacted for his views and a state— ment of his interpretation of the odd-lot theory but none was forthcoming. It might be pointed out that Mr. Drew was most cooperative in this regard. As far as can be determined the preceding traces the evolution of the odd—lot stock trading theory from the 1870's to 1969. Summary The primary objective of this chapter was to trace the evolution of the odd—lot stock trading theory from its beginning in the 1870's to 1964. When the literature was reviewed for earlier concepts of the theory it was found that there were so many scattered and fragmentary articles and ideas about previous theories that it was best to construct the history of the theory. The theory was traced back to the 1870's when the Wall Street brokers themselves had a timing device based upon the actions of the odd-lot traders. Their belief, which definitely paral— lels today's version, was that when there was a preponder— ance of odd—lotters willing to sell it was profitable for them to buy and vice versa. This idea never was given U2 much consideration because of the few financial publications existing then as well as the fact that only the floor brokers actually knew who was buying and selling In the 1930's Humphrey B. Neill began writing his bi— weekly letters of contrary comment on current economic trends. He was primarily interested in gauging public sentiment about the stock market. He felt, since the public owned most of the stock, that if it could be determined how different stimuli would affect their market behavior, a person could invest ac- cordingly. Neill did not use odd-lot statistics as such as a basis for arriving at an opinion concerning the market. How- ever, he provided impetus to the search for a device to measure the actions and reactions of odd-lot traders by using the newly published oddelot statistics. The first study to extensively utilize odd-lot statistics was the BrookingsInstitute Study be Charles 0. Hardy, in 1939. Hardy gathered these statistics of odd—lot purchases and sales by months for the years 1920-1938. Al- though Hardy was not seeking a timing device from the statis— tics, his publication indirectly encouraged a search for one. In the study Hardy found that the public net sales were gener— ally followed by price advances and public net purchases by price decreases. In Hardy's judgment this was of little value as far as forecasting went because it was a mirror reflection of the movements of the market itself. However, it closely parallels the current day theory. “3 One year after Hardy's study was published Garfield A. Drew introduced his Indexes. Drew asserted that the public, which could not compete with the professional sector of the market, was usually "wrong." In order to gauge what the public was doing Drew investigated the odd-lot statistics. Drew's entire odd—lot theory was built upon the assumption that it was not the number of odd-lot shares bought or sold on balance that was impor~ tant, but the proportions of buying or selling to each other. He elaborated on this when he pointed out that while the public is never "wrong" in the sense it buys around every bottom, it is almost invariably "wrong" in that it buys proportionately less at the bottom than it did on the way down. Drew measured this proportionate buying or selling by his indexes. He originally used one major index and three confirming ones. As time went on and he gained experience with his indexes, only one confirming index was found to be necessary. He devised his Major Balance Index by dividing daily odd—lot sales by odd—lot purchases and constructing a ten day moving average of these Balance Ratios. The reason sales are divided by purchases instead of purchases by sales was because the market should go up ordinarily when there is a tendency on the part of the odd-lot public to become more bearish, and it is easier to think of a rising line as having bullish connotations. 144 Drew then indicated that, after there was a divergence between this Balance Index trend and the market trend represented by the DJIA, turning points could be identi— fied. The tOp of a bull market would be considered near~ ing its end after ten to fifteen days of a consistently decreasing index trend and an increasing DJIA. Drew claims his technique will almost infallibly determine the climactic bottom of a bear market. He said that six to twelve days of a rising Balance Index and a decreasing DJIA signal the turning of the DJIA upwards. Drew added that the above had to be confirmed by a minor index. He called this minor index the Short—Sales Index. The Short-Sales Index is found by dividing odd— lot short-sales by all odd-lot sales. This would give a Daily Short—Sales Ratio and by compiling a five day moving average of these ratios, Drew determined his Short-Sales Index. In brief, the Short—Sales Index had to confirm the above divergence between the Major Balance Index and the DJIA to indicate an actual turning point in the market. Along with this confirmation Drew would also consider other external factors such as economic, military and political events before affirming that a turning point in the market was at hand. Drew claims that, when decisive divergencies between his indexes and the DJIA have appeared, they have never been wrong in the sense that the market failed to reverse “5 its trend in the indicated direction. In other words, the errors of the Odd-Lot Indexes are errors of omission rather than positive errors of commission. The current day theory on which the rest of this study is based was investigated. In short, the followers of today's theory believe odd—lotters always buy more stock as prices decline from a high, instead of buying near the bottom of the market. The theory also states that odd— lotters sell more stock at the bottom of the market instead of selling while the stock is near its high. This theory indicates that one should do the Opposite of the odd—lotters in order to maximize profits. In April, 1962, Mr. John Wright's version of the theory was first publicized. His theory was related to Drew's indexes except that he reversed them and established buying and selling points from them. As far as can be determined, this chapter represents the first history of the theory. CHAPTER III METHOD OF INVESTIGATION The Past The purpose of this thesis is to empirically test the current-day odd-lot theory by means of an investi- gation of individual stock issues. The analysis, which will be described below, will be the first empirical study either to add support to the theory or to challenge its validity by means of investigating individual issues. One individual wrote to the editors of the Stock Exchange Maga— gigg (September, 1957) and asked, "What available evidence exists to support the claim of the odd—lot theory?" The editors replied, "None at all, so far as we know." Since this time, it is believed, no supporting or challenging empirical evidence of the theory by means of investigating issues has been published. To review from Chapter II, the followers of the theory believe odd—lotters always buy as prices decline from a high, instead of buying near the bottom of the mar— ket. On the other hand, supporters of the theory maintain that odd-lotters sell at the bottom of the market instead of selling while the stock is near its high. Unless other- wise specified the odd-lot theory discussed in this thesis will refer to the above current—day notion. A6 47 In the past, an attempt to give empirical evidence has included the comparison of the Dow-Jones Industrial Average (DJIA) to Customers' Odd—Lot Balances by months or quarters. An illustration of this attempt is seen in Chart 2. In the 11—year period studied in Chart 2 (see page “8) the odd-lotters came into the market in greater numbers than every before. When this is weighed against the background of a sharply rising market, it would ap- pear to give support to those market observers who believe that, while odd—lotters as a group may be slow to antici— pate important shifts in the market, they have demon- strated good long—run judgment.l This thesis sets out to test the reliability of the market observations found in the preceding paragraph. The "Drew Odd-Lot Studies" also attempts indirectly to lend empirical support to the odd-lot theory even though Drew would probably deny this. In his article in Barrons, two years ago, Drew said, His (the analyst) sole concern lies in being able to make deductions from the sort of behavior which usually appear? at significant turning points in the stock market. In another sentence in the same paragraph he states, For in the interpretation of odd-lot statistics, notably by means of "Odd—Lot Indexes” developed by lMarvin L. Krasnansky, "A Look at the Odd—Lot Inves- tor," The Exchange Magazine, (February, 1961) pp. 738. 2"The Misunderstood Odd—Lotter," Barrons, Uune 25, 1962L p. 11. ”I" m M. 700 +1’ COOr / "t O 500L 3 f 5 322:3:0~\\ "V 400» f" + e f L 3/ ‘+ 3 200? ~+-2 IOO' +I 0 0 g 1 l i 1._ 1 1 _L 4' "' ' 050 '5' '5! ' 53 ' 04 {’55 '5. ‘57 '3. '5’ [“0 A8 Chart 2.-—Customers' Odd—Lot Balances Related to the Dow Jones Industrial Average, 1950-1960. 49 the author (Drew) some 20 years ago, the analyst is not interested in whet er odd—lotters as a group make or lose money. The two sentences seem to contradict one another. If Drew is interested in calling the turning points in the market it must be to either maximize profits or mini— mize losses. Otherwise, what good are the "Odd—Lot In- dexes" to investors to whom Drew sells his "Weekly Stock Market Letter"? Indirectly he is actually interested in whether the odd—lotters as a group are making a profit or not. As illustrated in Chapter II (page 11) there is only one individual who can actually claim to have made a maximum profit in the real sense of the word. Therefore, if the odd-lotters made it all, the professionals would not be professionals, and Drew's interpretation of the theory would be to no avail for practical usage. These two attempts to give direct or indirect empirical evidence to the theory are the only ones found. This thesis is based on the premise that the only valid test of the current theory must include an investi— gation of individual stock issues to see whether or not the odd-lotters as a group make less profit or have greater losses in their investments than the professionals or the so-called "round-lotters." The two major odd—lot dealers on Wall Street have indicated that an investigation of the different individual stock issues involved is necessary lIbid. 50 either to substantiate or to refute the theory. They place little confidence in previous attempts to do so. The Wrong_Approach The comparison of odd—lot balances to the thirty stocks used in the DJIA does not prove that the odd-lotters as a group are less successful in their timing of pur— chases and sales than the round—lotters. The majority of round-lotters might possibly trade stocks from among the other 1572 stocks listed on the New York Stock Exchange (NYSE),1 rather than the thirty stocks used in the DJIA. The DJIA also does not take into account non-industrial stocks such as utilities, railroads, and finance or ser— vice stock issues. The probability of a few of the non- industrial stock issues appearing among the most active round-lot stocks traded for a month is suspected to be high. In addition to the doubts of the two odd—lot dealers about the validity of the theory, this gives further evi— dence that the comparison of the DJIA with net balance of purchases and sales is not a valid proof of the odd—lot theory. To say that odd-lotters are slow to anticipate changes in the market may not be true if the profitability of the most active issues traded by both the odd-lotters and roundnlotters are considered for respective time 1The number of stocks listed on the NYSE as of Feb— ruary 1, 196A. 51 periods. Actually, the most active odd-lot stocks bought or sold are only computed on a yearly basis. Also, the most active round-lot stocks traded are not necessarily the ones comprising the DJIA. Consequently, to compare monthly net balances of total odd-lot transactions to the DJIA for statistical analyses, as Drew and the current chartists do, not only fails to substantiate the timing element of the odd—lot theory, but actually fails to draw a meaningful comparison between the odd-lot investors as a group and the round—lot investors. An extreme example to illustrate the pitfalls of the above method could be useful here. Assume that in a month 90 per cent of all round—lot transactions deal with stocks other than the thirty that comprise the DJIA. The 90 per cent repre— senting the volume of shares traded as well as dollar value. Then assume that 90 per cent of all odd-lot trans- actions for the same month are made in the so-called "blue chip stocks" or the thirty stocks used in the DJIA. According to the current empirical evidence no weight is given to the fact that in this case the odd—lotters purchased or sold better stocks. It is true that there are "good" stocks other than the thirty used in the DJIA. However, for the purpose of the illustration assume that there is a limited number. With the round—lotters ac— tively participating in only 10 per cent of the "blue chips" for the month, the DJIA is subject to magnifying 52 fluctuations which are not representative of the overall round-lot picture. Subsequently, an investigation of individual stock issues is a more representative approach to the theory. A New Approach This thesis will give a more meaningful comparison of the profitability of these two groups of investors (odd—lotters and round—lotters) based on the twenty most active stocks traded each month for the years 1955 to 1962. The years 1955 to 1962 were chosen because one odd- lot dealer did not have data for the years previous to 1955. The dealer said that the firm kept their records for about seven years for income tax purposes. The other odd- lot dealer, however, was able to furnish statistics as early as the 1900's. The most active stocks for each group will be taken only from the NYSE. (The actual method of comparison will be discussed in more detail later.) Furthermore, no consideration is given to the brokerage fees involved in all the various stock transactions. Profitability in the stock market is largely based on the timing of buying and selling of different "quality” stock issues. By determining the profitability of each respective investment group, the timing aspect of the theory will also be considered. This will not only tell whether 53 the odd-lotters buy later or sell sooner than they should but also if they have demonstrated good judgment in the long—run. The sample, which is stratified because it is limited to the NYSE and the twenty most active stocks traded each month, is probably as good a sample as can be taken for any stock market study. Several statisticians were consulted as to the reliability of the sample and all advised that it was well chosen. Standard deviations from both arithmetic means and geometric means were programmed into the computer analysis of this thesis to determine the nature of the sample for the seven year period under consideration. Determination of Sample The twenty stocks on the NYSE with the largest monthly volume of odd—lot purchases and sales were deter— mined from the records of the two odd-lot dealers in the country who execute over 98 per cent of all the odd-lot transactions on the NYSE. After looking at literally thousands of monthly volume figures for all the stock traded in odd-lots on the NYSE for the years under consideration, it was determined that a volume figure of 10,000 shares each month on one dealer's books was required to qualify a stock for the list of twenty most active stocks for that month. Actually, hindsight indicates that a much larger figure was sufficient but to make sure that each stock was 54 given an equal chance of being included in the sample, the 10,000 volume figure was used. After this deduction the records of the odd-lot stock transactions of one dealer were inspected by months for the seven years, stock by stock. Each stock which showed a volume figure for one month of 10,000 or more was recorded as indicated. After investigating the seven year span by months at one dealer's establishment, the other dealer's records were reviewed in the same manner. Subsequently, the lists of stocks taken from the records of both firms were combined. All together there were four lists: from each dealer a list of odd-lot stocks purchased and a list of odd-lot stocks sold. The twenty most active odd—lot stocks purchased and twenty most active odd-lot stocks sold by months for the seven years were determined from these lists. The offices of the odd-lot dealers are the only places in the country where this type of data is available. Both odd-lot dealers stated that no one had contacted them for such data for the same purpose. They did say that during the last twenty years two individuals had secured data of like nature for different purposes. This lends additional evidence that this study is the first of its type to test the odd—lot theory. The round-lot data was easier to obtain and compute. There are several financial periodicals and newspapers which carry either the daily or weekly round-lot volume 55 figures. The Commercial & Financial Chronicle, Barrons, New York Times and the Wall Street Journal were used to determine the twenty most active round—lot stocks traded each month for the seven years. The Sunday edition of the New York Times was used to determine the weekly volume figures for each stock. Once again, by trial and error, it was discovered that a stock needed at least a 30,000 volume figure for any one week to make the monthly list of the top twenty stocks traded. With this information, the Sunday New York Times' list of the week's transactions on the NYSE was consulted. Each stock on the NYSE was reviewed and the ones with a volume of 30,000 or more for any one week were recorded at the indicated volume figure. At least a A5000:fligure could have been used as well but to assure every stock an equal opportunity to appear in the sample, the 30,000 minimum was established. All the weekly totals for a month were then added to give a monthly total. However, many of these weeks would overlap in one month or another. Where this was the case the Commercial & Financial Chronicle or Barrons was consulted, depending on which was available, to adjust the monthly figures. For example, if at the end of July one day was in July and the other four days in August, the monthly figure for July would have subtracted from it the transactions for the first four days in August. Similarly, the August monthly figure would have subtracted from it the one July figure. This 56 procedure was followed in determining the round—lot data for all seven years. After all the monthly adjustments were made, the twenty stocks with the greatest volume were selected as the monthly sample. The sample actually consists of 5,0AO different stock selections for this seven year study as well as 20,160 different price considerations.* There is no denying that there is overlapping in individual stock selections for the same time periods among the groups compared. Part of this problem was alleviated by a weighting factor soon to be discussed in full. In short, the weighting factor is the volume of each stock each month. This factor eliminates identical representation of the stock in all three groups. Furthermore, the selection of the stocks used in the sample were investigated before computations were begun.» It was found that approximately seven or eight stocks would overlap between and among groups. Of course, there were months when there were as few as one and as many as fourteen which overlapped. As pointed out, the weighting factor helped to resolve some of this overlapping. Almost all the overlapping was done by the so-called "blue chips" such as General Motors, Standard Oil of New Jersey, General Electric, United States Steel, Westinghouse Electric, and *Note: A list of the actual stock selections used in each group for each month for the seven year period is shown in Appendix A. 57 American Telephone and Telegraph. Subsequently, it was felt that the overlapping would not distort the statistical findings of this thesis. Weighting Since the sample of stocks of each investors group to be used in the study is suspected to have some extreme price ranges as well as overlapping among respective samples, a weighting factor is applied. The weighting factor simply is the respective volume figure of each stock each month. The volume of each stock is multiplied by its respective prices at the different time intervals of comparison. This in effect puts all stocks on their cost basis. When all cost bases of the stocks in each monthly sample are combined, the total dollar cost of the portfolio value for each group of investors in this study is found. Comparisons are made on the basis of this portfolio value for each group of investors to determine which group has done the best. This gives a stock such as IBM, for example, with a price as high as $500 per share more equal representation in the monthly sample with a stock such as Benguet selling at $1 per share. The current theory uses no such weighting factor to alleviate the extreme price range problem. A geometric mean was also programmed for these data to test if its use would contribute to bringing the dispro— portionately priced stocks into a more representative sample. 58 Although the geometric mean would not give the profitability figures desired, it did indicate that the weighting factor employed (volume) was highly satisfactory and reliable for testing the theory. Comparison The success of different groups of investors can be tested only by comparing their respective profitability. Thus, the profitability of odd-lot investors relative to round-lot investors will be determined primarily by price appreciation and secondarily by dividend yield. The extent of profitability as indicated earlier will be determined by both the timing of purchases and sales as well as the individual stock selections. This thesis will take the twenty odd—lot stocks from the NYSE with the largest volume of purchases and sales each month from 1955 to 1962 and compare their profitability to: 1. The twenty round-lot stocks with the most active trading for the same periods, 2. The Standard & Poor's Composite 500 Stock Index of industrial, rail, utility, service and finance stocks for the same time interval and 3. The Dow-Jones Industrial Average. The S & P is used because it includes a broader selection of stocks and is thought to better depict the market's action. The DJIA is also used to show how it compared with individual stock selections rather than with net volume balances, as it is used by the current theorists. 59 The comparisons of individual stock selections will be made at six month, one year, and two year intervals. It was stated, in the 1957 study of the Stock Exchange, that approximately 80 per cent of odd-lot transactions by the public were investments for more than six months. From this evidence, the periods of comparison were chosen. The Three Groups Round-lot trading requires a match of buyer and seller or purchases equal sales (P=S). With regard to the odd—lot trading, however, purchases do not usually equal sales (P78). It is possible for odd-lot purchases to match odd-lot sales but the probability is infinitely small. The two odd-lot dealers stand ready at all times to buy or sell any odd-lot quantity on the NYSE (at a price differential over the first quoted ticker-tape price following the placement of an ordem and therefore P#S. Consequently, this thesis will investigate three separate groups of investors. The first group will be the round-lot traders. The second will be odd-lot buyers and thirdly, odd-lot sellers will be considered. Since the nature of the current theory is to review the net balance of odd-lot purchases or sales and draw interpretations from them, it is necessary to consider the odd-lot sales as a separate group. If the odd-lotters in general have poor timing then, the possibility that they sold too soon 60 has to be considered. More properly stated, the opportunity cost has to be determined. The round-lot figures, whether for sales or purchases, will be identical because of the matched trading require- ment. Consequently, the opportunity cost of round-lot sales is the same as profit for the round-lot purchases. Price Selection The price of the different stock selections in the samples will be determined as follows. The initial price to be used in the original period will be the closing price of each stock on the last business day of each month as indicated by the Wall Street Journal. At the six month, one year and two year intervals, the price will be the closing price on the first business day of the month following the lapse of the indicated time period. For example, if General Motors (GM) is in the January, 1955, sample at $50 (the closing price of GM on January 31, 1955), the price to be compared with $50 at the six month comparison period would be the closing price of GM on August 1, 1955. This extra day is added because the investor then has a chance to sell at any time after six months and still qualify for the capital gains tax and/or take the capital gain/loss in another taxable year. The extra day is added at the one year and two year intervals in order to be con- sistent throughout the study. This price selection is used for all periods as well as for all comparisons. 61 Price Appreciation or Depreciation In testing for profitability or the lack of it, the relative price increase or decrease will be computed for each group. Each group will have a monthly sample of twenty individual stocks and the price of each stock will be multiplied by its respective volume (weighting factor) to give a dollar value. All twenty stocks in each group will be represented by a dollar value and the individual groups (three for every month) will be represented by the summation of the dollar value of the twenty stocks for that month. This summation of the dollar value (total cost) each month is the total dollar amount of investment by each group, or their portfolio value. After finding the initial dollar portfolio value of each group every month, it will be compared to the respective dollar value of the portfolio six months, year and two years later. This comparison will show either a relative increase or decrease for the separate groups each month for the periods considered. A relative increase will represent price appreciation or profit while a relative decrease in the portfolio value will represent price depreciation or a loss. It is useless for the purposes of analysis to work with absolute dollar values because of the different dollar amounts invested by the various groups. The round-lotters 62 naturally invest larger dollar amounts each month than the odd-lotters. As a consequence, the only basis of comparison is on a relative basis. To determine whether the odd—lotters or the round— lotters have performed better, the monthly price appreciation or depreciation of the three groups will be charted and statistically measured against one another. Also, the three groups will be compared to the S & P as well as the DJIA in an identical manner to see how individual selections compare to the averages. The S & P and DJIA price apprecia— tion will be determined in the same manner as the other groups, except that their respective portfolio value will be represented by their index numbers. The arithmetic means of the 8A monthly price apprecia- tions and/or depreciations for the monthly groups of samples as well as for the DJIA and S & P will be found after all three periods of comparison. After the arithmetic means of all five have been computed, the standard devia- tions of each will be computed as well as the estimated standard error of the respective means. This will indicate the reliability of the relative averages. A six month moving average of the divergencies between the round-lot data and the other four entities will also be charted for all three periods of comparison to give visual support to the conclusions drawn. The round—lot data is arbi- trarily being used as a comparative base with the other 63 groups. Any one of the other four entities of comparison could have effectively been used. However, if one of the odd-lot groups was used as the base, then additional computations would be necessary to determine how the odd- lot data, not used as a base, compared to the round-lot data as well as the averages. Since all the data representing each group are on relative terms, this permits choosing any one group as a comparison base. If the relative results prove favorable to the round- ‘lot purchasing group, it will be concluded that at least part of the odd-lot theory, as it is known today, is true. If the conclusions favor the odd-lot data, it will be sur- mised that the theory is questionable. If the computed data indicates that the relative price increase for odd-lot sales is substantially smaller than the relative price increase for round-lots sold (found in the above purchase analysis) it will be concluded that the oddelotters are selling at the proper time. A larger relative price decline of odd-lot stocks compared to a smaller relative price decline for round-lot stocks would indicate that the odd-lotters are selling at the proper time, too. However, if the reverse holds true, the aspect of today's theory which deals with sales is true. In addition, comparing the odd-lot averages for each period with the averages of the S & P and DJIA will help provide additional proof or disproof of the theory. This is 614 because the S & P and DJIA are comparable to the round- lot group in that no odd-lot transactions are considered. However, this study holds that the round—lot sample utilized is probably more representative of the market than is the DJIA. Dividend Yield The dividend yield will be determined each month for the three groups in this manner: the dividends paid during the last twelve months for each stock in the sample will be multiplied by the stock's volume figure to obtain the total cash value of dividends received by the twenty stocks in each sample group. This total value of dividends for each sample group will be divided by the respective portfolio dollar value of each sample group at the designated periods of comparison. This will indicate the relative dividend yield for the monthly sample of each group. This is the best way to measure the dividend aspect of investment performance. The dividend yield is computed on the current prices of the stocks in the monthly samples instead of the prices paid for the original portfolio because the current price is the actual amount of purchasing power an individual is surrendering (time value of money) by leaving his investment with the respective corporations. In short, the investor is being compensated for loaning his current purchasing power to the corporation, and not for his financial history. 65 The possible effect of different cash dividend flows was considered. Because of the fact that the dividends of the last twelve months would be paid at different times for different stocks the time value of money was considered. A sample test was run on a thirty day basis to determine the significance of the time value of money for each group. The sample indicated that it was not necessary to consider the time value of money for dividends and that the arithmetic mean of dividend yields would suffice. Since the real test of profitability is the rate of price appreciation, dividend yields are given secondary consideration. When stock dividends were issued their effect was not allowed to enter the calculations. A stock dividend actually increases the number of shares out-standing and should theoretically reduce the price of the stock accord- ingly. Consequently, the current stockholder received nothing but an increased number of shares. The stock— holder is possibly less fortunate after a stock dividend because the high nuisance cost for handling such a trans- action reduces the corporation's retained income. On this theoretical basis stock dividends were not considered in the data used in this thesis. Any adjustment for a stock dividend appears hidden in the relative price increase or decrease computations which were previously discussed. It is assumed that the market reacts to such a dividend 66 accordingly by a price adjustment. Stocks which paid no dividends contributed nothing to the total cash value of dividends of their respective group. These stocks with no dividends had a lowering effect upon the monthly dividend yield of their group. In order to determine whether the odd—lot purchases, odd-lot sales, round—lots, DJIA or S & P did better with regard to dividend yield, the statistical measurement that was utilized previously in price appreciation or depreciation will be employed. If the results indicate that the dividend yield con- clusions favor the odd-lot purchase sample rather than round-lot sample, as would the previous test for price appreciation, the odd—lot theory is questionable. However, if the reverse is true, today's theory would have to be accepted. Furthermore, if the dividend yield of the odd- lot purchase sample is larger (or smaller) than that of the round-lot sample and if the round-lot sample of price appreciation is greater (or less) than the odd-lot sample of price appreciation for stock purchases, the con- clusion will challenge the theory. If the results are mixed the strength of the challenge will be estimated and indicated as such. If the results of the dividend yield test, as well as the price appreciation test, would favor the odd-lot sales sample, instead of the round-lot sample, the odd-lot 67 theory is still questionable. If the reverse is true, however, the theory would have to be accepted. If the dividend yield of the odd-lot sales sample has a larger (or smaller) opportunity cost than that of the round-lot sample and if the opportunity cost with regard to price appreciation for the round-lot sample is greater (or less) than the odd-lot sample, the conclusion will challenge the theory. Once again, if the results are mixed the weight of the challenge will be estimated and indicated as such. The S & P and DJIA dividend yields would enter into the conclusions in the same capacity as they did in the price appreciation or depreciation analysis. After combining the purchases and sales analyses there either will be empirical proof or disproof of today's odd—lot stock trading theory.* Other Considerations When discussing the current concept of the odd- lot stock trading theory, the question of mutual funds and the monthly investment plan frequently is raised. Some people believe that these two programs capture a large part of the stock investment capital of odd-lot traders. This is sometimes thought to have a distorting *Note: Appendix B will be included to give an example of a completed worksheet used in this thesis. Al- so, it will go through the basic computation of finding the average profitability and dividend yield of each group. 68 effect upon the published odd-lot statistics. In reviewing the theory, the impact of the stock-insurance programs upon the statistics was explored. Several large New York brokerage firms were contacted for their opinions of the stock insurance programs. They were critical of them because of legal implications as well as the fact that the records were difficult to maintain. Because of the lack of available information, this study omits the possible influence of stock insurance programs upon the odd-lot statistics. Mutual Funds Mutual Funds are usually cited as the major culprits who steal odd-lot investors from the odd-lot statistics. There is no denying that some investors, who would otherwise be odd-lot buyers, have purchased mutual fund shares. If the mutual funds have been absorbing money that ordinarily would have been used for odd-lot purchases there should have been a noticeable and gradual shrinkage in the propor- tion of odd-lot buying to total volume during the past fifteen years or so. No such shrinkage appears in the odd- lot purchase figures for these years. In fact, except for 1963 and the first half of 196A, the odd-lot purchases overall have increased substantially in relation to sales as well as absolutely.1 Hence, outside of the possible 1These statistics were received from the Securities & Exchange Commission, Division of Trading and Markets, Washington, D. C. 69 slight effect of a change in total volume, there seems to be no solid evidence that the mutual funds have had a definite effect upon changing the ratio of odd—lot purchases to total volume. In 1963 and so far in 196A the odd-lot purchases have decreased substantially in relation to sales. A speculative explanation of the situation is that the odd-lotter still has his fears of late May, 1962, when the market dropped drastically. They have not become convinced of the bullish trend as yet. Consequently, they are selling for fear of another so-called "correction" in the market. This Speculative explanation agrees with Neill, Drew, and current ideas as to the thinking of the odd-lot traders. Only time can tell whether this trend of odd—lot sales exceeding odd-lot purchases for the last one and one half years is not in accord with the theory. The market has been notably bullish since the extreme set back in stock prices in late May, 1962, The last one and one half years of odd-lot trading is not considered at this time to be a significant sign of a change to mutual funds. Consequently, mutual funds are not considered to have distorting effects upon the odd-lot statistics and the conclusions to be used in this thesis. It is also recognized that the mutual funds have an effect upon the round-lot statistics. To what extent the mutual funds do influence the round-lot statistics 70 is not known and is a thesis in itself. It is assumed that the mutual funds do not distort the round-lot statistics used in this study. The Monthly Investment Plan This program, known‘as MIP, was initiated ten years ago by the NYSE as a means of attracting Small investors to the stOck market. It aims to help investors buy stocks on a periodic payment basis. According to the plan, an investor can arrange with his broker regular monthly or quarterly purchases of a stock listed on the NYSE. Investments can be as large as $1,000 every month or as small as $AO every three months. The investor's account is credited with the exact number of shares including fractions, that his payments can buy. An investor in MIP can also have any dividends from his stock automatically reinvested. In 1960, MIP's peak year, 989,573 shares (or a little more than 0.1 per cent of that year's NYSE volume 767 million shares) were purchased through the plan. The number of shares purchased through the MIP subsequently declined steadily, falling to 829,000 shares in 1963. At the same time total volume has risen to more than 1.1 billion shares in 1963. This means that the 1963 MIP trading was 0.075 per cent of the total volume.1 l"Big Board's MIP Perks up Following Three Years of Decline," Wall Street Journal, April 2, 1964, p. 21. 71 MIP share volume is said, however, to have increased during the first two months of 196A and the number of MIP accounts has currently risen to more than 100,000 from 96,899 at the end of December, 1963. (The record is 108,8A9, set in November, 1961),1 Chiefly responsible for the increased interest has been the publicity a few brokerage houses have given MIP's tenth anniversary and a new MIP program devised by Merrill Lynch, Pierce, Fenner & Smith, Inc., the nation's largest securities firm. Merrill Lynch, which traditionally has accounted for about 60 per cent of all MIP business, began working with individual corporations late in January, 1964, to persuade the companies' employees to sign up for the plan on a payroll deduction basis. The employee accounts at each corporation are consolidated, resulting in a considerable reduction in bookkeeping expense for Merrill Lynch. And the corporation, in agreeing to the plan, pays all commissions--a saving for the employees. SO far Merrill Lynch says it has signed twelve companies including Gulf, Mobil & Ohio Railroad, Rexall Drug & Chemical Co. and William Wrigley, Jr. Go.2 Merrill 72 Lynch estimates 1,000 investors who never would have signed up otherwise have enrolled in MIP through the new program. But many brokerage firms remain apathetic toward MIP. And the stock exchange, which initiated the program, says it plans no special efforts to strengthen it. The apathy of the brokers stems mainly from the low profits in MIP business. Commissions on MIP accounts generally are small because most purchases are small. At the same time expenses for a broker run high because of the book- keeping involved in figuring fractional shares and in reinvesting dividends. "Our customers' men generally recommend mutual funds rather than MIP to small investors," says a partner in one New York brokerage house.1 He explains that sales charges for many mutual fund shares run as high as 8 1/2 per cent while the maximum commission the firm can earn on MIP business is 6 per cent. Sales expenses are lower on mutual fund shares because, for one thing, there is no sale of fractions of mutual fund shares. This same partner defends the practice on still other grounds, saying profits are not the only motive. lIbid. _ 73 We feel mutual funds are a little better for most customers than MIP, because the funds offer more diversification.l Another broker calls MIP "a flop". "It just has not worked out," he says.2 Because the MIP accounts for such a small percentage of total volume on the NYSE it is not considered to be a distorting influence upon the odd—lot statistics and the conclusions to be drawn in this thesis. In addition, it is possible that some Of MIP participants would not be investors at all if it was not for this plan. This being the case, the actual number of independent odd- lot buyers attracted to the MIP would not be as great as indicated by the MIP total volume figures. This would also lessen the possible effect of MIP upon the odd-lot statistics. Because of the apathy of many brokers toward the MIP due to its low profits, the MIP is not suspected to cause independent odd-lot investors in the immediate future to switch to the plan. Only time can tell how successful Merrill Lynch will be in attracting new members to the MIP through its payroll deduction technique. Then again, how many of these will be odd-lot buyers already in the market who will switch entirely to MIP? lIbld. 2Irwin Friend, "Stock Ownership," Fortune, February, 196“, p. 19“. 7A The question of the MIP's future has no bearing on the theory of the past or on this thesis. The MIP will perhaps be significant in the future but it is not fore- cast as such. Summary In the past empirical evidence was directly and indirectly used to try to prove today's odd—lot theory. Most of these attempts were in the form of a comparison of the trend of monthly net balances of odd- lot purchases and sales to the Dow-Jones Industrial Average; The DJIA, however, is not a true representa- tion of all stocks because it omits such non-industrial stocks as utilities, railroads, finance or service stock issues. The current theory also fails to consider that the majority of the monthly most active stocks may be those not comprising the DJIA. Consequently, it would be better to investigate different stock issues rather than to continue with the current method. The new method proposed in this chapter would give a more meaningful comparison of the profitability of the odd—lotters and round-lotters. Profitability in the stock market is largely based on the timing of buying land selling of different "quality" stock issues. If the profitability of the odd-lotters and round-lotters is determined then the timing aspect of the current theory 75 will also be tested. This test will not only indicate whether the majority of odd-lotters buy too late or sell too soon, but it will measure the performance of their investments. The statistical analysis of the current theory will include a monthly sample of twenty different stock selections for a seven year period (1955 to 1962). There will be three different groups considered. One group will be the round-lotters, another will be the odd—lot purchasers and finally, since there is Opportunity cost to consider, the odd-lot sellers. The monthly sample of twenty stocks for each group will be comprised of the stocks with the most volume of trading for the respective months. After all the monthly samples for each group have been determined the prices of these stocks at four different time intervals will be found. The initial price of each stock will be its closing price on the last business day of the month in which it appears in the sample. The closing prices six months, one year and two years, plus one day later will also be recorded for the same stocks. After the 20,160 price considera- tions are determined for the 5,0A0 different stocks in the total sample the monthly volume for each stock will be multiplied by all four prices. This will give a monthly figure called the total dollar amount invested by each group for the seven year period, as well as each group's investment dollar value at the three periods 76 of comparison. The initial amount invested each month by each group will then be compared to the group's port— folio dollar value six months, one year and two years later to see how profitable each group has been, if at all. This will render evidence as to the validity of the current-day odd—lot stock trading theory. The jprofitability will be tested from the dividend yield aspect as well. Dividend yield is considered although it is of secondary importance in determining profitability. The cash value of the dividends paid during the last twelve months for each stock in the sample will be multiplied by the volume of the respective stocks. After the multiplication, the total amount of dividends received by each stock in the sample will be added to give the total amount of dividends received by the monthly portfolio of stocks. The total amount of dividends received by the portfolio will be divided by the dollar value of the stocks in the portfolio. This will result in the relative dividend for each of the groups. The dividend yield for the three groups will then be compared to determine which group was most successful. This procedure will be followed for all three periods of comparison. At the end of this chapter consideration was given to the effect of mutual funds, the monthly investment plan, and stock insurance programs upon the published odd-lot statis- tics. If these programs lured sufficient numbers of odd-lot 77 investors away from the ranks of "regular" odd—lotters, the validity of these statistics would jeopardize the con- clusion of this thesis. It was concluded that the mutual funds did not affect the odd-lot statistics since for the last fifteen years the Odd-lot purchases as reported by the Securities & Exchange Commission have increased ab- solutely as well as relatively (to total volume on the NYSE). The monthly investment plan employed mainly by Merrill Lynch was found to represent only 0.075 per cent of the total NYSE volume in 1963. Because of this low representation of the MIP in relation to the total NYSE yearly volume as well as general broker apathy to the plan due to low profits, it was also concluded that the plan did not distort the statistics used in this study. Finally, little evidence was found about the stock insur- ance programs. Since the brokers on Wall Street contacted about this program were critical of it because of complex legal measures as well as formidable record keeping requirements, it was assumed that the program did not exert a misleading influence upon the statistics used herein. CHAPTER IV STATISTICAL RESULTS OF PRICE APPRECIATION/DEPRECIATION In this chapter, the actual detailed analysis of the theory in the area of price appreciation or deprecia- tion is discussed in full. The various statistical measurements utilized in arriving at conclusions are fully explained. The size of the samples in relationship to respective total volumes is presented. Furthermore, a table distinguishing the price range of stocks purchased and/or sold by the odd-lotters and round-lotters is found. All the statistical analysis shows that one aSpect of the theory is questionable but the other aspect is acceptable. The Sample The sample for the odd-lotters and round-lotters consists of their twenty most active (by volume) stocks each month for the years 1955 through 1961. It is felt that the investor expresses his uttermost convictions about the stock market by placing his money where he does. Talk is cheap. Consequently, by discovering where he casts the majority of his dollar votes in the stock market, in short, by determining the twenty most active stocks by volume, one can best measure his rationale. From this 78 79 reasoning, that the individual investors will put their money into stocks that they feel are the best ones at the time, the twenty most active stocks were chosen as being representative of the convictions of each group about the stock market. Since no one odd-lotter can exert in- fluence upon the twenty most active list alone, many odd-lotters have to express the same convictions before an individual stock reaches the top twenty list for a month. The usual case is that no one round-lot trader can influence the market, either. There must be two parties involved in order to consummate a round-lot trade. If no one is willing to sell a particular stock, no one can buy it and this stock does not even appear as "traded". This is not true of Odd-lot buying and selling. In summary, the dollar vote does indicate the convictions of investors in the market better than verbal pronouncements. A relatively large percentage of the dollar value is usually represented by the twenty stocks with the greatest volume each month. Therefore, the profit or loss of the twenty stocks for each of the groups is considered to be represen- tative of the performance of the investors in each group. As previously discussed, the period (seven years) is delimited because of the availability of data. It is, however, though to be representative of the current trends and thinking in financial fraternities. The period is free 80 of any major wars and depressions. However, it is subject to the recession started in late 1957 and ending approximately in early 1958, as well as the recent market setback of May, 1962. Overall, the possible distortion of the statistics or samples contained within is considered relatively small because of the lack of any abnormalities in the market brought about by major wars, depressions or deepening recessions during this period. The market in general from 1955 to the current date has had a rising character. However, there have been enough reversal points of the DJIA to provide sufficient testing of the theory by the chartists. In this thesis it is not proposed to single out any such reversal points and make comparisons to them. Its purpose is simply to establish which group of investors has the most profitable performance record. In order to be the most profitable, the investor has to buy cheap and sell dear. In short, stock market timing determines the degree of profitability or loss for investors. By looking at the timing aspect of purchases and sales of the odd-lotters and round-lotters, it will not only be determined which group is the most profitable but whether or not the odd-lotters are less successful than the round-lotters. This principle of the poor showing of the odd-lotters in comparison with the DJIA (round- lotters) is the basis of today's theory. ‘This thesis, in contrast, is built upon the idea that the group with the 81 least profit or greatest loss is the least successful regardless of the investor's classification. These notions will be tested by the analysis to follow. The actual twenty stocks involved in the monthly sample of each group are free of any deliberate bias. There are SOHO stocks used during the seven year study. This does not mean SOHO different stocks. Each of the 8A months (seven years) has sixty "most active" stocks so the total number is 8A x 60, or 5040. In many months there were individual stocks which overlapped as previously discussed. There were approximately 2A2 different stocks used during these seven years. (See Appendix A.) The sample is stratified in the sense that it is limited to the NYSE and to the twenty most active stocks by volume each month. In order to give an idea as to the percentage that each sample represents of its own universe, Table 1 is presented. As shown in Table 1, approximately 17.0 per cent of the total amount of all shares actually traded on the NYSE for the seven years (whether odd-lot or round-lot) are represented by the samples used in this study. This is a very high sample representation for any stock market study. Within the actual group by group representation the range of 15.3 per cent (for the odd-lot sales) to 19.6 per cent (for the odd-lot purchases) is not great. Furthermore, if one were to alleviate the 1955 figure of 10.8 per cent for the odd-lot sales, the range would 82 o.~a m.ma m.ma m.mH m.ma w.ma o.ma m.©H m.ma m.ma w.mH m.sa ©.©H 0.0m m.©H m.wa H.mH >.wa H.ma w.©H m.ma w.om m.©H m.oa m.ma m.am w.:m m.ma m.mH m.mH m.oa mpHQEmw pocHoEoo an UppCmmoLQmp oESHo> Hmpop go mwmucoopmm oHQEmm poa-pcsop an noncomosdos oEsHo> poH-ocsos Hmuou mo ownecoopmm mad -EMm mommsossa poa qUUo >9 Umpcmmmsdop mommnoLSQ poH-UUo Hmuop mo ommu2mosom OHdEmm poa-opo an poucomos -Qms mofimm poH-UUo Hmp0p mo owmpcoopmm ommsmaa Emmy 5 Hood owma mmma m wmma mmmfi wmma a B z m o m m m mmma Hmmfi nmzosne mmma mummy on» now pcmmondom moadsmm mSOfism> one once momso>flc2 o>flpooomom mo mowmucmosom--.H mqm mOHMm uoaluuo cam ossao> uoanvssop ho mwmucmohma no.“ mHmuou $3» a.“ DEMO .HmQ OCH BOA.“ mocmhmhhfiv .029 "0902 no.eos mmm.amo.s no.eoa amm.moa ae.ma mmo.sa «H.HOH mma.mmw macros He. won ea. cow nu u- u- I- eosuooo ma. mmm.H am. emo.a am. mom nu .. ooeuoom as. mms.H mm. mao.H mm. ads I- u- oemuoos mo. mam om. ear Hm. mam .. n- oosuoom mm. mw:.m mm.H mmm.s mm.a mmo.a c~.H =mo.s oomuoom _=m.m emm.sm m=.m mmH.m :s.m ome.m m=.~ =am.am oomnooa os.H =oe.ss em.H mm=.H. Ho.~ mmmsfl mm.H oec.HH oosuom Hm.m mmm.om ms.m moo.= 0a.: mse.m mm.m mem.mm omuom =e.m mmm.mm .oa.= Hs=.= Hm.= msa.m om.m ssm.om omuoe mm.m sem.mc HH.A e=A.s ma.m mom.e me.m oas.m= canoe Hm.HH oam.mmfi =m.=a =sa.ma ow.:H mo=.HH m~.HH Hmm.sm omlom .oo.cs som.meH .mw.H~ mme.mm ma.om mao.wa cm.=a mmm.mma omuoa em.ma mmm.mma mm.~H s:c.ma mm.HH mma.m ao.ma mmm.mHH canom om.o~ em=.mam mm.mH mam.sa om.ma oas.aa mm.am osssmms emnom mm.MH mmm.m=a Hm.c mam.m ss.m ==:.= ma.ma ~HO.:MH omuoa He.m mwm.oe em. mam as. mam mo.m sem.mm osuo a Hence a menopause a modem a con Ans oceaosoo coqneco canoe ounce uoqucco Aooov mead oe.mmmH sons mousse ncHHoa ece.so ncaosnm poo Ivcsom one uoalcvo on» how oszao> «0.:zocxd0hm.ommucoonmm ocm,hmHHOQII.m mqm¢e 86 distort the statistics used in this thesis. lAs previously indicated, the weighting factor would place these stocks, as well as all others, on their dollar basis in the portfolio. Consequently, one month a low priced stock can have a volume of 500,000 shares more than the other nineteen stocks in the monthly sample but at the same time have less representation in the dollar portfolio value. This is due to the weighting factor which is the price of the stock times its volume. As an example, suppose that Benguet, selling for $1 per share, has a volume Of 1,000,000 for one month, while General Motors, which sells for $50 per share, has a volume of 100,000 for the same month. By multiplying ($1) (1,000,000) the dollar representation of Benguet in the month's portfolio is found to be $1,000,000. General Motor's representation would be ($50) (100,000) or $5,000,000. Even though Benguet traded 900,000 shares more than General Motors for the month, General Motors has more representation in portfolio value, from which the comparisons are made in this thesis. Since the better stocks usually are thought to be higher priced and more representative of better invest- ments, they are given greater weight in the sample. In order to make the sample more equitable and to eliminate the individual stocks overlapping between and among samples this weighting factor was employed. This is more easily shown by considering once again a stock such as General 87 Motors. Even if GM appeared in all three groups one month, it would not be given the same weight in each portfolio because of its different volume figures. Consequently, by using the different volume figures for GM in each group, the extent to which GM overlaps among the groups for the month is lessened. An ideal sample would consist of the twenty stocks in which is invested the most money each month. Unfortunately, however, the data is not available and is not likely to be available in the future. At the other end of the spectrum high priced stocks such as International Business Machines (IBM) at $500 per share are thought to be traded mostly in odd—lots. Table 2 shows that this fact apparently is correct. Only the odd- lot sample shows trading of any stocks with a dollar value per share of more than $300. Furthermore, it is noticed that the odd-lot samples have a greater percentage of their total samples in the ranges from $50 to $300 than the round- lot sample. These high priced stocks are weighted as described previously in order to alleviate magnifying distortions of the statistics. Portfolio Values The actual statistical measure of the performance of the three groups is now considered. After the 50A0 stocks which comprise the samples were determined and the respective 88 prices (20,160) associated with each placed in perspective, the dollar portfolio value of each group was found. The 8A monthly (seven years) portfolio values for each group were computed by multiplying each of the twenty (representing each group) individual stock's monthly volume figure by their respective original prices as well as their respective prices six months, one year and two years later. These multiplica- tions determined the four dollar portfolio values each month for the Odd-lot purchase, odd-lot sale and the round-lot samples. The value of these monthly portfolios six months, one year and two years after the original transaction were then compared to the original portfolio values to determine the relative increases and/or decreases. Any relative increase of the monthly portfolio represented price appreciation or a profit for that particular group at the indicated period of comparison. If a relative decrease in the monthly portfolio value appeared, it represented price depreciation or a loss for that group at the particular period of comparison. After all the relative increases or decreases of portfolio values were computed for each of the 8A months at the time intervals of comparison, the arithmetic means of these in- creases and/or decreases were found for each group studied. These arithmetic means represent the average percentage in- crease or decrease in the monthly portfolio values of the various groups of investors for seven years. In other words, the means indicate profit or loss for the various groups of 89 samples. Besides the odd-lot sales, odd-lot purchases, and round-lot investor groups as discussed above, the arithmetic mean of the DJIA and S & P were computed for the same time intervals in an identical manner. The monthly dollar port- folio values of these two indexes are represented by their corresponding index numbers. Relative increases or de— creases in the index numbers were considered as average pro- fits or losses for the portfolio values of the stocks which the DJIA and S & P represent. Average profits or losses for the five groups (odd—lot purchases, odd—lot sales, round-lots, DJIA and S & P) being analyzed were compared to see which group was the most profit- able. (Throughout this study profitability is referred to as an accounting profit rather than an economic profit.) Primarily, the average profits or losses of the odd-lotters and round-lotters were scrutinized to test the theory. In order to estimate the reliability of the averages, the estimated standard error of the means for each of the five groups for all three periods of comparison were computed. The procedure for computing the estimated standard errors of the means as well as the arithmetic means is outlined in Appendix C. Table 3 gives the price appreciation for all five groups of investors for all three periods. Not all the figures in Table 3 were computed on a per annum basis. The percentage figures in P (six months later) 1 90 TABLE 3.--The Monthly Average Price Appreciation or Deprecia- tion in Portfolio Value for the Round—Lotters, Odd-Lotters, Dow-Jones Industrial Average,_ Standard and Poor's Composite Averages for all Three Periods of Comparison: Six months, One Year and Two Years After Initial Purchase or Sale (Percentage) Odd-Lot Odd-Lot Round-Lot Purchases Sales DJIA S & P Pl“ " 2.56% n.53x 5.A8% 3.78% ' u.51% P2'l A.36 7.77 8.53 6.31 7.33 P3* A.19 12.56 12.81 12.02 13.A6 P1 = six months later P2 = one year later P3 = two years later must be doubled in order to estimate the per annum rate of price appreciation. In'P3 (two years later) the figures must be divided by two in order to estimate the rate of price appreciation per annum. For P2 (one year later), however, the figures are on a per annum basis. Since the rates for all five groups considered in the table were computed on the same basis for each period (P1, P2, and P3) valid comparisons can be made using the figures appearing in the table. Empirical proof or lack of proof for the theory is contained in Table 3. All the figures in Table 3 show price appreciation for each period for all groups. ‘The odd-lot sales sample (OLS) recorded the highest price appreciation figure of 5.A8 per cent in P1 (six months after the initial purchase/sale of the portfolio). This fact reinforces the 91 current theory because the OLS group shows the largest opportunity cost of any group in P1' In other words, the OLS group sold at the wrong time and consequently for- feited their right to the 5.A8 per cent profit. Conversely, the odd-lot purchases sample (OLP) has the second largest price appreciation figure or profit (A.53 per cent) of the five groups. In contrast to the conclusions reached by re- ferring to the OLS, the OLP figure denotes that the odd- lotters had timed their purchase of stocks better than the round-lot sample or the DJIA. Briefly, the results pertaining to the OLP sample repudiate the theory. In period two (P2), one year later, the relative results are identical to P1‘ It is recognized that the appreciation of portfolio values in P2 has substantially increased since Pl’ That part of the theory dealing with sales is again verified, while the part concerning purchases is repudiated. Period three (P3), two years later, shows almost identi- cal conclusions. There are substantial increases in port- folio values for each group except the round-lot group (R-L) where there is a small decrease of .17 per cent since P2. The Opportunity cost of the OLS sample has risen to 12.81 per cent. However, instead of the OLP group, the S & P shows the second greatest appreciation in portfolio value. In fact, the S & P shows the largest relative appreciation in value of any group in P3. Since the OLS opportunity cost 92 of 12.81 per cent is larger than that of the R-L figure of A.19 per cent and the DJIA figure of 12.02 per cent, the theory is still proved correct with regard to sales for all three periods of comparison. These results do indicate that odd-lotters sell at the "wrong" time. Therefore, the sales aspect of today's theory is correct. Since the OLP relative appreciation of 12.56 per cent in P3 is greater than that of the R—L figure of A.19 per cent and the DJIA figure of 12.02 per cent, the purchase aspect of the theory is again challenged. In all three periods of comparison the statistics indicated that odd—lotters did not buy at the "wrong" time. This fact repudiates the theory. Following the reasoning of Chapter III as to the accep- tance or rejection of the theory, the total theory.is rejected because one part of it is untrue.1 Table A gives the estimated standard error of the relative means in Table 3. These estimates are acceptable for indicating the range of the true mean. A "T test" for large samples was also employed to determine whether the samples were poorly chosen. If this was the case the results of the study would be distorted. The test was conclusive in that, at the most, one of the means would be subject to .001 per cent probability of not being significant due to a poor sample. The "T test" results are found in Appendix D along with the method used to determine them. 1The implications of utilizing the statistics in Table 3 for investment purposes will be explained in Chapter VI. 93 TABLE A.--Estimated Standard Error of the Means Used in the Study (Table 3) for Each Group for all Three Periods of Comparison: Six Months, One Year, and Two Years After Initial Purchase or Sale P E R C E N T A G E Odd-Lot Odd—Lot Round-Lot Purchases Sales DJIA S & P Pl 1.35% 1.15% 1.15% 1.02% 1.08% P2 2.02 1.92 1.77 1.58 1.66 P3 1.82 1.98 1.93 1.62 l.A2 P1 = six months later P2 = one year later P3 = two years later To give an illustration of the conclusions and the statistics used in this thesis, charts are included herein. In order to eliminate extreme fluctuations a six month moving average of the various relative increases and decreases of the value of the portfolios six months, one year and two years after the initial purchase or sale of the portfolio is used.1 These charts add no further empirical evidence to the tests of the theory. They do, however, indicate the monthly fluctuations of the relative increases and decreases of the portfolio values for each group. From these relative 1The individual monthly relative portfolio increases and decreases for all five groups can be found in Appendix E. mea owma mmma mama SmOH omOH mmma h m E h m E h m E H. m E h m E h m E h. m E IIT 4 l A a - 4 a A t c ”A o n t a A l a 1A c . A. a . 0.0m. 13.0mw 9A .Hwas reaches mmas .csom\eoncrcpsa was oases lusts HmHuHcH who Lough whosoz xflm mommzopsm on-eco .noscm oonlcco .aooqupcaom can do noasw> HaomBLOE CH mommmsooa pcm mmwmosocH o>flpmaom no comflsmdgoo mmmsm>< mcfl>og pesos xwmnu.m Bm< mpHmOQEoo a_poom w osmocmum ocm mmppo>< HmaaumSUCH mwcowuzoo one go mOSHm> oafiomuhom CH mommoaooo cam mommopocH o>HpmHmm mo cowahmafioo owmao>< mcfi>oz coco: menu.: BmHermr no . . flsnthp password mcHnOerfiZewa xmmnu.m emmgio nu .u v.1w io.oas 43.01.; 97 mea coma mama mama mmma mama mwmfi .LI m h z _ m h z t m h E r m h z s m m z m h E m m E _ A l . a a a _ a . a _ 4 A q 4 .1 0 $ A 0 v + l 0 L4 0.0m .O.mm _ icon _ _ Mo.mm Iao.oos w 4 0.9.4 1. 0.0HH a. 1. OemHH /. i o.omH a o.mmH a o.omH .Homfi sweeten mmms .csom\eomccossa was aHeo . o.mms OHHomupom HwHOfiCH one Lough who» one mommao>< mpfimOQEoo m.aoom a osmocmum one ommpo>< . amaspmSUCH mOCOhnzon on» mo mosam> oaaow . 0.0:H Iphom CH homeomomo one mommopocH o>fipmaom mo :omapmasoo owwno>< mafi>oz coco: xfimuu.© em t p . - q s a q 4r 4 a a — A a a w .1 4 1+ + 1 + L111+ + $ L4 * ¢ A 98 Kimmmeosz .Heas cmaonro mama .csom\concropaa mes ossoeosoa , / \xu coaloco- II: 7 In: - Hescacg ore Conan memos oss noncrcpaa ocs-cco ”N / woscm oosncoo uuuuuuuu .nosem poouceo .nooa'ccsom one no mosses oasoe “<22 .. moon pesom uppom CH wmmmmCooQ UCm memmoCOCH m>flpmaom mo » Comfipdeoo mmmso>< mCfl>oz Coco: xwmll.m Bm 4> .somfi rmaoocn moms .osom\comeccpsa was oasodopoa HmeHCH ocp Looms happy 03% mowwso>< opfimOQEoo m_Coom cw Uhmncmpm UCm owwmo>< HmahuwzoCH wmcowuzoa one go mosad> OHHomuhom CH momsopooo ocm mommoCoCH o>apmaom Co COmHLmQEoo omwho>< wCH>oz Coco: xfimns.m quxo v v r O O x 7 ()\ LD (7\ lOO increases and decreases each month, the average profitability of the various groups studied was found and presented in Table 3, page 90. Summary In any stock market study, the reliability and validity of the sample used is always questioned. During the years which were used in this study there were no abnormalities such as major wars, depressions or deepening recessions to distort the statistics. Furthermore, the samples used were investigated for proper representation. The percentage of the total transactions on the NYSE represented by the odd-lot and round-lot samples was calculated. The Odd-lot sample was found to represent on the average for the seven years 15 to 20 per cent of all Odd-lot transactions on the NYSE, while the round-lot sample for the same period represented 17.0 per cent of all round-lot transactions. Therefore, the samples were accepted as representative of the various groups discussed. The fact that low priced stocks will more often appear in the round-lot volume figure and the high priced stocks in the sample of the odd-lots does not give unfair representation to the various groups. A weighting factor consisting of the volume of each stock in each sample was employed to give more equitable representation to each type of investment. 101 Following the discussion of the sample the actual statis- tical analysis for price appreciation or depreciation was ex- plained. After the samples of stocks were compiled and the corresponding prices recorded, the monthly dollar portfolio value of each sample was computed. The index numbers of the DJIA and S & P represented their portfolio value. After the original portfolio values were determined, the portfolio values of each group were computed six months, one year and two years later. Then these later portfolio values were compared to the original portfolios to determine relative increases or decreases in value. A relative increase represented a profit while a relative decrease meant a loss. After these mOnthly increases and decreases were found their arithmetic means were computed. These means represented the profitability of each group six months, one year and two years after the initial portfolio was purchased or sold. An estimation of the standard errors of these means was computed to indicate the reliability of the means. A "T test" for large samples was also utilized to see.if, by chance alone, the samples were not significant. The tests con- clusively proved the samples to be meaningful. After the determination of these means and standard errors, the profitability of the groups was compared. It was found that in all three periods of comparison the theory was partially wrong. In periods one and two the OLS group had the largest price appreciation of any of the five 102 groups. Since investors sold at these times, it represented opportunity cost. Consequently, since it had the highest Oportunity cost of any group, the OLS group, by selling the stocks when they did, forfeited the most profit of any group. This substantiated the sales phase of the theory. Conversely, in periods one and two the OLP group had the second greatest profit. This indicated that the timing of the OLP group was better than the DJIA, S & P and R-L groups. Consequently, it repudiated the purchase side of the current theory. In period three, the S & P showed the highest profit- ability Of any of the five groups. The OLS group had the second highest increase in portfolio value and consequently, showed a larger opportunity cost than the R-L group and .the DJIA. Period three, in addition to P and P2, proved l -the sales phase of the theory correct. Conversely, the R-L group in P3 showed a decrease in-profitability from periOd two. The OLP group, however, had a larger appreciation in its portfolio value than either the R-L or the DJIA. As it did in the previous two periods, this fact repudiated the current theory. It was concluded that the sales aspect of the theory was correct but the purchase aspect was not true. Since one part of the theory is false, the total theory cannot be true. 103 Concluding this chapter, charts were presented to give a visual representation of the statistics used in the price appreciation/depreciation test of the current odd-lot stock theory. CHAPTER V STATISTICAL RESULTS OF THE DIVIDEND YIELDS AND COMPLETE TESTING OF THE THEORY This chapter presents the dividend yield test Of the theory. The computation of the dividend yield is discussed in full. Also, the statistical results of the dividend yield tests are given for each group and the interpretation of these statistics is presented. The overall conclusion is that the sales aspect of the theory is correct but the purchase phase is challenged. Dividend Yield Computations The dividend yields were computed in the same manner as price appreciation in the previous chapter. The dollar dividends received by each stock during the twelve months immediately preceding the comparison periods of six months, one year and two years were found. For Pl the six months during which the stocks are con— sidered plus the six months immediately preceding the original purchase or sale of the portfolio constitute the twelve months used. In P3 the twelve months of dividends are the dividends received between P2 and P3. In P the twelve months of dividends are the dividends 2 received by each stock since it was originally bought 10A 105 or sold. This method of determining the last twelve months of dividends received by each stock was used for all groups of investors. These dollar dividends for each stock were multi- plied by the corresponding volume Of each stock. These dividend figures, representing each stock in the monthly sample, were added. This resulted in the total amount of dividends received by each monthly sample for all periods of comparison. Finally, the sum of the dividends received by each monthly sample was divided by the correlative portfolio value. (The portfolio value is the same one described in the preceding chapter.) This procedure determined the dividend yield for each monthly sample at the time intervals of six months, one year and two years. This method was applied to all round—lot and Odd-lot monthly samples. The monthly dividend yield of the S&P was taken directly from the Standard & Poor's Yearly Statistic Book of 196A.1 Several bankers, libraries, offices of investment brokers and the Dow-Jones Company were con- tacted for the monthly dividend yields of the DJIA, but they were not able to provide this information. Conse— quently, Barrons was consulted for the monthly dividend yield of the DJIA. 1Standard & Poor's Trade And Securities Stgtistics, 196A (Orange, Connecticut: Standard & Poor's Corpora-, tion, 196A), p. 125. 106 The final issue of Barrons each month was consulted for its DJIA dividend yield. Since the monthly closing prices were used as a basis on which to compute the divi- dend yields of the other four groups, the same procedure was adopted for the DJIA. The DJIA dividend yield figure in Barrons for the last week is based on that month's closing stock prices. It is recognized that there is some error possible in these DJIA dividend yield figures because some monthly figures include data from the one or two days preceding or following the month. This over- lapping of days, however, was held to a minimum by al- lowing a maximum of two day's dividend yields to be in— cluded from the month before or after in the month in question. For example, when July ends on a Wednesday, Thursday and Friday of the last week are August first and August second. Since three business days of July appear in this week, it is used to represent the monthly dividend yield for the DJIA. The August first and August second dates illustrate the maximum number of "outside" days that could possibly enter into a monthly yield figure. Since the prices of the DJIA stocks do not vary much in one or two days, the dividend yield figures used are ac— ceptable. After all the monthly dividend yields were com- puted, the arithmetic means of these yields were deter— mined. These means represent the per annum dividend 107 yield for each group. The estimated standard errors of these means were computed in the same way as previously described (Appendix C). Actual Dividend Findings The average dividend yields for all groups are found in Table 5. They are on a per annum basis. It is recog— nized, however, that at P1 the stockholders are entitled only to six months of dividends. Also, at P3 the stock— holders have received two years of dividends but the figure given represents only one year. They are all recorded on a per annum basis to facilitate the comparisons. Later in the chapter the breakdown of the relative dividends actually P and P are considered. received in P1, 2 3 Table 5.--Yearly Average Dividend Rates of the Portfolio Values Found for the Round-lots, Odd-lots, Dow—Jones Indus- trial Averages, and Standard and Poor's Composite Averages at all Three Periods of Comparison: Six Months, One Year and Two Years Later (Percentage) Odd-Lot Odd-Lot Round-Lots Purchases Sales DJIA S&P Pl* 3.A6% 3.32% 3.36% 3.89% 3.66% P2* 3.47 3-31 3.32 3.85 3.63 P3* 3.A6 3.23 3.31 3.67 3.A9 P1 = six months later P2 = one year later *‘U ll two years later 108 The greatest percentage difference between any two groups for any one time interval is .57 per cent, in P1' The DJIA has the highest yield of 3.89 per cent and the odd—lot purchases the lowest yield of 3.32 per cent. The difference of a little more than one half of one per cent, which on the surface does not appear substantial, can represent a notable amount of dollars when the dollar portfolio values are also substantial. This fact (one half of one per cent return on an investment being a substantial amount if the portfolio itself is large) is hardly applicable to the indivdual odd—lotter because of his very nature of investing small sums. However, when the odd—lotters are considered as a group it can make a difference in indicating which group is the most success— ful. Table 5 Shows that the DJIA has the highest dividend yield of any group for all three periods. The odd—lot pur- chases sample has the lowest dividend yield for all three periods. These facts support the purchase side of the theory and repudiate the sales Side. Since the DJIA has the highest dividend yield of any group, it received more dividends than the odd-lot sales sample. The DJIA, therefore, had the largest Opportunity cost with regards to dividend yield of any group. Although all five groups forfeited a certain amount of dividends by selling when they did, the DJIA forfeited the largest 109 dividend yield during each of the three periods (Pl-- 3.66%; P2--3.63%; P --3.A9%). The round—lot Sample for- 3 feited the second largest dividend yield. The theory maintains that the odd—lot sales sample Should have for- feited the largest dividend yield. Consequently, the sales side of the theory is repudiated by the dividend yield test but supported by the price appreciation test. Because the OLP sample has the lowest dividend yield, it has realized less profit than the other groups. The theory states that the majority of odd-lot purchasers earn less profit than the round-lotters. Thus, the purchase aspect of the theory is proven true. Summarily, the pur— chase aspect of the theory is supported by the dividend yield test but repudiated by the price appreciation test. The results of the dividend yield tests are directly opposed to the results of the price appreciation tests. But, on the basis of the dividend yield test, the theory is proven to be partially incorrect since the purchase aspect of the theory is supported while the sales aspect is challenged. It was stated earlier that if the results were directly Opposed or mixed, as they are, the strength of the challenge of the theory would be estimated and indicated as such. Before concluding the analysis of the dividend yield test, the estimated standard errors of the yields used in the study (Table 5) are presented in Table 6. These esti- mates are acceptable for indicating the range of the true yields. Table 6.-—Estimated Standard Error of the Dividend Yields Used in the study (Table 5) for Each of the Groups for all Three Periods of Comparison: Six Months, One Year and Two Years Later (Percentage) Odd—Lot Odd—Lot Round-Lots Purchases Sales DJIA S&P P1* .O9% .11% .09% .08% .06% P2* .08 .10 .09 .07 .06 P3* .08 .10 .09 .07 .05 P1 = six months later P2 = one year later P3 = two years later Note: The formulas used to determine the above are found in Appendix C. Overall Testipg In view of these mixed results and in order to indi— cate which group has been the most successful in each time interval, the findings of the two tests will be combined. The relative portfolio value appreciation for each group (Table 3) will be added to the corresponding dividend yield (Table 5). This will determine the total profita- bility and/or Opportunity cost of each group's portfolio Since the initial portfolio was purchased or sold. The theory will be tested by comparing the total profitability and/or Opportunity costs of each group. Since this entire study is in relative terms the combination of the dividend yield and price appreciation figures is feasible. 111 Table 7 gives the combined relative results of price appreciation (Table 3) and dividend yield (Table 5) at the six month period~for each group. The dividend yield figures in Table 5 are on a per annum basis. These figures in Table 7, however, have been divided in half because the buyers/sellers of the stock are entitled only to Six months of dividends. Table 7.-—Total Relative Profitability of the Portfolio for Each Group, Six Months After the Initial Portfolio Was Purchased or Sold (Percentage) Odd—Lot Odd—Lot Round—Lot Purchases Sales DJIA S&P Dividend Yield 1.73% 1.66% 1.68% 1.95% 1.83% Price Apprecia- tion 2.56 A.53 5.A8 3.78 A.51. Totals A.29- 6.19 7.16. 5.73 6.3A. There is a possibility that for some stocks the dividends paid during the last Six months (in this case, the six months during which the stocks are actually owned) are higher than those of the first Six months—-immediately preceding the original purchase or sale of the portfolio. It is assumed that this does not Significantly, if at all, distort the dividend yield figures used at the Six month period in the overall analysis. In P the portfolio of the odd—lot sales group has 1 the largest total relative profitability (7.16 per cent). 112 The S&P1 has the second largest portfolio profit of 6.3A per cent followed closely by the odd—lot purchase sample's portfolio profit of 6.19 per cent. The important fact, however, is that the DJIA portfolio profit of 5.73 per 1 cent and the round-lot sample's portfolio profit of A.29 per cent is less than the profit of the odd-lot purchase sample (6.19 per cent). Since the portfolio of stocks that the odd-lotters had purchased six months ago has a greater profit than that of the DJIA and round-lot sam- ple, the theory is challenged. The theory implies that the odd—lotters purchase the majority of their stocks near the top of a market trend. If this is true, they should either earn less profit or have greater losses than the round-lotters and the DJIA. 'In this case, they have earned more profit than the round-lotters and the DJIA. This fact does not support the theory. Table 8 gives the combined relative results of price appreciation and dividend yield tests one year after the initial purchase or sale of the portfolios. The figures are taken from Tables 3 and 5. Dividend yield figures are not halved because the full twelve months have matured. 1Since the S&P has such an encompassing number of stocks compared to the other groups studied, it is not- considered to influence the theory in any way. It is used to show how a sample of a few stocks such as the R-L, OLP and OLS samples of twenty each and the DJIA sample of thirty compare to such a large sample (five hundred) of stocks. 113 Table 8.--Total Relative Profitability of the Portfolio for Each Group, One Year After the Initial Portfolio was Purchased or Sold (Percentage) Odd-Lot Odd-Lot Round—Lots Purchases Sales DJIA S&P Dividend Yield 3.47% 3.31% 3.32% 3.85% 3.63% Price Apprecia- tion u.36 7.77 8.53 6.31 7.33 Totals 7.83 11.08 11.85 10.16 10.96 The portfolio of the odd—lot sales group again has the largest relative profitability (11.85 per cent). In terms of Opportunity cost, the OLS group has forfeited more pro— fit than any group that sold their stock one year ago. Subsequently, the results presented in Table 8 add more proof to the sales aspect of the theory. The OLP sample has the second largest total rela- tive profitability (11.08 per cent). The OLP sample has earned more profit than the other groups who bought stocks one year ago. This is in direct contrast to the current notion of the odd—lot stock trading theory. The combinedrelative results of price appreciation and dividend yield for P are presented in Table 9. These 3 results are derived from Tables 3 and 5. Two years have elapsed since the portfolio was first purchased or sold. The different groups have now received dividends for two years instead of one year or Six months as in the two 11A previous cases. In order to facilitate the computations, it is assumed that the dividends received are taken out of the market. The dividends taken out of the market, however, do represent profit and are included in the total relative profitability figures for the portfolio. Table 9.--Total Relative Profitability of the Portfolio for Each Group, Two Years After the Initial Purchase or Sale of the Stock Portfolio . (%) Round- Odd—Lot Odd-Lot Lots Purchases Sales DJIA S&P Dividend Yield 3.A7% 3.31% 3.32% 3.85% 3.63% (first year) Dividend Yield 3.A6 3.23 3.31 3.67 3.A9 (second year) Price Apprecia- tion A.19 12.56 12.81 12.02 13.A6 Totals 11.12 19.10 l9.AA 19.5A 20.58 In Table 9, for the first time in this overall analy- sis, the Odd-lot sales group does not have the greatest total relative profitability. The S&P has the largest profitability of 20.58 per cent while the DJIA has 19.5A per cent. The profit of the odd-lot sales group is l9.AA per cent, only .10 per cent less than the DJIA. The odd— lot sales profit, however, is 7.89 per cent greater than the profit of the round-lot sample. Since the round-lot sample is considered more repre— sentative of the majority's action in the market than the 115 DJIA, the results of the odd—lot sales sample in P3 sup— port the theory. This is indicated by the larger oppor— tunity cost of l9.AA per cent for the odd-lot sales as compared to the round-lot sample's opportunity cost of 11.12 per cent. The sales aspect of the theory states that oddelotters should forfeit the most profit (have the largest opportunity cost). This was the case for all three periods of comparison. Even though the DJIA forfeited only .10 per cent more profit than the odd—lot sales sample, it cannot be ignored. It merits recognition because the current theory is based upon the DJIA movements. The DJIA is not neces- sarily more representative of the total dollars invested in the market than the round-lot sample. The fact that it lacks the weighting factor of volume can have magnifying and distorting effects upon its portfolio values used. within this study. Only one Share of each stock in the DJIA is considered in arriving at its index number, which represents the monthly portfolio values. In the samples used throughout this study, however, a stock such as GM (which is also in the DJIA) could drop one point and, be— cause it is represented in the samples by price times volume (number of shares), would have a greater relative change in the portfolio values of the samples than in the DJIA. Once again, this points out one of the inadequacies of using the DJIA to measure the action of the majority in the market. 116 Even if the assumption were made that the DJIA is more representative of the action in the market, the sales aspect of the theory would still be substantiated in P3. By examining only the price appreciation (Table 3) of each group it is apparent that the odd—lot sales sample has a larger rate of appreciation than either the DJIA or the round-lot Sample in all three periods. Since the price appreciation figures in Table 3 were found over a seven year period, they are considered as an average rate of appreciation for each group. It is assumed that these average rates of price appreci- ation for each group will remain fairly constant in the future. If each group were to reinvest their respective dividends at their corresponding rates of appreciation, the Odd-lot sales sample would still Show the largest opportunity cost of any group for all three time intervals of comparison. Whether the DJIA or the round-lot sample is considered more representative of the market, the theory is supported in P3. The sales aspect of the theory main- tains that the odd-lotters should have the largest Oppor-' tunity cost. This is the case for all three periods of comparison. "Summarily, the overall analysis of the sales aspect of the theory proves that because the odd-lot sales sample has the largest opportunity cost (has forfeited the greatest amount of profit) of any group in all three periods of 117 comparison, the theory is correct. The empirical data in P1 and P2 the DJIA or round—lot sample was considered more representa- substantiated the theory regardless of whether tive of the market's action. In P3, by considering the round—lot sample as more representative of the market, the theory was again found to be valid. During the same period, however, the DJIA oppor- tunity cost was .10 per cent greater than that of the OLS sample. This fact is inconsistent with the theory and if the DJIA is considered more representative than the round— lot sample, the theory is disputed. But, if all groups reinvested their dividends at their respective appreciation rates the Opportunity cost of the OLS group would exceed that of any group at the end Of P3. By forfeiting the most profit (largest opportunity cost) in all three periods the odd-lot sales samplessupport the thoery. In the overall analysis of the purchase phase of the theory (Table 9) the profitability of the S&P (20.58 per cent) is the largest among the groups. The DJIA profita— bility of 19.5A per cent is the second largest, followed by the odd-lot sales figure of l9.AA, which does not enter into this part of the analysis, and the odd-lot purchases figure of 19.10 per cent. The round-lot sample has been the least profitable (11.12 per cent) of any group. 118 These results are contrary to the results of the first two periods of comparison. In the first two periods the total profitability of the odd—lot purchase sample exceeded the profitability of the DJIA and round-lot sam— ple. This proved that the odd—lotters were more profitable than the round—lotters and consequently disproved the theory. The OLP sample has a greater profit in P3 than the round—lot sample, which again means that the theory is challenged from the purchase aspect. In P3, however, the question of whether the DJIA, rather than the round—lot sample, is more representative of the market's action is raised again. The DJIA profit- ability exceeds that of the OLP sample by .AA per cent. The current theory uses the DJIA as its basis of comparison and, therefore, the greater profitability of the DJIA must be accepted as proof of the theory. However, an investi— gation of the breakdown of each group's profit reveals that the Odd-lot purchase sample has a larger rate of price appreciation than either the DJIA or the round—lot Sample (Table 3). Consequently, if each group would invest their respective dividends at their corresponding rate of appreciation, the odd-lot purchase sample would Show the greatest profit of any group that bought stocks. It is assumed that the average rates of price appreciation found in Table 8 will remain fairly constant in the future. This fact is true for all three periods of comparison. 119 Therefore, in P3 the theory is challenged from the pur— chase aspect whether the DJIA or the round—lot sample is assumed to be more representative of the majority's action in the market. Summarily, from the purchase aspect of the theory in P1 and P2 the odd-lot purchase samples repudiate the theory. In both periods the total profitability of the OLP samples exceeded that of the DJIA and round-lot sample. In P3, by assuming that the round-lot sample is more representative of the majority's action in the market, the theory was once again challenged by the statistics. However, by assuming, in P that the DJIA is more representative of the market's 3, action the statistics supported the theory. In order to further test the theory for an unquestion— nable solution, for P3, the reinvestment of each.group's dividends at their corresponding rates of price appreciation was considered. For all three periods of comparison the OLP sample then had the greatest amount of profitability of any group. Since in all three periods the OLP sample showed a greater profit than the DJIA or round—lot sample, it was concluded that the theory was not true from the purchase aspect. The theory states that odd—lotters purchase the majority of their stocks at the "wrong" time. If this is the case, the odd-lotters should not be as profitable as the round-lotters and the DJIA. This was not the case. 120 As previously pointed out in Chapter IV, if one part Of the theory is false the whole theory cannot be true. Subsequently, the previous empirical evidence presented does challenge the complete theory even while it supports the sales aspect of the theory. Summary In this chapter the odd—lot stock trading theory was empirically tested by considering the dividend yield for each group of investors. The actual description of the computation of the various dividend yields was outlined. The different yields were found by determining the total dollar dividends received by each monthly sample. This was done for all three time intervals of comparison by multiplying the volume of each stock by the corres— ponding cash dividend received during the last twelve months. Then by adding the dividends received by each stock (volume times dividends) the total cash dividends received by a monthly sample were determined. This total dividend for each monthly sample was then divided by the respective portfolio value of the sample as found in Chapter IV. This result of total dividends divided by the portfolio value determined the various monthly divi— dend yields for each sample. The S&P dividend yield was directly taken from Standard and Poor's Yearly Statistic Book of 196A. The DJIA dividend yield was computed from the yield as reported 121 in the last week's issue of Barrons each month. The possi~ bility of one or two day's additional data being included in the DJIA yield was discussed and regarded as not af— fecting the statistical results. After all the monthly dividend yields for all five groups and each period of comparison were found, the monthly average dividend yield of each group was determined. The monthly average yield was the simple arithmetic mean for the seven years studied. Also, the estimated standard er— ror of these yields was presented in Table 6. The results of the dividend yield test were the exact opposite of the conclusion drawn in Chapter IV. The results were mixed in that the findings of the price ap- preciation/depreciation analysis in Chapter IV supported the sales aspect of the theory while the purchase aspect was challenged. In this chapter the results of dividend yield tests question the sales phase of the theory while supporting the purchase side. Consequently, these mixed results were investigated further. An overall analysis consisting of a combination of the relative profitability of the price appreciation and the relative profitability of the dividend yields was utilized to determine the total relative profit of each group. This total profitability of each group was found for all three periods of comparison. At the six month period of comparison the fact that the dividend yields were on an annual basis instead of a 122 Six month basis was discussed. The annual yields were divided in half to represent a six month yield. It was recognized that some error was possible because the divi- dends of the last six months might be larger than the dividends for the first six months. However, this possi- bility was assumed not to affect the results. The total relative profitability of each group at the six month interval was presented in Table 7. The OLS sample had the greatest total profit of any group. This meant that it had the largest opportunity cost, or had forfeited the most profit of any group who had sold their portfolio Six months ago. Consequently, this supported the theory because the theory states that odd— lotters should have the largest Opportunity coSt. Concerning the purchase phase of the combined tests, the opposite conclusions were drawn. The OLP sample had a larger total relative profit than the DJIA or round-lot sample. This fact challenged the theory. The theory states that odd-lotters should earn less than the round- lotters or the DJIA. The one year comparisons were presented in Table 8. Once again, the same conclusions drawn for the six-month period were found. The sales aspect supported the theory while the purchase side challenged it. Table 9 was used to present the facts for the two year comparison. The dividend yields from the first year 123 and second year were added to the price appreciation figure‘ in order to determine the total relative profit. Upon in? vestigating Table 9 it was found that the conclusions were not as definite as the conclusions of the two previous peri- ods. On the sales side the difference between the profita- bility of the DJIA and the odd-lot sales sample was only .10 per cent. However, the round—lot sample was assumed to be more representative of the market and the profit of the odd—lot Sales sample exceeded the round-lot sample's profit by approximately eight per cent. Since the odd-lot sample had the greatest Opportunity cost of the two groups, the theory was supported. When the DJIA was used as a basis of comparison-the results challenged the theory. On the condition that each group would reinvest their dividends at their corresponding rates of price appreciation, it was concluded that the odd- lot sales sample forfeited the most profit of any group in P This now being the case, the theory was supported, 3. even if the DJIA was assumed more representative of the market's action. The current notion of the theory from the sales as— pect was substantiated by the statistical results. This was due to the fact that in all three periods the OLS sample showed the greatest Opportunity cost of any group. Since from the sales side the odd-lotters forfeited the most profit of any group, the round—lotters and DJIA must have 12A bought better stocks and/or timed their sales better. This evidence corroborates the theory. The results of the combined tests of the purchase phase of the study challenged the theory. In periods one and two the empirical evidence definitely questionned the theory. In P3, if the round—lot sample was considered as representative of the market, the theory was challenged. This was demonstrated by the larger profitability of the odd—lot purchase sample (19.10 per cent) over the round-lot Sample (11.12 per cent). However, if the DJIA was considered more representative of the market's action, the results of P3 supported the theory. Once again, the reinvesting of dividends at the corresponding rates of appreciation was discussed. As a result, the OLP sample Showed a greater profit than the DJIA in P This being the case, the 3. theory was challenged in P3 regardless of which group of stocks were considered more representative of the majority's action in the market. For all three periods the results indicated that the odd-lotters had earned more on their investments than the round—lotters or the DJIA. The theory, however, claims this cannot be the case. Consequently, the statistical evidence of the purchase aspect of the theory does not corroborate the theory. Finally, since one part of the theory was proven incorrect, the complete theory was determined to be in— valid. CHAPTER VI CONCLUSION The purpose of this study was to empirically test the current idea of the odd-lot stock trading theory by investi— gating individual stock issues. After inspecting every available source of information concerning the theory, it, was concluded that no attempt had yet been made to give a history of the theory. Literature concerning the theory was practically nonexistent. Also, no where in the litera- ture was there an attempt to Significantly test the theory. The little empirica1_evidence found was concerned with ex- plaining the point of view Of the individual writer. It was illustrated that Drew indirectly tested the theory but that he probably would deny it. Furthermore, the only other empirical evidence was found in financial publica— tions, in the form of charts comparing the DJIA movement with the monthly net balance of odd-lot purchases and sales. Since these two attempts were not convincing or considered adequate, a method was devised to test the current theory. In addition to this evidence of the weakness Of the pre- vious empirical tests, the two odd-lot dealers on Wall Street (who do over 98 per cent of all the odd-lot business on the NYSE) encouraged a test of the theory be investi- gating individual stock issues. ' 125 126 Before considering the technical aspects, a history was traced from the beginning of the odd—lot market in 187A. In the early 1870's the theory was more or less the hoary belief of the stock brokers on Wall Street. Due to the lack of financial publications and mass communications the actions of the various investing factions of the market were known only by the brokers directly involved in the trading of stocks. These brokers knew that if they would buy stocks when the majority of odd-lotters wanted to sell, or vice versa, they would make more profit than usual. From this early practice of the men of Wall Street the odd-lot stock trading theory has evolved. This idea largely parallels the concept of the theory today. The only difference is that the DJIA, used today as a basis of comparison, was not available in the 1870's. The theory was then traced to Humphrey B. Neill's "Letters of Contrary Opinion" in the 1930's. The published statistics were not available to Neill (statistics of the odd-lot transactions) at the time he published his letter. He reasoned that the professionals were the only peOple who could make a profit in the market. By trying to analyze the actions of the professionals, however, he found himself going contrary to general opinion about the market. Conse- quently, Neill pointed out that investors Should ascertain the general consensus of opinion and do the exact opposite. He would try to determine the action of the public by 127 analyzing all the factors of the market, whether they were economic, military, political or of any other nature. By trying to second guess the general public, Neill indicates that the belief of the early 1870's had been kept in tact up to the 1930's. Neill is given credit for introducing the additional factor of mass psychology as a guide to in- vesting in the stock market. The Brookings Institute Study in 1939 followed Neill's publications. Charles 0. Hardy investigated statistical data concerning the odd—lot traders from 1920 to 1938. Al- though he did not attempt to empirically test the theory, he did set into motion a search for a timing device using Odd-lot statistics. He found in his study that, "Public net sales are generally followed by price advances and: public net purchases by price decreases . . . ."1 From this quote have come the many interpretations of the Odd-lot theory found in current financial publications. One year after Hardy, Garfield A. Drew's interpreta- tion of the theory appeared. Drew was the first writer to actually use published odd-lot statistics to achieve a timing device for investment purposes. His idea was to construct indexes from the newly published odd-lot data made available by the SEC in 1938-1939 in order to determine when the odd- lot traders were "wrong." Drew believed that the trend of lHardy, Odd-Lot Trading on the New York Stock Ex— change, op. cit., p. 61. . 128 the odd—lot indexes, when compared to the DJIA trend, was the key to determining turning points in the market. He. also acknowledged that there is not and probably never will be a perfect system for calling the turns in the market. Drew, like the other people preceding turn rests his as- sumption on the fact that the odd-lotters are "wrong" more often than "right" when significant turning points in the market occur. Drew's book, New Method for Profit in the Stock Market, was the first publication to put into writing the implications of the odd-lot statisticp cpncerning mar- ket turning points. I 5‘5“) Finally, in tracing the history of the theory, the current notion of the theory was presented. That is, the Odd-lotters purchase more stock as prices decline from a high, instead of buying near the bottom of the market. Con- versely, odd-lotters sell more stock at the bottom of the market instead of selling while the stock is near its high. This concept is found in almost all the leading financial periodicals and newspapers of today. In-keeping with the history of the theory, this current idea is similar to the hoary belief of Wall Street in the 1870's.) Because of mass communications and the publication of odd-lot statistics by the SEC, it is better known to investors today. Price Appreciation Test The contention of this study was that the current theory was not completely true. If the Odd-lotters do sell and buy 129 more stock at the wrong times then they must not be as successful (or profitable) as the round-lot investors. By investigating individual samples of stocks traded by odd-lotters and round—lotters, this thesis tested the theory. The test was to see which group of investors were more successful over various periods of time. Success was considered synonomous with profitability. Only by testing to see whether the odd-lot investors or round-lot inVestors were more profitable could the theory be proven true or false. If the theory is correct, that is the odd-lotters tend to buy and sell the majority of their stocks at the "wrong" time, then the odd-lotters would not be as profitable as the round-lotters. On the other hand, if the Odd-lotters are more profitable or have a smaller opportunity cost than the round-lotters, the theory is not correct. Thus, the method if investigating which group was the more profitable was devised. The theory was tested from both the selling and buying aspects. A sample of the twenty most active stocks by volume each month from the NYSE for the odd—lot sellers, odd—lot buyers, and round- lotters was utilized to test the profitability Of each group. The period of study was from 1955 through 1961. The study was limited to seven years due to the lack of data. 130 It was recognized that a sample based on the amount of dollars each group invests is a better Sample than one based on volume alone. Since such data is practically im— possible to obtain, it-was assumed that the volume basis- was the next best method of securing a representative sam— ple of each group. The profitability, in an accounting sense, of each group was determined from both price appreciation/depreci- ation and dividend yield. The price appreciation/depreci- ation phase of the testing was done by establishing an ini- tial dollar portfolio value of the twenty stocks in each of the monthly samples. The dollar value was found by multi- plying the closing price of each stock on the last business day of the month by its respective volume for that month. Then by adding the dollar value of the twenty stocks in each monthly sample, the initial dollar porthl 0 value of each group's monthly sample was found. Next the porthliO values of these same samples of stocks were found six months, one year and two years later in the same manner. To test for price appreciation/depreciation, these portfolio values at six months, one year and two years were divided by their corresponding initial portfolio values. The division of the later portfolio values by the initial values determined the relative profitability of each group at the designated periods of comparison. By computing the arithmetic mean of each group's profitability during the seven year Span, 131 the average relative profitability at six months, one year and two years later was found for each group. The results of testing the theory on the basis of price appreciation/depreciation conclusively substantiated the sales aspect of the theory. This was demonstrated in Chapter IV where the odd-lot sales sample had the largest Opportunity cost of any group considered for all three time intervals (six months, one year and two years). The theory holds that the majority of the Odd-lotters sell.their stocks at the bottom of the market. If this is true, then the mas jority Of Odd-lot stocks sold should show the greatest Op- portunity cost. They did and consequently, the sales side of the theory was said to be true. From the purchase aspect, the theory maintains that the majority of the odd-lotters buy their stocks near the tOp of the market. If this is the case, the odd-lot pur- chases sample should have shown a lower profit than the round-lot sample and DJIA. Instead, the odd-lot purchase sample registered the highest profit of the three groups for all three time intervals of comparison. Therefore, the price appreciation/depreciation test of this thesis repu- diated the theory. Dividend Test The dividend yield phase of this study was discussed in Chapter V. The cash dividends received by each stock in the samples during the twelve months immediately preceding 132 the three periods of comparison were multiplied by each stock's respective volume each month. The product of this multiplication was the cash dividends received by each stock. Then by adding the cash dividends of the twenty stocks in each sample, the total dollar dividends received by the monthly samples were found. By placing the monthly total dollar dividends over the corresponding monthly portfolio values each period the monthly dividend yield of each sample was determined. (The portfolio values are the same ones as previously explained.) Once again, the average dividend yield for the seven year period was com— puted for all three time intervals of comparison. These per annum dividend yields were then used to test the theory. The results of the dividend yield test were the exact Op- posite of the results of the price appreciation test. This meant that the odd-lot sales sample did not have the greatest Opportunity cost but that the round-lot sample and DJIA did. In other words, the DJIA and round-lot sample forfeited the most profit by selling when they did. Therefore, the sales aspect of the dividend test challenged the theory while the price appreciation test supported it. In all three periods the dividend test showed that the odd-lot purchase sample had the lowest dividend yield of any group. This meant that the round—lot sample and DJIA made more profit from dividends than the odd-lot purchase sample. In keeping with the theory, the round-lotters did 133 out—perform the odd-lotters when it came to dividends. Subsequently, from the purchase side of the theory, the dividend test supported the theory while the price appreci- ation test questioned it. Combined Test Since the results of the price appreciation/depreci- ation test and dividend yield test for both the purchase and sales aspect of the theory were not consistent, the results of both tests were combined. The results of the combined tests for profitability were identical for the six month and one year periods of comparison. The odd—lot sales sample had the greatest combined relative profit of any group. Since this meant that the odd-lot sales sample had the greatest opportunity cost of any group, it supported the theory. The theory maintains that the odd—lotter sells the majority of his stocks at the "wrong" time and consequently, should end up missing out on more profit than usual. This was certainly found to be the case in P1 and P2. The purchase aspect of the theory was also investi- gated by combining the results of the price appreciation/ depreciation test and the dividend yield test. Once again, the combined results of the two tests showed identical results in P1 and P2. The odd-lot purchase sample had a greater relative profit in both periods than either the round-lot sample or the DJIA. Since the theory holds that 13A the odd—lotters are supposed to make less profit than the round—lotters, the statistics proved the theory false. In the two year period of comparison, however, the results indicated by the statistics were not as clear as was desired. For the first time the DJIA had the greatest appreciation of any group except S&P. This meant that the DJIA had the greatest opportunity cost and because of this the results of P challenged the sales aspect of the theory. 3 This was not consistent with the results found in P1 and P2. The odd-lot sales sample, however, did have a greater and more substantial relative profit than the round-lot sample. Thus, the sales aspect of the theory was supported as in the first two periods of comparison. Since the round-lot sample was assumed to be more representative of the market throughout this thesis, the results from the sales point of View unanimously supported the theory. However, the fact that the DJIA had a greater opportunity cost than the odd— lot sales sample was not ignored. It was maintained that the twenty most active stocks each month were more representative than the DJIA because the most active stocks actually reflected the action of the majority of investors in the market. The DJIA average is computed with no regard for the trading action of the thirty stocks included in the average. Theoretically, the DJIA considers only one Share of each stock in arriving at its average, whereas selection of the twenty most active 135 stocks in the sample is based strictly on the action of the majority in the market. The stocks in the samples are re— presented by their respective volumes while the DJIA con— siders no such weighting factors. It is true that some DJIA stocks may be included in the monthly list of most active stocks but the entire list Of DJIA stocks does not represent the action of the majority, as do the samples utilized in this study. From this reason— ing, it was assumed that the round-lot sample was more re- presentative of the action of the majority in the market. This being the case, as previously indicated, the sales aspect of the theory was unquestionably challenged in all three periods of comparison. A weakness in this study lies in using the index num- bers Of the DJIA as its dollar portfolio value. Because the DJIA index number is not based on the trading activity of the DJIA stocks, the DJIA dollar is not exactly comparable Ito the portfolios of the samples, which do consider total volume traded. However, the portfolio comparisons of the DJIA and the samples were made in order to approximate the profitability of the stocks representing each group of investors. If a person was not willing to accept the assumption that the twenty most active round-lot stocks are more re- presentative of the market than the DJIA, the reinvesting of dividends by each group at their corresponding appreciation 136 rates resulted in a unanimous conclusion. The odd-lot sales sample still forfeited the most profit in P3 as well as the other periods. This, of course, meant that the sales aspect of the theory was supported whether the round—lot sample or DJIA was considered more representa- tive of the market. From the purchase aspect of the theory, the results found in P were again not as definite as desired. Once 3 more in P the DJIA had a larger profit than the odd-lot 33 sample. This time, it was greater than the odd-lot purchase sample rather than the odd-lot sales sample. This meant that, instead of the OLP sample challenging the theory, it now supported it. In P and P the results from the pur- l 2 chase point of view also questioned the theory. It was assumed, however, that the round—lot sample was more representative of the market. This being the case, all three periods of comparison challenged the theory because the OLP sample had a much larger profit than the R—L sample. Furthermore, it was shown that if the DJIA was considered more representative of the market than the R-L sample, the theory would still be challenged in P This was demon- 3. strated by considering that each group of investors rein— vested their dividends at their corresponding rates of appreciation. Subsequently, regardless of which average was used, the purchase side of the theory was definitely challenged. The odd-lotters were shown to have made more 137 profit than the round—lotters in all three periods but since the theory says just the opposite should have tran- spired, the theory was proven wrong. After considering the combined results of the divi— dend yield test and price appreciation/depreciation test, the entire theory was not acceptable. Even though the sales aspect of the combined tests in all three periods of compari- son indicated the theory to be true, the purchase part of the tests proved that the theory was incorrect. Subsequently, if one part of the theory is false, the whole theory cannot be true. Implications The question that has occurred throughout this study is, "What do all these statistics mean with regards to an investment policy?" Do they mean that the odd-lot theory is of no use or can part of it be profitably utilized? Are the DJIA stocks and the most active round-lot stocks better in- vestments than other stocks? Or can a combination of all these findings be profitably applied to future stock invest- ments? 8 Since the statistics presented in this thesis cover only a maximum investment period of two years, the implica- tions have to be based on a short-term investment policy. The long-term stock investment policies usually cover a time period of not less than five years and usually ten 138 years on the average. It is recommended that as time elapses and more data becomes available, this method of investigating the odd-lot theory be applied to a longer period of time. If a person is interested only in the short run, he is probably more attracted by price appreciation than by dividend yield. This is why inan earlier chapter it was indicated that the dividend yield test was not as important as the price appreciation/depreciation test. In order to receive the greatest appreciation on his dollar investment, an individual should invest in each one of the twenty most active odd-lot stocks sold each month the same percentage of money as the percentage of dollars each stock in the odd-lot sales sample represents (based on the closing prices each month). This investment would be more profitable than an investment in any of the groups of stocks studied. In fact, he would have to wait only six months and one day to achieve the greatest price ap- preciation possible. Since in Table 3 (page 90) the six month price appreciation figures are determined on a six month. basis, they must be doubled to put them on a per annum basis. After placing the figures on a per annum basis, it is found that an investor would receive the greatest profit after six months. After holding the stocks for six months, he would have received, on the average, 10.96 per cent profit (per annum) from price appreciation alone. Whereas by investing the same dollar amount in the DJIA ("blue 139 chips") on the same basis as above, he would have received a profit of only 7.56 per cent. Even though the price appreciation figure of 12.81 per cent in Table 3 for the OLS sample after two years ap— pears to represent a greater profit than the 10.96 per cent (of the OLS sample after six months), it is not as profit- able. It took two years to make this profit of 12.81 per cent. Whereas, assuming that these average profit figures will be about the same in the future, the 10.96 per cent figure must be doubled in order to make it comparable to the two year period of comparison since it represents only one year of profitability. This not only demonstrates how the short—term investor can maximize his profits, but, also, that his capital has to be invested for only six months instead of a longer time interval. If the greatest profit— ability was found to be at the one year or two year period of comparison, his capital would have to be invested for a longer time. Also, it should not be forgotten that he is entitled to the capital gains tax privileges on this 10.96 per cent of profit. There is one problem in this most profitable method of investing. That is, the volume of the odd-lot stocks bought and sold are not made available by the odd-lot dealers. Without this information, the theory is impossible to imple- ment. However, if the volume figures could be obtained, an investor would, by investing in the twenty most active 1A0 Odd-lot stocks sold each month on the NYSE, as explained above, do better than the DJIA "blue chips." Another interesting aspect of this study was that if an individual invested in the twenty most active stocks each month purchased by the odd-lotters, on the same basis as previously described, he would also do better than the DJIA or "blue chips" after six months and one day. He- would have received a return from price appreciation alone of 9.06 per cent versus the DJIA return of 7.56 per cent. This being the case, the odd—lot theory seems to indicate that the odd—lot purchasers generally invest in more profit? able stocks. Many publications now tend to believe that overall, the odd-lotters do buy good stocks at the right time. This study tends to support their belief. Also this study supports the widely held belief that the Odd-lotters sell at the "wrong" time. These findings are very closely associated with Garfield A. Drew's convictions. That is, the odd-lotters as a group almost invariably sell at the wrong time but over the long run they pick good stocks. One further point of interest was that the twenty most active round-lot stocks had the poorest performance record of any of the groups involved. This points out that the stocks most frequently appearing on the ticker tape are not necessarily the best buys. By considering dividends alone as the main interest of an investor, one would do best by investing in the DJIA 1A1 stocks. In all three periods of comparison the DJIA dividend yield had the highest percentage of any group. (Table 5, page107J The yield of all groups, was at least 3.23 per cent, while the best dividend yield of the DJIA was 3.89 per cent. 8 Finally, by considering the combined results of both dividend yield and price appreciation, the same results were again found. By investing in the twenty most active stocks of the OLS group each month as previously explained, an investor would have received an average return of 1A.32 per cent per annum on his investment. The odd-lotpurchase sample would have returned on the average 12.38-per cent’ per annum on an investment in its twenty stocks. The DJIA, during the seven year periOd of investigation, Would have returned only 11.A6 per cent on the average each year. Therefore, the best investment policy appears to be to buy the stOcks that the odd—lotters are selling. These stocks will return not only the highest profit on a dollar (lA.32 per cent), but require capital to be invested for only six months which qualifies the profit for a capital gain tax treatment. lThe odd-lot theory is correct in indicating that the odd-lotters sell at the wrong time but, more important, that the odd—lotters are selling the stocks that should be bought. On the other hand, the stocks most often bought by the Odd-lotters in a month are also more profitable than 1A2 the "blue chips." In short, the purchase aspect of the theory is not true because the odd—lotters purchase stocks that make more profit than the DJIA or round-lotters. Therefore, the entire theory is not true since one aspect of it is incorrect. APPENDICES 1A3 APPENDIX A LIST OF THE ACTUAL STOCK SELECTIONS USED IN EACH MONTHLY GROUP FOR THE SEVEN YEAR PERIOD 1955 THROUGH 1961 1AA APPENDIX A LIST OF THE ACTUAL STOCK SELECTIONS USED IN EACH MONTHLY GROUP FOR THE SEVEN YEAR PERIOD 1955 THROUGH 1961 The following is a list of the New York Stock Ex- AA AB AC ACY ADL AF AFI AH AK“ AL AM AMF AML AMM AMO AMR APX APY ART" AS ASH AST AT AUM AVT AZ BA BAA“ BAB change ticker tape symbols and their corresponding names, alphabetized by symbols. The Anaconda Company Aluminum Co. of America American Bosch Arma Corp. American Can Company American Cyanamid Co. Admiral Corporation American & Foreign Power Co, Inc. Atlantic Refining CO. Allis-Chalmers Mfg CO. A.J. Industries, Inc. Alaska Juneau Mine Co. Aluminum Limited Armour & Company American Machine & Foundry Co. Aeronedical Laboratory, Inc. American Metal Climax, Inc. American Motors Corp. American Airlines, Inc. Ampex Corporation American PhotocOpy Equipment Co. Artloom Armco Steel Corporation Ashland Oil & Refining Co. American Radiator & Standard Sanitary Corp. American Tobacco Company Automatic Canteen Company of America Avco Corporation Avnet Electronics Corp. Atlas Corporation Baldwin-Lima-Hamilton Corp. The Boeing Company Bell Aircraft Babbitt (B.T.), Inc. 1A5 BC BF BGH BHW .1A6 The Brunswick Corporation Benguet Consolidated, Inc. The Budd Company. Burroughs'Corporation Bell & Howell Company iBath Iron Works Corporation Baltimore & Ohio R.R. Co. Bethlehem Steel Corporation Burlington Industries, Inc. Bulova Watch Company, Inc. The Bendix Corporation Chrysler Corporation Colorado Fuel & Iron Corp. Columbia Gas System, Inc Chock Full O'Nuts Corp. Chance-Vought U. S. Pipe & Foundry Co. Callahan Mining Corp. New York Central R.R. Co. Continental Motors Corp. Canadian Breweries, Ltd. Cheasepeake & Ohio Railway Co. Canadian Pacific Railway Co. Collins Radio Company Campbell Red Lake Mines, Ltd. Certain-teed Products Corp. Crowell-Collier Publishing Co. Cuneo Press, Inc. Commercial Solvents Corp. Curtiss-Wright Corp. Celanese Corp. of America Douglas Aircraft CO.,Inc. Detroit Steel Corp du Pont de Nemours (E.I.) & Co. Dome Mines, Ltd. Dow Chemical Company National Distillers & Chemical Corp. Consolidated Edison Co. of N.Y., Inc. Eastman Kodak Company El Paso Natural Gas Co. Electric & Musical Industries, Inc. Emerson Radio & Phonograph Corp. FOrd Motor Company Fairchild Camera & Instrument Corp. Fairchild Stratos Corp. Fairbanks, Morse & Co. Foremost Dairies, Inc. Fruehauf Corp. Fairbanks Whitney Corp. GA GAP GD GE GEN GET GLI GM CM CO GP GPA* GPV GRI GRN* GY HR HVG IBM IT JI JL KLU KN KYR LIO LIT LJ LK LL- LN LSG LSI LTR LTV LUC LW MAC MAG MCS MD“ MGM ML MM MMM 1A7 Greyhound Corp. Glen Alden Corp. Great Atlantic & Pacific Tea Company, Inc. General Dynamics Corp. General Electric Co. General Telephone & Electronics Corp. Getty Oil C0. General Time Corp. General Motors Corp. Great Northern Railway Co. Gulf Oil Corp Georgia-Pacific Corp. Graham—Paige General Public Service Corp. General Instrument Corp. Green (H.L.) Company General Tire & Rubber Co. Hupp Corporation International Harvester Co. Haveg Industries, Inc. International Business Machine Corp. International Telephone & Telegraph Corp. Standard Oil Co. (New Jersey) Case (J.I.) Company Jones & Laughlin Steel Kaiser Aluminum & Chemical Corp. Kennecott COpper Corp. Kayser-Roth Corp. Sinclair Oil Corp. Lionel Corp. Litton Industries, Inc. Libby, McNeill & Libby Lockheed Aircraft Corp. Lorillard (P.) CO. Louisville & Nashville R. R. Co. Lone Star Gas Company Lear-Siegler, Inc. Loew's Theatres, Inc. Ling-Temc04VOught, Inc. Lukens Steel Company Loew's, Inc. Montgomery Ward & Co., Inc. McDonnell Aircraft Corp. Magnavox Company Merritt—Chapman & Scott Corp. Minute Maid Company Metro-Goldwyn-Mayer, Inc. Martin-Marietta Corp. Marine Midland Corp. Minnesota Mining & Manufacturing Co. MO MOH MRK MS MSB MTC MYO* NAC NAF* NAT* NDS* NMK NOC NP NV 0* OLM OM PA PAC PCG PDC PEG PEP PFE PHI PN PO“ PRD PRX PTX PUB RCA RD REV REX RHO RJR RKO RLM RMB RR“ RS RTN SE SA SC SCM SD 1A8 Philip Morris, Inc. Mohasco Industries, Inc. Merck & Company, Inc. McCrory Corp. Mesabi Trust, Units of Beneficial Int. Monsanto Chemical Co. Monteray Oil National Can Corp. NAFI Natus National Department Stores Niagra Mohawk Power Corp. Northrop Corporation Northern Pacific Railway Co. North American Aviation, Inc. Oliver Olin Mathieson Chemical Corp. Outboard Marine Corp. Phillips Petroleum Co. Pennsylvania Railroad Co. Pacific Telephone & Telegraph Co. Pacific Gas & Electric Co. Parke, Davis, Co. Public Service Electric & Gas Co. Pepsi-Cola Co. Pfizer (Chas.) & Co., Inc. Philco Corp. Pan American World Airways, Inc. Panhandle Oil Polaroid Corp Purex Corp, Ltd. Penn-Texas Publicker Industries, Inc. Radio Corp. of America Royal Dutch Petroleum Co. Revlon, Inc. Rexall Drug & Chemical CO. Rhodesian Selection Trust, Ltd. Reynolds (R.J.) Tobacco Co. RKO Pictures, Inc. Reynolds Metals Co. Royal McBee Crop. .Remington Rand Co. Republic Steel Corp. Raytheon Company Servel, Incorporated Sears, Roebuck & Co. Safeway Stores, Inc. Shell Transport & Trdg Company, Ltd. SCM Corporation Standard Oil of California SDX SF SGL SH SK SKO SN SND SOH SOM SPK SRG SRT SSC ST SX SY TA TEL TG TGT THI TR TRN TT* TX TXL TXN TXT UA UBO UCL UF UFO UK UMT UOP UPJ UPK USH USI UWC VAR VCR VIS WB WIL WK WRS WU 1A9 Sunray D X Oil Co. Atchison, Topeka & Sante Fe Railway Co. Siegel (H.I.) Company Schenley Industries, Inc. Studebaker Corpbration Standard KOllsman Industries, Inc. Standard Oil Co. (Indiana) San Diego Imperial Corp. Standard Oil Co. (Ohio) Socony Mobil Oil Co, Inc. Standard Packaging Corp. Schering Corp. St. Regis Paper Co. Sunshine Mining Co. Chicago, Milwaukee, St. Paul and P. R.R. Southern Pacific Co. Sperry Rand Corp. American Telephone & Telegraph Company Transamerica Corp. TelAutograph Corp. Texas Gulf Sulphur Co. Tennessee Gas Transmission Company ThiokOl Chemical Corp. Texas Gulf Producing Transitron Electronic Corp. National Theatres Texaco, Inc. T.X.L. Oil Company Texas Instruments, Inc. Textron, Inc. United Aircraft Corp. U.S. Tobacco Company Union Oil Co. of California United Fruit Company U.S. & Foreign Securities Corp. Union Carbide Corp. Universal Match Corp. Universal Oil Products Co. The Upjohn Company United Park City Mines Co. United States Hoffman Co. U.S. Industries, Inc. United Whelan Corp. Varian Associates Victor Comptometer Corp. A.V.C. Corp. Warner Brothers Pictures, Inc. Wilson & Company, Inc. Westinghouse Air Brake Co. Western Pacific R.R. Co. Western Union Telegraph Co. WW WX X XA Y Z ZE 150 Walworth Company Westinghouse Electric Corp. U.S. Steel Corporation Crucible Steel Co. of America Alleghany Corporation Woolworth (F.W.) Company Zenith Radio Corporation Symbols used by the author when there were no official symbols available. 151 1955:RL 1955:0LP 1955:0LS 1955:RL 1955:0LP 1955:0LS January January January February February February SK TG T H T T PA X SDX PA PA RS CN T RS EMI GD GD SDX KLU GM B SDX SDX Y SDX SK FCI WK X X RS RCA BAA RS PA CW GM SRG CHV SK GM GE GE J AV J GE ”I ML J SOM CW CHV MO A EMI ML WK AB X RCA 2 BA SOM GE GE GM CHV 7 RS PEP BS GP GE J Eur LJ PCG M RS CW BAA JL PA CN IT ML WK GM JL JL ON C CW, C NV C SDX RR SOM PEP RCA ML AMR SOM MCS B WK LK GM LK‘ UF NOC SRG CO C NV NV IT SX SO MCS RCA TR 1955:RL 1955:0LP 1955:0LS 1955:RL 1955:0LP 1955:0LS March March March April April April B T T AV T T PA PA SDX LJ GM X GD X GM CN PA MO C GM GE PA A GE AV RCA X GD C GM IT SK RS C X RS C LK B B SY SDX GPA RS RCA BF SK GD A J PA Y ‘ MRK PEP GM A J BA LK A GE SOM CD A GE WX RD C L TT BA LK REM BS AMR GE J J CN GE NV GM GD C Y SDX LK PN BS AMR AMR ML C PEP CN MRK AB WX RD ACY LJ P BA WK BAA MCS AT ACY SY GD A MRK B PA ST CW SOM NOC CO MCS 1955:RL May BE GD BA BS CP RCA TXT PA CN SDX C PN LW GE EMI CW GM ACY B MCS 1955:RL July NDS WU SY GM X C AV CMN GD BUR WX ON IT RD PN GE CF PA OLM Y 1955:OLP May T RCA SY PA GM WX X SK LK NV C BA M A J GE GD SOM. MRK PEP 1955:0LP July SY T GM X C J WX SK OLM GE GEN DD BS PA A Z LN ‘NV AT JL 1955:0LS May T RS SDX RCA WX MO NV GE MRK SY LK GM J M UF GD BA RR‘ MCS RJR 1955:0LS July SY T X UF WX RS GE OLM 1955:RL June SY X Y PA ASH KLU PN SDX WX B RS GM CN C LW CF GE AV VIS A 1955:RL August T RHO SY X CMN C WX CW 1955:0LP June T X PA GM SY KLU WX J RCA WK RR C GE GD BS AMR JL SOM RJR SK 1955:0LP August SY T X GM WX 1955:0LS June SY X T RS WX SDX GM KLU PA RCA J GD L OLM PN GE P UK MO UF 1955:0LS August T SY WX GM X TR TG GE RS AMR J UF P AC RJR RCA OLM A GEN MTC 1“... In. . e . I 153 1955:RL 1955:0LP 1955:0LS 1955:RL 1955:0LP 1955:0LS September September September October October October X X T X WX T C SY X CN T WX BE T WX C X SY GM GM P ML SY RS SY WX RS WX GM UK P C SY PA SK X RHO RS GM SY MTC P RS SK KLU GM J MTC CN PA S GE RS RCA AMR P C CW C PA IT UK SDX P GD TG CUN J UK TXT GE GE WX M OLM RS A J GE A RCA A DD C CG KLU GE J CW L ST GE RLM BA P CF RD RCA TG ASH UA UF CF DD NV BS RCA DD M BS Z RD BS RJR AB VIS PTX GD KLU S 1955:RL 1955:0LP 1955:0LS 1955:RL 1955:0LP 1955:0LS November November November December December December GM GM GM BE WX T SY WX T GM GM WX PO T WX SY SY SY C SY J WX SK PTX WX X SY X KLU SRG J C PTX B NV KLU X SK M PTX SRG X PTX J X PA T MRK M M C UFO ML ML CW GE DD C X P GE DD P GD VIS RS MRK GD MTC ML C C B CW RS SK CF GE GD A GE AV J J PA KLU GD PO TR ACY FTR BS S GE AMO AC RHO BA L NOC GE AST AV IT AC JI BA L CF MTC ACY MRK PA AMR BE UA AST EMI MTC DD 15A 1956:RL 1956:01P 1956:0LS 1956:RL 1956:OLP 1956:0LS January January January February February February AF A T A AMR AMR AV BS AFI ASH T AST BE BA BA AV CW ACY C T C BE DOW T EMI C DD C DD CG GE VIS GE FTR GE GE GM CG GM GE GM GM IT DD MTC GM GO GO LW FKM PTX LW MTC FTR DR GE P MCS PTX OLM PO GM RS CN P PTX PA MTC S PTX RLM P CN P L RS S RLM PTX S SOM RHO SD S SY SRG SY RD J SOM J SY SN SY SY SY TXT J J SN SK SD USI TR UF J SDX SDX X X X X X X WX WX WX WX WX WX 1956:RL 1956:0LP 1956:0LS 1956:RL 1956:0LP 1959:0LS March March March April April April AM T T AM T T ' A A A Y A BA AV BA BA AV BA F BE C F BE C FTR CG F FTR BA DD GE FTR GD GE CMN F GM GM GM GO FTR GE KLU IT GO IT GM GM OLM KLU IT KLU H MTC PTX DR KLU MTC DR PA PA PA KN OLM PTX PTX P RHO MTC P PA RLM RLM RD PA L RLM S S SY RLM SN RD SRG SRG J SY J SY SY SOM SDX SDX SY J SD SY SK J SDX SK J J X X X X X X WX WX WX WX WX WX GE GE GM F FTR GO 1956:RL 1956:0LP 1956:0LS 1956:RL 1956:0LP 1956:0LS May May May June June June Y T A Y AMR T AB A BA T AT BA A BA C BE T DOW BE C ED BA C DD C DD F DOW DOW ED FTR F GE F F F GE GD GM GE FTR FTR GM GE GO GM GE GE G GM FTR KLU GM GM LW GO T NMK GO GO MRK MRK MTC PRX JL MTC NAC RLM P RD NMK NMK RD S RLM S S RLM SY SOM SY SY SOM SC J SY SD J SY SOM SX SD J SX SD S SK J SDX TXL J SY X SK UF X SK SD WX X X WB X J RLM WX WX WX WX X 1956:RL 1956:0LP 1956:0LS 1956:RL 1956:0LP 1956:0LS July July July August August August T T T T T T AV AS AMR A A BA BE BS DD BS BA CG GE C GD CG C GM GD F GM CRT F GO GM GE KLU GD KLU KLU HR GD MTC GE GD MTC KLU GM OLM GM GE M RCA GO P GO GM OLM REX JL RS JL GO PEP RS KLU RLM .KLU RS P RD RS S ML RLM RS SX RLM SY RS RD SY SY SOM SD RD SOM SD J SY J SY SY J SDX SD SDX SN SD SDX CJ J TX J J TX X SDX UF SK TR UF WX X WX X X X PO WX X WX WX WX 156 1956:RL 1956:0LP 1950:0LS 1956:RL September September September October T T T T AV C BA AV SF GD FTR BS BA GE GD C C GM GE CG GE F GM FTR GM FTR GO GE GO IT KLU GM JL LUC ML GP KLU ML MTC GO ML RS NV KLU NAC RD P LSG NV SA RS CN RS SOM RLM PA RD SY SOM RS S SD SY SY SY J SD J J X J TG X WX X X WX MTC WX WX 1956:RL 1956:0LP 1956:0LS 1956:RL November November November December T T T AST AV A AMR BE BS BS BS BS C BIW CG BA CG C CW C GD CW DOW DES GM DD DD FTR GO F GD GD JL GE GE GM ML GM NV GO NV GO P ML RCA MTC RCA MTC RS RD RS CN RD SOM RLM NV L SY L PA SD SD SY P J SK SD RCA SK UF J RD X X X SY WX WX WX SN 1956:0LP October T AA AMF A C D DD F FTR GE GM GO RLM S SOM SY SD J X WX 1956:0LP December T BS BA C DD F FTR GE GM GO KLU MTC PTX RCA S SY J SK X WX 1956:0LS October T C CG ED FTR F GE GM GEN GO JL MTC P RCA RLM SOM SY WX 1956:0LS December T AMR BS CG DD F GD GE GM MTC NV P RCA S SY J UF X WX AST 1957:RL January AZ AV BE BA BS C CG ELG GD GE GM NV RCA RTN RD J SK SY USH X 1957:RL March AMO A SF BS BA C CG CW ELG GM MOH NV RD S SC SOM J USH SD X 1957:0LP January A T BS C F FTR GD GE GM GO IBM KLU ML MTC S SOM SY J X WX 1957:0LP March T AMR ACY A C F GD GE GM GO RD MTC 8 SOM SY J SRG TX X WX 157 1957:0LS January A BS CG ED DOW ELG FTR GD GE GM MTC NV P RCA S SY J UP UF X 1957:0LS March T A AST BA BS C CG ED ELG FTR GD GE GM NV P SOM SY SD J X 1957:RL 1957:0LP February February AB T AV A A BA BA BS BS C C CW CG F ELG GD GD GE GE GM GM GO GO JL NV MTC NOC NV RD S SOM SOM SY SY J J USH X X WX 1957:RL 1957:0LP April April AB T AF A BS BS C C CG ELG ELG F GD GD GM GE GPA GM LUC GO NV IT RTN LUC RD RD SRT SY SD S J SD SK J TG SOH USH X X WX 1957:0LS February AST ARM T A BA BS CG ED ELG FTR GD GM MTC NV P S SOM SY J X 1957:0LS April T AST BS C CG ELG GD GE GM GO IT LUC NV P S SRT SD SY J TG 158 1957:RL 1957:0LP 1957:0LS 1957:RL 1957:0LP 1957:0LS May May May June June June SF T T AMO T T BE BS BS BS BS BS BS C CG BA A CG BA F GD C C ED C FTR GE GM F GD GM GD GM GET GD GE GET GE GEN LUC GE GM LUC GM GET OLM GM IBM NP GEN GO P GET LUC NV GO IBM REV IBM OLM OLM GET IT RD LUC P P IT NV S MTC PEG RTN LUC OLM SC 8 SC RD NV P SOM SY SOM SC S SOM SY SOM SY SY SOM SY SD SD SD SDX SY SD J J J J J J SDX TG SDX TR X SDX X X S X WX WX WX BA WX 1957:RL 1957:0LP 1957:0LS 1957:RL 1957:0LP 1957:0LS July July July August August August AV T T AL T, ACY BS BS BS Y A T BA C C A AST A B0 ELG CG ' BS BS BS C GD ELG BA C BA ELG GE GD C F CG GD GM GE GD IBM ELG GM F GM GM IT GD GET IBM IBM GET GD GE RKO JL JL LUC GE GM NV NV NV P GM IBM OLM OLM OLM RTN GO IT P REV P RD LUC OLM RTN S REV NV S P REV SRG SRG S SOM SOM S SOM SY SY SY SY SY SY J SN SD SN J J TG J J J SSC X X SSC X X X WX WX X WX WX 159 1957:RL 1957:0LP 1957:0LS 1957:RL 1957:0LP 1957:0LS September September September October October October AL T T AL T T A A' A A A A Y BS BS BS BS BS BS C CG BA BA BA BA F CW 0 F CG C FTR ELG XA FTR CW CW IBM FTR FTR GD FTR GD IT GD GD GE GD GE GD GE GM GM GE GM GE GM GY GO GM GO GM LUC LUC IBM IBM NV GO IBM ML LUC F P P OLM NV ML LUC RD S P PA NV NV S SY SY RD P PA SY SOM SN SY SOM P J SD J SN SY SN TG TG TG J J SY X X X TG TG TG’ WX WX WX X X X ' 1957:RL 1957:0LP 1957:0LS 1957:RL 1957:0LP 1957:0LS November November November December December December AL T T SF T T . BS A A AL A A BA BS BS BS' BS AH C F BA BA BA BS CW FTR CW C C C BO GD GD CW CW CW GD GE GE ELG F F GM GM GM F FTR GD GY IBM IT» FTR GD GM GET IT NV GD GM IT LUC LUC OLM GM NV JL ML NV PA LL OLM M NV OLM P NV RLM NV OLM P SF PRD SY‘ OLM PA SOM SOM PA SN PA RD SY SY RD J P SY J SN SY TR SY J TG UA J TG J TG X X TG PA UF X WX WX X X X 160 1958:RL 1958:0LP 1958:0LS 1958:RL 1958:0LP 1958:0LS January January January February February February SF A ACY AMO T ACY T T T T A T BS BS A BS BS BS AMO BA BS C C C AV ED C XA F CW CW F CG CW GD F. ELG GD CW FTR GE GD F GE ELG GD GM GE FTR GM F GM GO GM GD IBM GD LL IBM LL GM LL GE NV LL MO LL MTC GM SRG MO OLM CN NV X P NV RD NV RCA OLM RTN RTN SA PA S P REX SA SRG RMB SOM RD RD SOM SY SY SY TG SA SY SN J J SY SC J J TG X J J X UK X WX WX X WX X 1958:RL 1958:0LP 1958:0LS 1958:RL 1958:0LP 1958:0LS March March March April April April AMM T ACY AMO AST ACY BS AST AST SF T AMO BC A T BS BS AST Y BS A BA BA T C DOW BS AL C BS GM F CG C ED C KLU GD F ELG F CG LL GE GD GE GE F PRD GM GE GM GM GD OLM IBM GM FCI IBM GE P LL LL LL LL GM REX MRK OLM OLM MTC IBM SA OLM P RD OLM LL RD PRD PRD RTN S MTC SY SRG SY SC SOM OLM SC SOM J SY SY SY J SY UK J J J UBO J UF SK TX UK X X X TA X X WIL WX WX X WX WX 161 1958:RL 1958:0LP 1958:0LS 1958:RL 1958:0LP 1958:0LS May May May June June June AMO T T AMO T T BAB AMO AMO AL AS ACY BS AS AH AV AMO BS JI BS BS BS BS C CMR C CG BA BA CG EMI DOW ED C C ELG GM F F _CG F GE FCI GE GD . GM GE GM HVG GM' GE LL GM GEN LW LL GM PTX IBM IBM LL MTC GEN NV LL LL PRD OLM LL RTN MTC MTC OLM RTN MTC RD OLM OLM RD ‘SA OLM SC P P SC SRG P SE RTN PEP SE S RD SY SOM RTN SY SY SA J SY SY J J SY SPK J J SK X J UBO X X X WX X X WX- WX 1958:RL 1958:0LP 1958:0LS 1958:RL 1958:0LP 1958:0LS July July July August August August‘ AL AST ACY AL AMO ACY ACY T AST AMO T AMO AMO AS T AV A T AV BS BS BS BS A BA F CG JI 0 BS BS GD ED GM F CG XA GM GD GET GD ED JI GO GE LW -GE GD GM LL GM OLM GM GM LL MTC GEN PTX JL GEN NV OLM GO RTN KLU. KLU OLM P IBM RD OLM MTC PTX RS LL SA P OLM RD RD MTC MD RS AST SE SOM_ OLM SH S SOM- SY SY P SY SH SY J. SD SOM J SOM J S J SY SK SY TG UK X J X J X X WX X WU X WX 162 1958:RL 1958:0LP 1958:0LS 1958:RL 1958:0LP 1958:0LS September September September October October October Y AMO AMO AL T T SF T T AMM A A T A A AMO AMO AMM AL AS BS AV BS AV AMO BS X BE BA AMO ART C CG BS C BS AV F ED BA F CG BS GE GD EMI GD GD GM GM GM GM GM GM FTR IT GO GPA IT IBM CN LW IBM H KLU MRK PTX OLM IT LW OLM MTC RD PA MTC CN P OLM SH SH OLM REX RS RD J SOM SF SC WX SH SPK SY SH SY SH SOM SK J SOM J SOM SY LW SK SY SK SY ' J X X SK X J SK WU WX J SE X X 1958:RL 1958:0LP 1958:0LS 1958:RL 1958:0LP 1958:0LS November November November December December December Y AMO AMO Y T T AL T T AL AMO AMO AMO A BS AMO A AV AV BS CG AST AV BS BS F GD T BS C FTR FTR GM AV C CG GD GD GEN BE F ELG GM GE GRL BS FTR GD GY GM IBM C OLM GM GRL MTC LK EMI P GEN LW OLM MTC GM GM IBM PN PA OLM GPA SOM IT PA RS OM FTR SY OLM RD SOM RD OLM J PDC LSI SX SGL RD SK SOM SKO SY SOM PDC UF SY J SK J SY X SD SK UF SK J WK J SY X SY SK WX SK X WX UF LW TG UF 163 1959:RL 1959:0LP 1959:0LS 1959:RL 1959:0LP 1959:0LS January January January February February February AL AMR AMO AL AMO 'AL AMR AMO T AMO T ACY AMM T AV AV A AMO AMO A AL BS BS T AST BS BS FTR DOW AV Y BC CG GM F BS AV F GD GPA FTR BA AM FTR GM GY GM CG BE GD GEN LW GY FTR BS GM GAP LUC IBM GD BA MTC IBM MD MTC GY JI OLM OLM MOH OLM CW FTR PN PN PN RD MTC GM SOM PDC PTX SOM OLM MCS SY PFE RD SY P PN J RD SY J SOM RD SK SOM SKO SK SY SY X SY J X J J UPJ J SK UPJ SK SK WK UPJ TXT WX THI 1959:RL 1959:0LP 1959:0LS 1959:RL 1959:0LP 1959:0LS March March March April April April AL A ACY AC AL T AMO T AMO AST AMO AC AK BS AL AL T AL BE BA T AMO BS AMO BA C AV AV BA AV BF AV BS Y C BS AV AMO BA BS F BA CMN F BGH CQ FTR F EMI FTR CG F GM CW F GM C GE LTR CW GM GY GM GY NV GM H IT GEN GRN OLM GEN MD WX IT MOH RCA IBM PTX NV LK PA SOM IT RCA RCA MTC RCA SY LK RD SY RCA RD J P SE J SOM PN SK PN SY SOM SY J TXN SY J SK J SY UPJ J SK THI THI SK WX TXN 1959:RL May ACY AL T ADL BE BS F GRL GM GY GA IT RCA RTN SY SKO J SK THI WW 1959:RL July AL AMO T AV BS BUR CF FW FTR GM GA GEN H CN RD SOM SY J SK TXT 1959:0LP May AL AMO T AV BS C F FTR GD GM ML OLM RCA RTN SOM SY THI WX 1959:0LP July AL T AMO BS C F GD GE GM GEN OLM SOM J SY SK TG THI UCL UPJ 1959:0LS May AL AMO T AV BS CG CZ GD GM GEN IT ML MTC PFE RCA RTN SOM SY J THI 1959:0LS July ACY AL AMO T BS BUR CG EK GD GM GEN IBM LL MTC PFE P SOM SY TG UPJ 1959:RL June AL AMO T AV BS FW F CM GA KLU LK LL PA RCA RTN RD SY J SK THI 1959:RL August AH AL AMO T AV BS GM GEN GY IT LK NV PN TRN. RD SY J SK TG UF 1959:0LP June AL AMO T BS F GD GM IBM LL OLM PFE PA KLU SY ‘ J THI UF X UK ZE 1959:0LP August AH AMO T CZ F GD GE GM GEN IBM OLM NV SH SY J THI TXN UF X ZE 1959:0LS June AL ACY AMO T AV BS CG GD GM GEN ‘ IBM LK LL P PFE 'RTN SOM SY J ZE 1959:0LS August AL AH AMO T AV BS BGH ZE CW GD GM GEN IBM IT LK PFE SY J THI UF 165 1959:RL 1959:0LP 1959:0LS 1959:RL 1959:0LP 1959:0LS September September September October October October AL AH AH Y AMO AMO AMO AL AMO AMO T T T AMO T AV B8 B8 AV T BS BS BC BC BS CZ CZ EMI CZ C CG F CG GM 0 GD Y GE GD GY F GM F GM GM GA GD GEN GM GEN GEN IT GM GO GY GY GO LSI GY IBM GA IBM IBM RTN IBM IT IT MTC IT RD CN NMK CN SOM MTC CN SOM P RD SY NMK SOM SY SOM SY J PFE SY J SY J SK SOM J SK SD SK THI SY SK THI SK THI TXN SK THI TXN THI UF UF J X UF VAR X X THI T WX X 1959:RL 1959:0LP 1959:0LS 1959:RL 1959:0LP 1959:0LS November November November December December December Y AMO AMO AL AL AMR AL T T AMR AMO AMO AV AV AV AMO T T BUR BC BS T ’AV BX C CW BC AV BA BC AMO F CG UF C CG CW FTR CW CRI CG EMI FTR GD EMI CW CW F GM GM GD EMI F GD GY GY GM, F GD GM GA IBM . GEN GM GM GEN IT IT GY GEN . SOM (IBM LSI SOM IBM GA SY L 0 SY P H J SOM RTN J L PHL SK SY SY SK SOM SOM TG SD J TG SY SY THI J SK THI J J UA TG THI UF SK SK UF THI VAR ZE THI UCL UPJ UF 166 1960:RL 1960:0LP 1960:0LS 1960:RL- 1960:0LP 1960:0LS January January January February February February AL AH AMR AH AMO AC AMR AMO AMO AMO APY AMR AMO T T T T AMO AJ BC BS BS BS T T CZ BC BC BC BS BS CG C C CG BC BC FW CG EMI CRI CG C F FW FW EMI CRI AH GD F F F F FW GE GE FTR GE GEN F GM GM GE GM GO GE GO GO GM GO IBM GM IBM IBM GA ‘IBM MTC GPA SOM JL H SOM PFE GO SY PFE NAF SY L H SN SOM PAC J SOM J J SY RCA SK SY SK SK SD J THI SD THI THI J SK TRN J X WX THI X WX THI 1960:RL 1960:0LP 1960:0LS 1960:RL 1960:0LP 1960:0LS March March March April April April AL AL AL AMO AMO AMO AMO AMO AMO T T T T T T APX BS APX APX APX APX BS F' BS EMI BS BS BC GE CG FW BC CG C" GM F F CRW CRI CG GEN GM GM GM F GM IBM GEN GO GEN X GEN IT IBM GA GO GE GO RCA IT H IT GM IBM SOM LIT IT NAF GO IT' SY LK LK PFE IBM LK J MTC NAT PHL IT PFE SK PFE PHL RCA PHL RCA THI SOM RCA J SOM SOM TXN SY J SK SY SY X J SK THI J J UPJ THI UOP UOP SK SK WU TXN X X TRN X WX RCA 167 1960:RL 1960:0LP 1960:0LS 1960:RL 1960:0LP 1960:0LS May May May June June June AL AUM AMO AUM AMO AMO AMO AMO T AMO T T T T AUM APX BA AMF APX AV APX AV. BC APX AV BC AV BC CRI BS BC CRI BS CRI F BC CRW ERP BC CV GD C GRL GRL CRI ERP GRL ,CRI . 1 GM GM CG EMI GM GD GEN GEN GRL GM GEN GRL . GLI GO GM GEN G0 GM A GA IT GEN GLI IBM GEN AA IT PFE IBM IT IT IBM NAF SOM MMM LSI RTN IT SND SY .PFE NAF SOM LK RCA J SY PFE SY SOM SY THI SKO RCA J SY J TRN J SY THI J SK SKO THI SKO TRN THI THI UMT UMT J X TXN 1960:RL 1960:0LP 1960:0LS 1960:RL 1960:0LP 1960:0LS July July ' July August August August AUM AUM AUM . AMO AMO AMO AMO AMO AMO ' T T T AV AV AV AV BA BS BA BC BS BS BC BA BC F BC BA CG BC F GE CRI BC GE CG GE GRL CG BVA GM ELG GM GM DD VCR GEN GM GEN GEN F GM IBM GEN IT GO GM GEN LIO IBM ML IBM GEN LIO ML LK NAF IT GO LK LK LIO NV ML IBM MAC NV MAC RCA NV IT MGM M MMM SY SOM PFE M P M J SY RCA NAF SOM SY SK J SY J SY J UMT UMT J SK J TEL UWC WX UMT TEL UMT UMT T T T APX AV AV 168 1960:RL 1960:0LP 1960:0LS 1960:RL 1960:0LP 1960:0LS September September September October October October AMO AMO AMO T AMO AC T T T APX T ACY APX BS APX AV BS AMO AV BC AV BE BC T BE CRI BS BS F APX BS GD BC BC GD BS BC GE CRI CRK GE BC CRI GM ELG AMO GM EK GD GEN GD DM GEN ELG GE IBM X GE IBM GM GM M GM GM M GEN GEN P GEN GEN PRD IBM LIO SOM IBM GO P M MD SY M 0 RCA PRD MYO J SY RCA SOM PFE RCA SK J SY SY RCA J TEL SK J J SY SK TXN TEL SK THI J TEL X TGT WRS TXN THI X WX . TXN X X TXN 1960:RL 1960:0LP 1960:0LS 1960:RL 1960:0LP 1960:0LS November November November December December December AL AMO AMF AMO AMO AC AMO AMF AC T T AMF AC T T APX' BS AMO T BS APX AC BC T APX BA AMO BS C BHW AUM BC BS BA F BS BS C BA BC GM BA BA F BC CRI GEN ‘BC BC GD ELG CHF GO CHF GE GE GM GM IT C GM GM GEN GEN ' M GM GEN GEN IBM GA L GEN LK IBM ML IT SOM IBM. NAF M M PA SY ML SY SOM SY RD J M J SY J _ SY THI PRD TRN J THI J TRN SY X THI TXN SK UF J UMT UF TRN UF X THI UOP UMT UMT UOP UOP TRN 169 1961:RL 1961:0LP 1961:0LS 1961:RL 1961:0LP 1961:0LS January January January February February February AL AL AC AMO AMO ACY AMO AMO AMO T T AMO T T T APX APX T APX APX APX AV AV APX AV BS BS BA BA AV BS BA BC _ BC BC BS BC BC CHF CRT CZ BA CRT CRT CRT FW CRT BC FW ELG ELG GE ELG CRT F F GD GM F GE GE GE GE GEN GE GM GM GM GM KYR GM GEN GEN GEN GEN LK GEN KYR LTV IT IBM MOH KYR LK TT LTV LTV PHL LK ML RD SOM PFE SY MTC M SY SY TGT SND SY SY J J THI J J J SK TGT UMT SK THI THI WX THI WX WX WX WX 1961:RL l96l;OLP 1961:0LS 1961:RL 1961:0LP 1961:0LS March March March April April April AMO AMO AMO Y AMO AMO T T T AMO T T APX APX APX T APX APX AVT BA AV APX AV AV AV BC AVT AVT AVT AVT BUR CZ BS BC BC BS BC GD BA FW CZ BC FW F BC GE ELG CHF GE FW ELG GM FW ELG GM GE FW GEN GE GE GEN GM GE H GD GD Y GEN GM LK GM GM LK IT GEN MS GEN GEN RHO LK SND SND LK FW SCM PFE SY SE PFE LK SY SY SKO SCM SOM PFE SND J J J SY SY SKO SKO WX SK J J J TRN SK UWC TGT UMT SK WX TRN AV WX WX 170 1961:RL 1961:0LP 1961:0LS 1961:RL 1961:0LP 1961:0LS May May May June June June AMR AMR ACY AMF T ACY AMO AMO AMF AMO VIS AMF T T AMO T APX T APX AV APY VIS~ AV AV AV AVT T APX BA BS AVT BC AV AV BC BC BC DD AVT BS CZ ELG CGI ELG BS BC ELG ~GD FW F BC 7 GD F GE FEN GD ELG GE GD GM GE GE GD> GM GE GEN GM GM GE GEN GM GO GEN GEN GM GP GEN IBM GP LK GEN GO GO LK GA PFE IBM LK IBM PDC LSI SOM MAC RTN LK SY PUB SY LK SY MTC J‘ SY J SY J SY TG J TGT J TRN J TRN >SK THI TGT UF TGT UMT 1961:RL 1961:0LP 1961:0LS 1961:RL 1961:0LP 1961:0LS July July July August' August August AMF AC ACY AMF~ AMO ACY AMO T AMO AMO T AMF T AV AMF AV AV AMO APX BS T BS BS APY. BS BA AV BC BA T BA BC BS B BC AV AV ELG BA CRT C- BS BC F BC C EL BC F GD ED F F F GD GE ELG GD GD GD GE GM F GE GM‘ GE GM GEN GD GM GEN GM GEN GO GE GEN IBM GEN GO IBM GM M LK IBM LK LK GEN RTN MTC LK ML MTC IBM REV PFE MAG OLM PFE LK SND REV REV SY SY SY SY SY _ SY J J J J J J USI TGT SK SK SK SK 171 1961:RL 1961:OLP 1961:0LS 1961:RL 1961:0LP 1961:0LS September September September October October October AMF APY ACY ACY AMF ACY AMO T AMF AL T AMF AV AV APY AMF BS T BS BS T AV BA AV BC BA VIS BS BC BS C BC AV BC ELG BC F C BS ELG F ELG GD F BC F GD F GE GD ELG GD GE GD GM GE F GE GM GM GPV GM GD GM, GEN IBM GEN GEN GE GEN IBM MAG FIR IBM GM MSB M M M LK GEN M PFE REV SND SY IBM PN SY RJR SY J SY SND J SND J SK J SY SK SY SK TGT SK" J TGT J TGT TXN SND SK SND TXN TRN WX TXN WX WX WX 1961:RL 1961:0LP 1961:0LS 1961:RL 1961:OLP 1961:0LS November November November December December December AL AMF ACY AL AH AH AMF AMO AMO AMF AMF AMF AMO T AMF AMO AMO AMO T BS T T T T BS BC BS BS BS BS BC BGH BC BC BC BA BGH C BGH BGH C BC C ELG F C F BGH FOR F GD GD GD ELG GM -GD GM GE GE GD GEN GEv GEN GM GM GM LTV GM IBM GEN GEN GEN ML GEN PFE RHO GO IBM PN IBM RJR RD M MM PA PFE SND SND SND .RD RD ' SND SY SY SOM SND SND J . J J SY SY J TGT WX SK J J SK WX UMT X TA WX WX SY ZE WX WX F APPENDIX B SAMPLE WORK SHEET USED TO RECORD ALL THE DATA USED IN THIS ANALYSIS 172‘ 173 oomamm nomaa oN.H om.H mam.am mmw.mm .mmh.ow .m.fim .mmm.o> .om . .mm N3 ooammu iIII IIII IIII m:m.am mum.m- mma. m m>.>. mm~.mm mm.» mum.HH. mm ooswmm m>.m om.m,o:.m umm.m=a .mw mmm. Ha msm.wm mmm.moa mma.am mum.m: h oomsmm III! IIII.IIII mm.om .HH www.mm mNH.0H . .ow mhm.oa mNH.mH sz oomzwm =N.H.mm.a om.H awm.hza mmw.m= www.mma mN.H= .mm=.>oa mNH.mm mmm.mm am oemmmm .om. mm. mm. Hum.mma mmm.mm. wmm.m> mpm.ma Hoa.:> mhw.ma mum.ua m>.om mmo.h~ msm.am Hh>.mb. m.HN msm.mm a: oowwmm ma. IIII IIII Hmm.mm ms.sfl www.mm msm.>H maawms mwm.ma m.mm >BA. oozmmm am.. up.. up. Nam.wHH .om mmo.mm m.mm ama.~m .mm mm.mm ,zmc Qoomww .00.: oo.m_om.m mom.m:H mwm.m> Hmw.Hoa mmm.mm. www.mm mmmuomm mmm.=m .26 oomwmm on. em. om. =>H.m~ mum.oH wwaymm mmfium-. mmo.mm. mmm.a .mum.:H mom OOHowm oo.H oo.H oo.H mhw.osm mhm.:w wmm.zma mm.o> mm~.hm mmwaz m.m= ,0 oomemm oo.H oo.H oo.H mm:.um mmH.mN www.ms ms.mm as=.mm mmmwhm .mm mom. oomomu om. ,om. om. mmm.om .mp.oa mm~.mm .mhm.sa Nom.mm .mm.wm .mm om oommom om.H om.m om.m Namemb mh.om wmm.>>. m.Hm sho.Hm .Nm mmw.ea mm oomhmw .cw.m om.m mz.m HmH.mOH .02H mam.mw mmm.=HH omwrama mh.HHH,mhm.HMH B oomoam .oo.H oo.H oo.H mmN.hHH m.mH Nmunooa m>.mH =m=.mm mum.=a mmm.wa 0:4 ooamHm om. om. .om. .mm.m= mmH.mH maa.sm .HN wmo.o> ms.mm m>.wm h£< oomhwa om. ow. om. o:m.am msm.:m m::.mm m~.NN shm.=m www.mm mmw.wm .qd NC :3 33 A3 A8 A: A3 Amy 2; Amy Amy 63 .1 manIocsom gamma nonao>oz mumsaeze mHma zH ammo «Ben mma.qs< amoomm as some awmww.emo3 Bunsen m NHozmmm< 17A In column one are the symbols of the twenty stocks used in the monthly sample. The symbols are the same ones found in Appendix A. Column two represents the initial price of the stock without consideration of the brokerage fee. It is the closing price on the.last business day of the month. Column three is the price of the individual stocks- six months and one day after_they were purchases or sold. (Throughout the study no computations for the brokerage fees are done.) Column four is the relative increase or decrease of the twenty stocks after six months. It is found by dividing -column three into cOlumn two (Col 3 e 001 2). Column five is the price of the individual stocks onerear and one day after the initial transaction. Column six is the relative increase or decrease in the twenty stocks one year later (Col 6 + Col 2). Column seven is the price of the individual stocks two years and one day later. Column eight is the relative increase or decrease in the twenty stocks two years later (Col 8 + Col 2). Column nine is the last tWelve months dividends paid on the twenty stocks. The twelfth month is the sixth month after the stock was purchased or sold. ‘ Column ten is the last twelve months dividends paid for the twenty stocks. The twelfth month is one year' after the stock was purchased or sold. 175 Column eleven is the last twelve months dividends paid on the twenty stocks. The twelfth month is two years after the stock was purchased or sold. Column twelve is the volume or the shares of the stock traded for the month. After all these data were gathered in the manner a- bove, the following computations were done. Columns 2, 3, 5 and 7 were multiplied by Column 12. This gives the total cost (without brokerage fees) of the twenty individual stoCks in the sample. Then the total cost of the twenty stocks were added to giVe a dollar cost of the portfolio value for the tWenty stocks representing this particular month and group_of investors. Then these portfolio values of Columns 3, 5 and 7 were placed over the portfolio value of Column 2. This gave a relative increase or decrease in the portfolio values six months (Column 3), one year (Column 5) and two years (Column 7) later.. The 8A relative increases and/or decreases for each respective column were added and divided by 8A. Eighty-four represents the seven ‘year~period studied, broken down into mOnths. After the division by 8A, the average profitability of this or that group six months, one year and two years later was found. The dividend yield was found in the following manner. Columns 9, 10 and 11 were multiplied by Column 12. This gives the dollar value of dividends received by each of the twenty stocks in the sample six months, one year and two 176 years after the initial purchase or sale of the stock. Next, the total dollar value of dividends received by all twenty stocks in the sample were added. This represented the total dollar value of dividends received by this sample for this month. Next the total dollar value of dividends of Columns 9, 10 and 11 were placed over the dollar port— folio values Of Columns 3, 5 and 7, respectively. This in return gave the dividend yield of the sample six months, one year and two years after it was purchased or sold. The 8A monthly dividend yields of the samples were then summed for the respective time periods and divided by 8A. This gave the_average dividend yield six months, one year and two years later for each group being studied. The worksheets were actually fourteen column accounting sheets. There were a total of 5,0A0 individual observations in each column of the worksheet. APPENDIX C COMPUTATION OF THE ARITHMETIC MEANS AND THE STANDARD ERROR FOR THE MEANS 177 APPENDIX C COMPUTATION OF THE ARITHMETIC MEAN AND THE STANDARD ERROR FOR THE MEANS 4-3:- - estimated standard error of the mean a‘- standard deviation of the population X — value of an individual observation (sigma) symbolizes proceSs of summation b4 H I XI I arithmetic mean N - total number of observations if = 2x1 .__x8Ll . N a“ = {x12 - (eXi)2 + N N — 1 tf; = U- V N 178 7.". APPENDIX D COMPUTATION OF THE "T-TEST" FOR LARGE SAMPLES AND THE "T" VALUES 179 APPENDIX D COMPUTATION OF THE "T—TEST" FOR LARGE SAMPLES AND THE "T" VALUES The round—lot data is always used as the base of comparison. From this base are compared the corresponding monthly arithmetic means of the odd-lotters, DJIA and S & P. The difference between the monthly round-lot means and the monthly means of the groups being.compared are added and divided by the 84 months for each period 0; comparison to arrive at the monthly average or the arithmetic mean re- presenting the group for the seven years. Hence, to these means the "T-test" for large samples was applied. t - monthly average for the round-lot data t - monthly average for the odd-lot sales data - monthly average for the odd-lot purchases data d monthly average for the DJIA data - monthly average for the S & P data 0.. W > N K: >4 l d- Cf <+ - difference between the round-lot monthly average and the monthly average of the group with which it is compared _ ' N - number of observations in the sample, or the months being averaged in this case 180 181 9| I arithmetic mean of the differences between the round- lots and the other groups d‘— standard deviation of the mean t - the measurement to see whether or nottnr chance the sample is not significant 2 - summation symbol 2 Y =< Y —--Y -x --—x at t tau t tau 2 z =:z —-—z -X ---X dt t 8H t t8“ 2 A = A ---A -x ---X dt t 8H t t8“ 2 B = B ---B -X ---x dt t 8H t t8“ 2 — = y - 8n Vt dt X E = z — 8a zt dt 2 dat=Adt — 8n bt t _ . 2 2 Sa't' - /X at ' (Zdt) * N a ' N - 1 t = E 35% & I¢N The "T" values for large samples can be found in al- most any advanced statistics book. After computing the standard deviations (a‘), the "T-test" was applied and the following results were found. 182 "T" VALUES FOR THE GROUPS COMPARED TO ROUNDeLOT DATA FOR ALL THREE PERIODS OF COMPARISON Odd-Lot Odd-Let Purchases Sales . DJIA S & P1” 3.61 a b 5.37 3.81 3.5“ P2” 3.38 _ 5.06 A.63 “.50 P3* 5.61 7.42 8.88 8.58 Pl - six months P2 — one year later P3 - two years later APPENDIX E THE MONTHLY PERCENTAGE VALUE OF THE ORIGINAL DOLLAR PORTFOLIO VALUES FOR ALL GROUPS STUDIED: SIX MONTHS, ONE YEAR AND TWO YEARS LATER 183 18“ APPENDIX E THE MONTHLY PERCENTAGE VALUE OF THE ORIGINAL DOLLAR PORTFOLIO VALUES FOR ALL GROUPS STUDIED: SIX MONTHS, ONE YEAR AND TWO YEARS LATER (%) Round-Lots 1955 P1“ P2* P3* 1956 P1* P2* P3* J 102.1 100.3 107.8 J 107.9 97.3 87.6 F 93.8 96.7 89.7 F 105.0 97.3 82.7 M 106.1 118.3 109.6 M 97.5 93.9 83.6 A 105.1 110.1 108.5 A 90.6 86.7 68.7 M 110.0 110.1 119.3 M 103.0 109.8 98.3 J 103.“ 97.6 102.6 J 100.1 10“.8 91.6 J 97.2 102.9 103.5 J 91.“ 100.2 97.7 A 101.9 10“.1 95.3 A 96.7 102.1 99.2 S 105.2 102.7 97.7 8 101.1 99.0 108.9 0 110.6 11“.1 95.1 0 10“.8 89.9 112.2 N 107.7 112.0 100.“ N 110.6 93.7 11“.6 D 8“.2 85.5 75.2 D 98.8 75.9 97.8 1957 P1* P2! P3“ 1958 P1» P2“ p3» J 106.1 89.“ 120.8 J 113.3 123.6 12“.3 F 105.8 89.1 11“.3 F 137.1 1“5.5 1““.5 M 96.1 83.8 11“.2 M 137.7 1“l.0 161.2 A 79.2 82.2 108.3 A 118.9 122.5 107.“ M 9“.9 103.1 123.3 M 137.7- 1“6.6 139.0 J 92.9. 101.8 128.2 J 132.“ 135.1 110.“ J 81.6 90.1 111.9 J 120.3 132.“ 110.2 A ”81.0 95.“ 106.8 A 122.1 132.7 120.“ S 89.“ 109.7 113.0 S 118.0 131.3 112.“ 0 98.6 121.5 12“.0 0 10“.3 138.“ 99.1 N 101.2 117.9 126.“ N 109.“ 129.2 9“.1 D 115.6 1““.5 15“.6 D 108.2 121.3 100.“ P1 - six months P2 - one year later P3 - two years later 185 fibundzLQLs 1959 P1* P2* Pu* 1960 P1 P2 P3“ 10“.8 11“.1 92.9 J 92.7 9“.0 101.“ 118.1 119.1 107.3 F 95.7 103.6 99.“ 112.3 111.3 115.“ M 88.1 109.8 110.2 115.7 105.2 100.2 A 92.8 116.1 103.2 105.2 9“.“ 10“.5 M 90.3 108.“ 78.7 109.0 9“.7 103.8 J 87.2 101.7 70.3 95.1 88.3 9“.9 J 10“.5 112.6 87.7 100.8 96.9 106.6 A 102.7 111.3 90.6 100.0 87.3 100.5 s 116.5 109.3 81.3 83.7 75.0 8“.8 0 120.“ 117.2 89.8 78.1 66.7 78.“ N 115.2 111.8 86.3 87.“ 80.7 99.7 D 12“.6 132.5 10“.8 1961 P1* P2* P3* J 109.“ 109.9 107.0 F 110.6 108.7 92.5 M 97.2 93.6 107.5 A 9“.9 89.7 89.3 M 95.“ 76.2 89.1 J 106.0 8“.5 100.2 J 99.8 81.9 92.3 A 99.0 79.1 100.6 S 95.2 77.3 125.7 0 92.8 77.9 101.5 N 8“.1 87.3 11“.9 D 79.8 88.“ 111.9 P1 P3 UZOC/Jibgc—ISPZ’IIC-I - six months - two years later P2 - one year later 186 Odd—Lot Sales 1955 21* P2“ 23* J 112.7 115.2 11“.“ F 96.1 105.9 102.3 M 107.“ 117.1 110.5 A 109.5 117.8 116.6 M 109.3 108.8 108.0 J 106.5 107.5 110.1 J 99.5 107.6 106.2 A 103.“ 95.“ 101.2 s 105.9 100.5 96.3 0 106.7 105.1 93.1 N 109.3 106.8 95.“ D 91.2 91.0 81.6 1957 P1* P2” 93* J 110.5 99.5’ 13“.2 F 103.5 91.8 121.“ M 99.6 92.“ 120.5 A 82.9 8“.1 109.7 M 95.5 101.5 127.5 J 91.3 103.5 129.1 J 89.0 96.3 125.1 A 92.3 102.6 12“.8 s 100.3 116.“ 132.0 0 106.5 126.6 136.9 N 103.6 12“.5 153.0 D 111.2 1“2.3 159.8 1959 21* 22* P3* J 110.1 117.7 126.3 F 113.3 11“.7 133.1 M 105.7.102.2 119.1 A 107.3 99.5 11“.“ M 108.6 92.1 101.6 J 112.“ 109.5 132.0 J 100.“ 91.“ 10“.2 A 99.1 10“.2 130.“ s 103.1 98.7 129.1 0 91.7 90.1 116.3 N 93.5 90.“ 110.7 D 87.2 87.0 109.6 1956 P1 P2 P3* J 10“.1 99.7 93.9 F 106.3 98.5 90.7 M 100.0 1o“.7 91.1 A 95.“ 96.1 83.8 M 102.5 107.5 96.8 J 99.1 10“.1 9“.“ J 92.“ 99.“ 93.5 A 93.3 98.9 9“.2 s 100.3 99.5 107.5 0 105.“ 90.5 105.6 N 109.3 9“.3 110.0 D 102.“ 8“.“ 111.8 1958 P1 P2 P3* J 112.1 137.5 1A9.9 F 116.9 1“6.5 160.“ M 119.1 1A5.3 1“1.3 A 118.9 1“3.3 126.5 M 125.7 1“3.6 138.7 J 131.3 135.3 129.9 J 120.2 129.1 117.9 A 120.9 131.9 120.3 s 118.3 12“.“ 117.3 0 113.1 120.8 106.7 N 117.1 12“.8 111.6 D 110.6 117.1 110.3 1960 P1 22 P3“ J 106.7 119.7 138.1 F 107.6 122.5 138.1 M 99.1 126.5 135.3 A 100.1 12“.1 120.8 M 115.5 1A5.2 115.0 J 99.3 109.“ 82.5 J 115.0 112.8 89.3 A 116.9 11“.2 93.9 s 126.2 128.0 92.3 0 125.2 133.2 91.7 N 122.7 131.5 102.5 D 118.7 130.2 110.7 187. Odd-Lot Sales 1961 P1” P2* P3* J 109.“ 111.“ 105.8 F 108.9 111.2 97.5 M 99.9 98.2 92.5 A 97.0 95.8 98.9 M, 107.0 90.7 107.1 J 113.6 85.0 102.9 J 107.3 85.9 99.1 A 103.7 82.0 101.9 S 98.9 76.3 108.“ 0 91.3 75.2 97.“ N 80.“ 83.1 102.9 D 79.1 89.5 110.7 Odd-Lot Purchases 1955 P1 P2* P3* 1956 P1“ P2 P3 J 106.“ 102.“ 101.“ J 106.1 98.3 90.8 F 96.1 10“.7 100.“ F 107.0 99.5 88.7 M 106.6 117.2 109.3 M 96.1 93.3 83.5 A 105.8 11“.l 112.8 A 95.6 97.7 85.7 M 106.9 108.7 107.9 M 103.5 10“.“ 93.5 J 103.6 103.8 108.6 J 96.6 99.6 92.9 J 99.6 112.“ ll“.7 J 90.3 9“.“ 93.2 A - 10“.l 99.“ 101.6 A 93.3 96.6 97.7 S 105.5 106:1 97.9 S 100.5 95.8 108.“ 0 107.7 93.“ 93.7 0 10“.9 93.2 111.6 N 109.7 10“.1 98.3 N 105.0. 93.5 113.“ D 91.2 90.3 83.5 D 100.7 83.1 111.9 1957 P1 P2“ P3“ 1958 P1” . P2 P3 J 10“.3 88.9 119.“ J 109.0 126.5 129.7 F- 101.5 92.2 123.“ F 116.1 133.5 133.6 M 9“.6 90.3 119.2 M 117.9 136.7 1“0.3 A 83.2 86.5 111.6 A 120.1 1“7.5 130.0 M 93.5 101.3 127.6 M 121.5 135.9 132.0 J 89.9 10“.9 131.2 J 129.8 133.1 135.5 J 90.7 99.1 125.5 J 122.6 135.2 13“.“ A 9“.5 106.6 12“.7 A 122.5 126.3 127.9 S 98.8 116.8 128.3 S 119.9 12“.3 126.2 0 105.6 127.7 137.9 0 117.0 12“.“ 120.7 N 101.6 123.3’ 1“2.0 N 110.1 11“.“ 111.0 D 110.0 138.7 151.5 ' D; 102.8 10“.7 113.5 188 Odd-Lot Purchases 1959 P1* P2* P3* 1960 P1* P2* P3* J 102.“ 103.2 118.7 J 105.9 117.0 137.2 F 10“.9 108.5 115.1 F 106.8 123.7 138.5 M 101.0 102.3 127.1 M 101.8 132.0 138.3 A 105.1 103.5 137.6 A 101.2 132.0 129.9 M 101.8 91.9 103.0 M 117.8 1A8.2 115.1 J 113.3 121.7 155.0. J 101.9 120.2 83.9 J 98.“ 10“.“. 129.2 J 112.8 109.0 86.5 A 100.8 111.8 135.2 A 11“.7 108.8 9 87:5 8 103.7 103.2 132.0 s 126.6 128.6 91.5 0 9“.6 95.8 123.3 0 126.9 136.0 96.6 N 98.3 98.8 119.2 N 12“.“ 131.9 99.9 D 97.5 100.7 129.8 D 118.9 130.6 98.6 In I! it 1961 P1 P2 P3 J 107.7 119.1 100.1 F 105.1 10“.2 90.8 M 98.5 92.“ 98.3 A 9“.5 90.3 91.1 M 109.8 8“.“ 98.3 J 115.7 81.9 96.5 J 105.“ 83.3 9“.9 A ' 101.9 106.2 92.3 s 97.1 71.7 99.5 0 89.5 70.9 92.7 N 81.“ 82.2 99.“ D 72.0 77.1 9“.0 Standard & Poor's Composite Averages 1955 P1“ P2 * P3“ 1956 P1“ P2* 23* J 118.2 121.2 122.8 J 112.8 101.8 . 95.9 F 118.0= 123.9 119.0 F 105.6 96.5 90.7 M 116.2 133.1 120.7 M 92.2 91.0 86.5 A 111.“ 126.9 121.2 A 96.2 95.1 90.9 M 119.6 120.2 125.0 M 101.7 10“.8 98.0 J 110.1 11“.“ 115.6 J 98.“ 101.0 96.“ J 101.2 113.6 109.8 J 90.3 96.8 96.2 A 105.5 110.9 105.2 A 92.1 95.6 101.0 s 111.5 102.“ 97.9 s ‘ 97.3 9“.3 110.2 0 113.7 109.9 95.9 0 101.0 88.7 113.1 N 100.2 101.0 90.9 N 105.1‘ 91.7 116.8 D 103.0 101.“ 88.5 D 101.6 86.“ 118.8 1957 189 P1 P2* P3* 1958 P1* P2 P3 J 106.9 9“.0 123.5 J 113.9 132.“ 13“.2 F 105.0 95.1 128.8 F 117.5 136.5 137.1 M 96.9 95.1 126.3 M 118.7 132.3 131.7 A 88.“ 95.2. 126.0 A 118.7 132.7 12“.6 M 87.2 93.“ 123.6 M 119.5 133.0. 126.8 J 85.1 95.6 l2“.5 J 122.5 130.3 126.1 J 87.7 99.1 128.2 J 117.0 -128.7 117.7 A 91.0 106.1 130.2 A 116.7 123.3 119.6 S 98.8 117.8 13“.2 S . 111.2 113.7 106.6 O 106.0 125.6 139.8 0 112.3 111.8 105.1 N 106.2 126.3 1“0.7 N 111.7 111.9 105.“ D 113.2- 138.6 1“9.8 D 106.8 108.5 10“.3 1959 P1 P2* P3* 1960 P1“ P2 P3 J 109.5 101.0 111.7 J 99.9 111.3 12“.6 F 106.2 101.1 11“.5 F 101.7 113.0 125.1 M 102.7 100.0 118.3 M 96.“ 118.5 125.“ A 98.7 9“.0 113.2 A 99;2‘ 119.9. 120.8 M 100.0 95.2 113.“ M 99.1 119.2 106.“ J 102.5 97.6 111.5 J 101.1 11“.6 98.1 J 92.5 91.8 111.3 J 111.5 121.“ 10“.0 A 9“.0 95.8. 11“.“ A 111.“ 119.7' 102.8' S 97.5 93.8 117.“ S ' 122.6 12“.8 103.7 0 9“.1'- 93.8 119.5- 0 3122.1 128.7 107.0 N 95.9 9“.9 123.2 N 119.8 129.2 111.5 D 95.3 96.1 118.5 D 112.2 122.1 1107.9 1961 'P * P2“ P3 J 109.0 112.1 107.3 F 107.5 110.7 101.0 M - 102.6 106.6 102.8 ' A 105.2 100.6 107.1 M 107.8 89.2 106.2 J 109.8 86.“ 106.5 J 103.7 86.5 103.5 A 103.1 86.0 106.74 S 10“.0 83.2 108.2 0 95.7 83.2 107.6 N 83.3 .8618 103.3 D 78.1 87.6 105. m Dow Jones Industrial Averages ‘— Ii— 190 1955 P1“ P2* P3* J 112.8 115.8 116.7- F 11“.0 118.2 113.8 M 111.2 125.7 115.9 A 106.9 120.7 116.5 M 113.3 113.1 118.6 J 107.6 109.0 111.5 J 101.6 111.3 108.7 A 10“.o 108.3 103.8 s 110.“; 100.“ 98.8 0 113.0 107.2 95.6 N 99-5 99.5 92-5 D 100.7 101.6 90.0 1957 P1” P2* P3* J 105.6 9“.7 123.6 F 10“.6 95.“! 130.2 M 97.0 93.8 127.0 A 87.9 92.“ 126.“ M' 88.5 92.3 127.“ J 87.3 95.1 129.3 J 89.3 99-“' 133-3 A 91.5 105.7 135.“ s 97.6 116.“ 138.9 0 103.6 123.6 1“6.3 N 103.6 12“.5 1“7.7 D 109.9 13“.9 155.7. 1959 P1“ P2“ P3“ J 11“.2 105.“ 109.3 F 108.7 103.9 109.9 M 105.3 102.“ 112.6 A 103.5 96.1 108.5 M 103.2 97.1 108.0 J 105.5, 99.6 107.2 J 92.8 91.5 105.8 A 9“.3 9“.2, 108.5 s 97.5 91.5. 110.8 0 92.7 90.5 108.9 N 9“.8 90.2 110.6 D 9“.“ 89.8 106.7 1956, P 1 2 3 J 110.2 101.“ 96.“ F 105.0 97.0 91.7 M 91.6 92. 87.0 A 9“.5 96.1 88.5 M 100.5 105.“ 97.5 J 100.7 102.1 97.2 .I 92.2 97.8 97.6‘ A 93.“ 96.8 101.9 s 100.0 97.0 111.7; 0 103.3 90.6 113.6 N 106.6 9“.5 118.5 D 100.8 87.9 117.6 1958 P1“ P2* P3 J 112.3 131.6 139.1 F 116.3 137.5 1“2.5 M 118.8 135.0 137.9 A 119.6 137.1 131.5 M 121.0 139.1 135.1 J 122.9 136.1 13“.1 J 117.7 13“.8 122.8 A 119.0 129.0 123.1 s 113.3 119.1 108.6 0 115.1 118.8 107.7 N 115.“ 119.2 106.7 D 111.5 116.3 10“.6 1960 P1“ 22* P3 J -99.2 10“.3~ 112.8 F 99.“ 105.2 113.0 M, 93.7 109.9 11“.“ A 97.3 112.5 111.6. M 95.1 111.2 97.7 J 95.3 107.7 89.6 J 105.3 115.8 95.9. A 105.9 115.2 96.2 s 116.8 120.6 98.6 0 116.7 121.3 102.9 N 116.“ 122.0 108.2 D 112.0 117.7 105.0 191 Dow Jones Industrial Averages 1961 P1* P2* P3* J 110.1 108.“ 105.“ F 108.9 107.5 99.6 M 103.“ 10“.3 101.“ A 103.7 98.9 106.0 M 10“.6 87.7 10“.2 J 106.0 83.9 102.5 J 99.6 83.8 98.5 A 98.9 83.7 101.7 S 100.6 81.6 105.3 O 95.“ 8“.8 107.1 N 8“.7 89.6 10“.2 D 78.5 88.5 10“.8 APPENDIX F THE MONTHLY DIVIDEND YIELDS FOR ALL GROUPS“ SIX MONTHS, ONE YEAR AND TWO YEARS AFTER INITIAL PURCHASE OR SALE OF THE PORTFOLIO 192 APPENDIX F SIX MONTHS, ONE YEAR AND TWO YEARS AFTER INITIAL PURCHASE OR SALE OF THE PORTFOLIO THE MONTHLY DIVIDEND YIELDS FOR ALL GROUPS: (M Round-Lot 1956 P1 1957 P1 P2 P3 P2 P2, P3 1955 P1 25u2108032ll 3333332 33333 6 1628775535“ hwfii“hw315943153a3:5 921015907AInY“anZZ AJUJ“:¥“NH“ADUJ“M7“ JFMAMJJASOND 801965199769 00000000000000 u5u233u33332 3.42.“.01095979 OOOOOOOOOOOO DJ4thNH3fiHRKQUNHU. 97938u31u20nd . 333233uuuuu3 JFMAMJJASOND 861102100365 OOOOOOOOOOOOOO DJ“MHUJ“N“DZD:JEEHM- 7&8472962308 000000000000 “HUJJUfiqhnlnHUNHUQJ 76 38 38558099 uuuuu32u3u33 JFMAMJJASOND P2 P3 1959 P1 P2 P3 1960 P1 P2 1958 P1 88 78 7831 3888 222222333333 095511766000 322222222333 0709.“. 5085092 323222322323 JFMAMJJASOND 5413206007.“.0 ““3323333223 872314.38 57.421 223323333333“ .071918721075 323222233323 JFMAMJJASOND 86 9782 92 "6,769 33232“. 33333.3 Tu259.rn.41.u8/D.5IIH "I! 333323322222 “063641311180 “I“. 332332 3323 JFMAMJJASOND B3 194 Odd-Lot Sales Round—Lot P2 P3 1955 P1 P2 P3 1956 P1 P2 1961 P1 75128.“.170562 “.“.“.u33“.3.“.333 021083987577. “.“..“.hu.3333“..“.“.“. 18800u106919 “.33“.“.3“.“.“.3“.3 JFMAMJJASOND 86 776130 7998 “.“.“.“.“..“.“.5“.“.“.“. “.36 760133330 “.“.“..“.“.“.n“..“.“.“.|“.|“. 667859119118 “.“.“.“.“.3.“.“.3“.“.3 JFMAMJJASOND 317579570011 332222323333 164313817966 322233333333 9.“.2167069158 222222322333 JFMAMJJASOND P2 P3 1958 P1 P2 P3 1959 P1 P2 1957 P1 873205222009 323332322222 05“.62.76.“.5658 323332322223 O“.2l660655“.8 323322322223 JFMAMJJASOND 186068290220 OOOOOOOOOOOO 322332“.3..“.“.I“.“. 066837“. 33“.2 l 322232333333 62127875663.“ 333332 333333 JFMAMJJASOND 9562155“.“.662 233332222223 18.“.103u09825 “.“.“.“.“.3332233 7.3576 0 18558“ 3“.“.“.“.“.“.3333.“. JFMAMJJASOND 3389158“ BMW/09 OOOOOOOOOOOO 332232222222 08605906999“. 322332322223 975801.“.12u87 222232222223 JFMAMJJASOND 2225517.“.967“. 222223222223 320203201819 222222222122 6&5716229831 222222221123 JFMAMJJASOND 195 Odd-Lot Purchases P2 P3 1956 P1 P2 'P3 1957 P1 P2 1955 P1 57.8 5.3.. 25500:”..6 333322223333 928530.“..1 5209 “a. sun. 333333“. 3 271165062079 4.455334 3.4.4.44 JFMAMJJASOND 753238220197 uuuuundhwnwuhwoaoa 3328 37126 083 uuu3u2u44545 0819u93uu53u .434 342.44.43.4U. JFMAMJJASOND 888 57326 7““.8 uuuuuuuuusuu 555770922u2l uuuuuuajwhfiuu.“ 787967997081 uuuuu3333u 3.“. JFMAMJJASOND 1960 P1 P2 P3 P2 1959 P1 P3 P2 1958 P1 53u2u 5769788 OOOOOOOOOOOO 222222222222 641008211811 222221222122 866508119823 222221221122 JFMAMJJASOND 56 92 73315013 232222222222 62u006639uu7 233332222222 AulquibQu7$lRYunH7. 233222222222 JFMAMJJAerOND 9738 96092097 OOOOOOOOOOOO 3332 32333322 87“,». 78 5850867 333232233222 320199161888 uuu332333222 JFMAMJJASOND P2 1961 P1 7“. 1832 732 133 ..... o o O O o o I 233222222222 3889550566 59 Vn¢922a4924a39Zdog2nc 26“.. 7983990 59 222211211222 JFMAMJJASOND 196 Dow Jones Industrial Averages 1957 P1 P2 P3 ‘P3 1956 P1 P2 P2 1955 P1 3 09720 608917 uuuuuuuuu3333 UJLRZbQuoanZIQZUQJ 7:0nanBRu93IE:b:J2 M;D:JRflHUK4thfi4n7u JFMAMJJASOND 097203608917 976652 1085u3 o oooooooo .0 O o .uthJQMHUfiqanIJQifi “86233“ 18680 875555702.0 98 .HMTHnHHfiqflébfiibhfiq 56095uu86233 698 5578 75555 uuuuuhfihfiuuuuu JFMAMJJASOND UAU£u9253941LRibQuO Qu7LDCJRibvthcOZBRu .unqflfiHUfiHUéDR:DUfl4 71?:39I4R35Ku0nyfiid QldaterU)bn3Ru5197l HQHUJHUJHMTHHHHJHU. Qid:)01;2qIQZJDIHRV uuuuuuuuuuuu JFMAMJJASOND P2 1959 P1 P3 P2 1958 P1 “JUJUcufifibnwu41Ranc DZznw741016nufllbc¥u 3333.“. 33“. 3333 7.491.891.9332“. 111110000012 000000000000 3333‘33333333 8685677u9189 “776.421.111.110 333333333333 JFMAMJJA.SOND OOOOOOOO 333333333333 nwfifiqpufileibQufifiovu 2:4:2213h54nl7L0nn2 33333.3333333 205376u5u837 O 10 1033u533u. ...... _ I 0 o o o o 333333333333 JFMAMJJASOND nwfifiHRURZIRZOQuR¢OVI Qi4:2213ufiqvl7}onn2 OOOOOOOOOOOO «JQiJQijaJQZJQZJQiJ 063.“..12205376 322109010103 333332 33.3333 608917063u02 108543322119 uh». 3333333332 JFMAMJJASOND P2 1969 P1 3159838.“.8012 53.223u221313 333333333333 .3u0658uu7882 22nd. 7198 08 55“. 3333a. 33“». 3333 19332u3u0658 00001222u719 3333333333.“. 3 JFMAMJJASOND 197 Standard & Poor's Index 1957 P1 P2 P3 1956 P1 P2 P1 P2 P3 1955 256131u66u87 322221122212 333333333333 77398889hfl23u. U. 3310976 5.“. 32 JFMAMJJA.SOND 77398889“ 32.4 .4 331097652992 uuuuu3333333 4768.45713748 5.431.091.5566“ uuuuu3uuuuuu 2727414768.“:5 901223543109 34.4.4.4“.434UH3 JFMAMJJASOND 4768457174748 543109135664 UUUUHQJHUUUHH 47.4 9992 72 7H1 299008901223 u334u33uuuuu 72.4 55.4.47“ 999 879012299008 333uuuu33uu3 JFMAMJJASOND P1 1959 P3 P1 1958 5552800701001 990 376 56 7.5.4 3 2233333333333 3352 901.3le 57 109990 999889 332223222222 350118 3352 90 4565.42109990 335290131557 109990999889 332223222222 “17109350118 U.SIIHSMIIHHSKOBNHZ 89.“. JFMAMJJASOND P2 1961 P1 785360365433 221112100110 333333333333 555288701001 990376 5675.“. 3 22 3333333333 131...“.57555288 99988 9990 376 222222223333 - JFMAMJJASOND BIBLIOGRAPHY 198 BIBLIOGRAPHY Books Drew, Garfield A. New Methods for Profit inithe Stock Market. Boston, Mass.: The Metcalf Press, 1955. Hardy, Charles D. Odd—Lot Trading on_the New York Stock Exchange. Washington, D. C.: The Brookings Institution, 1939- Hoffman, Wright G. Character and Extent of Over-the-Counter Markets in 1952. Philadelphia: University of Pennsyl- vania Press, 1952. Leffler, George L. The Stock Market. New York: Ronald Press, 1957. Neill, Humphrey B. Tape Reading and Market Tactics. Saxtons River, Vermont: Neill Letters of Contrary Opinion, 1960. (Special Reprint Edition). Owen, D. B. Handbook of Statistical Tables. Reading, Mass.: Addison-Wesley Publishing Company, 1962. Schaefer, E. George. How I Helped More Than 10,000 Investors to Profit in Stocks. Englewood Cliffs, New Jersey: Prentice-Hall, Incorporated, 1960. Bulletins and Reports "A Shortage of Stocks?," Moody's Stock Survey, April 20, 196”. Cleveland‘TrusttCompany.. Business Bulletin, VL (January 25, 1964), Cleveland: Cleveland Trust Company, 196“. The Kiplinger Washington Letter of January 31, 196“. Wash- ington, D. C.: The Kiplinger Washington Editors, Incorporated, 1964.‘ New York Stock Exchange. The Odd-Lotter in the October 16, 1963 Public Transaction Study. A Report Prepared by the Department of Research & Statistics. New York: New York Stock Exchange, 1963. 199 200 New York Stock Exchange. Public Transaction Study. New York: The New York Stock Exchange, 1956. New York Stock Exchange. Public Transaction Study. New York: The New York Stock Exchange, 1957. New York Stock Exchange. Stock Market Activity--A Study of Public Transactions in the Nation's Market Place on June 8 and June 15, 1955. New York: The New York Stock Exchange, 1955. New York Stock Exchange. Year Book--1955. Compiled by the Department of Research & Statistics and by the Depart- ment of Public Relations. New York: The New York Stock Exchange, 1956. New York Stock Exchange. Stocks--January, 196“ Issue. New York: F. E. Fitch, Incorporated, 196“. Simpson, Kemper, and Ballinger, Willis J. The Feasibility and Advisability of the Complete Separation of the Function of Dealer and Broker. A Report Prepared for the Securities & Exchange Commission, 1936. Standard & Poor. Stock Guide--July, 1963. New York: Standard & Poor's Corporation, 1963 Articles and Periodicals "Are Market Turns Predictable?," Forbes, LXXXII (July 15, 1958), 13-16. "'— Biel, Heinz H. "Stock Analysis--The Speculative Fever Is Rising," Forbes, XIIC (February 1, 196H), 38-39. "Big Board's Monthly Investment Program Perks Up Following Three Years of Decline," Wall Street Journal, XLIV (April 2, 196“), 9. ' "Blue Monday and the Odd-Lotter," Exchange, XXIII (October, 1962), 9‘12. "Bulls Vs Bears," Exchange, XXIII (June, 1962), 7-8. Crane, Burton. "Small Investor is Often Right Unless He Sells Short," New York Times (April 29, 1962), l. Drew,Garfield A. "Misunderstood Odd-Lotter," Barron's, XLII (June 25, 1962), 5+. 201 Drew, Garfield A. "Odd-Lotter," Barron's, XXXV (October 31, 1955), 5-6+ The Drew Odd-Lot Studies of February.1, 196“. Boston, Mass.: Drew Investment Associates, Incorporated, 196“. The Drew Odd-Lot Studies of September 1,.1962.‘ Boston, Mass.: Drew Investment Associates, Incorporated, 1962. "Full of Doubts: Odd-Lot Trading," Forbes, LXXXII (Septem~ ber 1, 1958), 17. Gingold, Oliver J. (ed.). "Abreast of the Market," Wall "Street Journa1,;XLII (December 23, 1963), 13. Gingold, Oliver J. (ed.). "Abreast of the Market," Wall Street Journal, XLIII (February 2“, 1964), I5- Granger, C. W., and Morgenstern, Oscar. "Spectral Analysis of New York Market Prices," Kyklos, XVI (March, 1963), 1—27. Hayes, Kenneth. "The OddeLot Investor Grows in Stature," Exchange, XX (March, 1959), 12-15. Hillery, Victor J. "Small Investors Begin To Buy More Shares Than They're Selling," Wall Street Journal, XLIV (April 23, 196“), 1, u. Krasnansky, Marvin L. "A Look at the Odd-Lot Investor," Exchange, XXII (February, 1961), 7-9. Krasnansky, Marvin L. "Unraveling the Odd-Lot," Exchange, XXIV (June, 1963), 5-7. Malabre, Alfred L., Jr. "Economy's Rise Shows Little Sign of Slowing As It Sets a Record," Wall Street Journal, XLIV (April 2, 196“), 1, 8. Molodovsky, Nicholas. "Lessons From the Recent Past," Financial Analyst Journal (January-February, 196“), 50-51. "New Look at the Small Investor," Exchange, XV (February, 195“), 1—2. "New Look at the Stock Market,“ Exchange, XIV (July, 1953), 8-11. "The 1960 Odd—Lot Investor," Exchange, XXII (March, 1961), 5—7. T ’ 202 "The 1961 Odd—Lot Investor," Exchange, XXIII (March, 1962), 15. "The Odd- Lot Investor Looks Ahead, " Exchange, XIX. (February, 1958), 10- ll. "Odd—Lot Purchases, Sales and Balance Annually for 1937 through 1957," Exchange, XIX (February, 1958), ll. "Odd-Lot Trader," Financial World, CXIX (February 13, 1963), 11+. "Odd-Lot Trading: An Art in Itself," Business Week (June 7, 1952), 116+. "Odd-Lot Volume Expands," Exchange, XX (October, 1959), 19. "Odd— Lot Volume Leaders Disclosed, " Exchange, XIX (July, 1958), 9-11.‘ "Odd- Lot Volume Refutes Legend, " Exchange, XIV (March, 1963), l- 2. ' "Odd—Lots," Exchange, XVIII (September, 1957), "Odd-Lots Vs Round—Lots," Exchange, XVI (February, 1955), "Odd-Lotters & RoundaLotters," Exchange, XXIV-(March, 1963), 10-12. "Odd- Lotters Vs Round— Lotters," Exchange, XVII (November, 1956), l. ' Schulz, John W. "Technician's Perspective--Bubble Trouble?," Forbes, XIIC (February 15, 196“), 50-51. Schulz, John W. "Technician's Perspective--Chame1eon Market,’ Forbes, XIIC (March 1, 196“), “6-“7. Schulz, John W. "Technician's Perspective--Is A Bullish Public Bearish?," Fgrbes, XIIC (February 1, 196“), 140-41 I Schulz, John W. "Technician's Perspective You, The Public," Forbes, XVC (February 15, 1961), “2—“3. "Profile of Stockholders," Egchangg, XX (July, 1959), 7. Seligman, Donald, and Wise, T. P. "New Forces in the Stock Market," Fortune, LXIX (February, 196“), 92-95+. 203 "17,000,000 Shareowners," Exchange, XXIII (July, 1962), 1-6. "The Share Owner Census," Exchange, XIII (July, 1952), 1-5. "Share Ownership Whys and Whens," Exchange, XXIV (January, 1963). 11—13. "Side Lines-~The Year of the Exodus," Forbes, XIIC (January 15, 196“), 5—60 "The Small Investor," Exchange, XV (March, 195“), 1-2. "The Small Investor Is in Good Company," Exchange, XXIII (February, 1962), 21. "Small Investor's Boswell," Time, LXXVII (March 31, 1961), 69. ’ “ ”The Small Investor Isn't So Small, Exchange, XXII (November, 1961), 20— 21. Smith, H. C. "Odd-Lot Securities Business," Commercial and Financial Chronicle, CLXXVI (July 2“, 1952), 29“. Smith, H. C. "Odd-Lot System on the New York Stock Exchange," Commercial and Financial Chronicle, CLXXVIII (October, 22, 1953), 1936+. "Stock Prices and Business Prospects," Business Conditions (November, 1963), 6-10. (A reView by"the Federal'Reserve Bank of Chicago, November, 1963). ”Study of Investments Finds Stock Yield Tops That of Other Types," Wall Street Journal, XLV (December 2, 1963), 16. "Study of Odd—Lot Public," Exchange, XV (February, 195“), l. Thurlow, Bradbury K. "Investment Pointers--The Dull Blue Chips," Forbes, XIIC (February 1, 196“), “2-“3. Thurlow, Bradbury K. "Investment Pointers-—A Vulnerable Market," Forbes, XIIC (February 15, 196“), 52—53. Vartan, Vantanig G. "Odd-Lot Selling Is Short," New York Times, (April 2, 1963), 61,75. ”Who Buys Stocks--And Why," Exchange, XV (June, 195“), 9-12.