Price Movements in Speculative Markets: Trends or Random Walks by SIDNEY S. ALEXANDER, Professor of Industrial management There is a remarkable contradiction between the con behavior of speculative prices held by professional stock market analysts on the one hand and by academic statisticians and econo mists on the other. The profes sional analysts operate in the belief that there exist certain trend generating facts, knowable today, that will guide a speculator to profit if only he can read them cor rectly. These facts are believed to generate trends rather than ins tantaneous jumps because most of those trading in speculative markets have imperfect knowledge of these facts, and the future trend of prices will result from a gradual spread of awareness of these facts throughout the market. Those who gain mastery of the critical information earlier than others will, accordingly, have an opportunity to profit from that early knowledge The two main schools of profes sional analysts, the fundamen talists"and the "technicians, ' agree on this basic assumption. They differ only in the methods used to gain knowledge before others in the market, The fundamentalist seeks this early knowledge from study of the external factors that lie behind the price changes. In a commodity market he tries to estimate the future balance of supp In the stock market he general business conditions and the profit prospects for various i dustries, and for the individual firms within those industries, with The 'technician''operates on the same basic assumption, that facts existing at one time will govern the pi time, but he operates in a different manner. He leaves to others the study of the fundamental facts in the reliance that as thos others act on their knowledge there will be a detectable effect on te of the stock The technician, accordingly, studies price movements of the immediate past for telltale indica he Both schools of analysts thus assume the existence of trends hich represent the gradual recognition by the market of emergent factual situations trends which, if they exist, must depend for 4 The data gathering and processing. underlying this research were sup Po2 ch Fund of the School of Industrial man etts Institute of technol 7
their existence on a lagged response of the market prices to the derlying factors governing those prices. It might, at first blush, seem possible that the trends arise not from a lagged response of the market price to the fundamental circumstances, but rather from a trend in those underlying circumstances themselves. Thus although a stock's price might at all times represent a given mul tiple of its earnings, its earnings might be subject to a long run trend, If, however, there are really trends in earnings, so that an increase in earnings this year implies a higher probability of increase next year than do stable or declining earnings, the stock rice right ld reflect these prospects by a higher p and by a higher ratio of price to current earnings. Consequentl if there is no lagged response there should be no trend in prices By a trend in this connection we mean a positive serial correlation of successive changes or, more generally, a probability of future price change dependent on present The professional analysts would certainly not subscribe to th notion that the best picture of the future movements of prices can be gained by tossing a coin or a set of coins. Yet that is just what academic students of speculative markets say is the best way. The academic students of speculative marl the very existence of trends in speculative prices, claiming tha where trends seem to be observable, they are merely interpreta after the fact, of dom walk. A pri k if at any time the change to be expected can be represented by the result of tossing a coin, not necessarily a 50-50 coin, however. In par ticular, a random walk would imply that the next move of the speculative price is independent of all past moves or ever This probabilistic view of speculative prices is consistent with the theoretical bent of economists who like to talk about perfect markets. If one were to start out with the assumption that a stock commodity speculation is afair game' with equal expectation of gain or loss or, more accurately, with an expectation of zero in, one would be well on the way to picturing the behavior of speculative prices as a random walk. But in fact, this picture of a speculative price movement is as much based on empirical findings as on theoretical predispositions. In a pioneer work Bachelier,I a student of the great French mathematician Poincare derived, in his doctoral thesis in 1900, a theory that speculative prices follow random walks, largely from the as sumption of zero expectation of gain. He then compared the statistical dis ibution served distributions of price changes of certain government securities (rentes)on the Paris Bourse, and he found a close cor espondence between the observed distribution and that to be ex pected from his theory. M. L. Bachelier, Theorie de la Speculation, Gauthier-Villars, Paris 1900
The most impressive recent findings confirming the random walk hypothesis are those of Kendall. He calculated the firs twenty-nine lagged serial correlations of the first differences of twenty-two time series representing speculative prices. Nineteen ese were indexes of Britishindustrial share prices on a weekl basis.(See Table 1). Two of the remaining three were cash wheat t Chicago, one weekly and one monthly, and the last was the spot cotton price at New York, monthly. Essentially, Kendall was ask ing with respect to each weekly series: How good is the bes estimate we can make of next week's price change if we know this week's change and the changes of the past twenty-nine weeks and correspondingly for the monthly series Contrary to the generalimpression among traders and analysts hat stock and commodity prices follow trends, Kendall found, with two or three exceptions, that knowledge of past price changes yields substantially no information about future price change More specifically, he found that each period's price change was not significantly correlated with the preceding period's price hange nor with the price change of any earlier period, at least as p to twenty-nine periods. Essentially, timate of the next period's price change could have been drawn at random from a specified distribution with results as satisfactory as the best formula that could be fitted to past data. In the case of hat distribution was studied in detail and it turned out to be very close to a normal distribution There was one notable exception, however, to this pattern of random behavior of price changes, That was the monthly series on cotton prices in the United States since 1816 with, of course,a few interruptions for such events as the Civil War. For this seri there did appear to be some predictability, and Kendall felt im pelled to draw the moral that it is dangerous to generalize eve from fairly extensive sets of data, For, from the behavior of wheat prices and the stock prices, one might have concluded that speculative markets do not generate autocorrelated price changes and here was cotton providing a notable excepti Alas, Kendall drew the wrong moral, The appropriate one is that if you find a single exception, look for an error. An error e was, for the cotton price series was different from the others nvestigated by Kendall. Almost all the others were series of ob servations of the price at a specified time- say, the closing price on Friday of each week. Each observation of the cotton series was an average of four or five weekly observations of the corresponding month. It turns out that even if the original data - the Friday osing prices - were a random walk, with successive first differ ences uncorrelated, the first differences of the monthly average of The Analysis of Economic Time Series- Part I: Prices. I Journal of the R ety( Series A), vol Pp.I1-25
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four or five of these weekly observations would exhibit first-order serial correlations of about the magnitude Kendall found for cotton. So Kendall's exception vanishes, and we are left with the conclusion that at least for the series he investigated the serial correlations were not significantly different from zero. 4 But the question immediately arises whether a week is not an inappropriate period of observation, The market analysts might Pro ng smooth underlying movement on which is typically superimposed lot of short-term fluctuation. With weekly observations the short term fluctuations might very easily swamp the underlying trends In particular, the give and take of the market leads to a phenome on,recognized by all analysts, of reactions, usually called tech nical presumably associated with profit hese reactions are, of course, negatively correlated with the main price swings. That's what makes them reactions. Kendall's correla tions, close to zero, could possibly be a consequence of the com bination of the negative contributions of the reactions and the positive contributions of the trends The path of a speculative price might, accordingly, be repre sented by a sum of two components, a smooth underlying trend or cycle changing direction only infrequently, and a much shorter cycle of action and reaction,. Under this hypothesis the first-order serial correlations of daily price changes might be negative, the first order correlation of weekly changes might be close to zero, phile the first order serial correlations of monthly or bimonthly changes might be significantly larger than zero We can test this possibility by studying the first order serial correlations of Kendall's data using successively longer intervals of differen , serial correlation of one week changes, then of two week, four eek, eight week, and sixteen week changes, the influence of the reactions should become smaller and smaller and the trend effect if there is one, should become do relations, roughly calculated, 5 are given in Table 1 his point was independently The latter r discove ered by the author and by Holbrook ver he pleasure of first publishing it in Note on the Correlation of First Differences of Averages in a Randor Chain,"Econometrica, Vol. 28, No. 4, October 1960, pp.916-918. Another possible exception may be noted for Kendall's series 3, Invest ment Trusts, whose first five serial correlations were.301.0.356, 0.158 0. 164 and 0.066. This series will be mentioned again below. oughly, because they were computed, not from the original data, but rom the serial correlations published by Kendall. Since successive serial correlations are based on fewer observations because of the necessity of sacrificing end terms, a certain #lend term error is introduced by this procedure