The Adiustment of Stock Prices to New Information TORIo Eugene F. Fama; Lawrence Fisher; Michael C Jensen; Richard roll International Economic Review, Vol 10, No. 1.(Feb, 1969), pp 1-21 Stable url: http://links.jstor.org/sici?sici=0020-6598%28196902%2910%03a1%03c1903ataospt%3e2.0.c0%03b2-p International Economic Review is currently published by Economics Department of the University of Pe sylvania Your use of the JStOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at tp://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JStOR archive only for your personal, non-commercial use Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/ier_pub.html Each copy of any part of a jSTOR transmission must contain the same copyright notice that appears on the screen or rinted page of such transmission. jSTOR is an independent not-for-profit organization dedicated to creating and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support @jstor.org http://wwwjstor.org Fri Apr1405:32:162006
INTERNATIONAL ECONOMIC REVIEW February, 1969 VoL. 10. No. 1 THE ADJUSTMENT OF STOCK PRICES TO NEW INFORMATION* BY EuGENE F. FAMA, LAWRENCE FISHER MICHAEL C. JENSEN AND RICHARD RoLLI THERE IS an impressive body of empirical evidence which indicates that successive price changes in individual common stocks are very nearly inde- endent. 2 Recent papers by Mandelbrot [11] and Samuelson [16]show rigor- ously that independence of successive price changes is consistent with al efficient"market, i.e. a market that adjusts rapidly to new information. It is important to note, however, that in the empirical work to date the usual procedure has been to infer market efficiency from the observed inde pendence of successive price changes. There has been very little actual testing of the speed of adjustment of prices to specific linds of new infor- mation. The prime concern of this paper is to examine the process by which common stock prices adjust to the information (if any) that is implicit in a 2. SPLITS, DIVIDENDS, AND NEW INFORMATION: A HYPOTHESIS More specifically, this study will attempt to examine evidence on two related questions:(1)Is there normally some unusual" behavior in the rates of eturn on a split security in the months surrounding the split? and (2)if splits are associated with "unusual"behavior of security returns, to what extent can this be accounted for by relationships between splits and changes Manuscript received May 31, 1966, revised October 3, 1966. This study way suggested to us by Professor James H. lorie We are grateful to Professors Lorie, Merton H. Miller, and Harry V. Roberts for many helpful com- ments and criticism The research reported here was supported by the Center for Research in Security Prices, Graduate School of Business, University of Chicago, and by funds made available to the Center by the National Science Foundation 2 Cf Cootner [2] and the studies reprinted therein, Fama [3], Godfrey, Granger, and Morgenstern [8]and other empirical studies of the theory of random walks in specu lative prices 3a precise definition of" unusual"behavior of security returns will be provided
FAMA, FISHER, JENSEN AND ROLL In answer to the first question we shall show that stock splits are usually preceded by a period during which the rates of return (including dividends and capital appreciation) on the securities to be split are unusually high. The period of high returns begins, however, long before any information (or even rumor) concerning a possible split is likely to reach the market. Thus we suggest that the high returns far in advance of the split arise from the fact that during the pre-split period these companies have experienced dra matic increases in expected earnings and dividends. In the empirical work reported below, however we shall see that the highest average monthly rates of return on split shares occur in the few months immediately preceding the split. This might appear to suggest that the split elf provides some impetus for increased returns. We shall present evi- dence, however, which suggests that such is not the case The evidence sup- ports the following reasoning: Although there has probably been a dramatic increase in earnings in the recent past in the months immediately prior to he split (or its announcement) there may still be considerable uncertainty in the market concerning whether the earnings can be maintained at their new higher level. Investors will attempt to use any information available to reduce this uncertainty, and a proposed split may be one source of such In the past a large fraction of stock splits have been followed closely by dividend increases-and increases greater than those experienced at the time by other securities in the market. In fact it is not unusual for dividend change to be announced at the same time as the split. studies (ef. Lintner [10] and Michaelsen [14]) have demonstrated that dividends have been increased, large firms show great reluctance to reduce them, except under the most extreme conditions Directors have appeared to hedge against such dividend cuts by increasing dividends only when they are quite sure of their ability to maintain them in the future, i. e. only when they feel strongly that future earnings will be sufficient to maintain the dividends at their new higher rate Thus dividend changes may be assumed to convey important information to the market concerning managements 4 There is another question concerning stock splits which this study does not con ider. That is given that splitting is not costless, and since the only apparent result is to multiply the number of shares per shareholder without increasing the share holders claims to assets, why do firms split their shares? This question has been the subject of considerable discussion in the professional financial literature. (Cf Bellemore and Blucher [1].) Suffice it to say that the arguments offered in favor of splitting usually turn out to be two-sided under closer examination -e.g, a split, by reducing the price of a round lot, will reduce transactions costs for some rela tively small traders but increase costs for both large and very small traders (i. e for traders who will trade, exclusively, either round lots or odd lots both before and after the split). Thus the conclusions are never clear-cut. In this study we shall be concerned with identifying the factors which the market regards as important in a tock split and with determining how market prices adjust to these factors rather han with explaining why firms split their shares
ADJUSTMENT OF STOCK PRICES assessment of the firms long-run earning and dividend paying potential. We suggest, then, that unusually high returns on splitting shares in the months immediately preceding a split reflect the market's anticipation of substantial increases in dividends which, in fact, usually occur. Indeed evidence presented below leads us to conclude that when the information effects of dividend changes are taken into account, the apparent price effects of the split will vanish. 5 3. SAMPLE AND METHODOLOGY a. The data. We define a"stock split"as an exchange of shares in whicl at least five shares are distributed for every four formerly outstanding. Th this definition of splits includes all stock dividends of 25 per cent or greater. e also decided, arbitrarily that in order to get reliable estimates of the parameters that will be used in the analysis, it is necessary to have at least twenty-four successive months of price-dividend data around the split date. Since the data cover only common stocks listed on the New York Stock Exchange, our rules require that to qualify for inclusion in the tests a syso security must be listed on the Exchange for at least twelve months before and twelve months after the split. From January, 1927, through December 1959, 940 splits meeting these criteria occurred on the New York Stock Exchange. b. Adjusting security returns for general market conditions. Of course, during this 88 year period, economic and hence general stock market condi- tions were far from static. Since we are interested in isolating whatever ordinary effects a split and its associated dividend history may have on returns, it is necessary to abstract from general market conditions in examining the returns on securities during months surrounding split dates. We do this in the following way: Define Pit= price of the j-th stock at end of month t. P;t= Pit adjusted for capital changes in month t+l. For the method of Dit= cash dividends on the j-th security during month t(where the divi- dend ' is taken as of the ex-dividend data rather than the payment Rit=(Pit+ Di)/Pi t-1= price relative of the j-th security for month t L t= the link relative of Fisher,s"Combination Investment Performance Index"[6,(table AI)]. It will suffice here to note that L is a com- dividend changes, There is in our evidence which suggests that from information effects, in a perfect capital market dividend policy will ne the total market value of a firm The basic dat contained in the master file of monthly prices, dividends, and eapital changes, collected and maintained by the center for Research in (Graduate School of Business, University of Chicago). At the time conducted, the file covered the period January, 1926 to Decembe description of the data see Fisher and Lorie [7
FAMA, FISHER, JENSEN AND ROLL plicated average of the Rj for all securities that were on the N.y.S.E at the end of months t and Lt is the measure of genera market conditionsused in this study. One form or another of the following simple model has often been sug gested as a way of expressing the relationship between the monthly rates f return provided by an individual security and general market conditions: 8 loge Rst =a;+B,loge Lt+ ujt where a, and B are parameters that can vary from security to security and Wjt is a random disturbance term. It is assumed that ujt satisfies the usual assumptions of the linear regression model. That is, (a)uyt has zero ex pectation and variance independent of t;(b)the uit are serially independent and (c)the distribution of ui is independent of loge L. The natural logarithm of the security price relative is the rate of return (with continuous compounding) for the month in question; similarly, the log of the market index relative is approximately the rate of return on a port folio which includes equal dollar amounts of all securities in the market Thus (1)represents the monthly rate of return on an individual security as a linear function of the corresponding return for the market. c. Tests of model specification. Using the available time series on rit and Lt, least squares has been used to estimate a; and B; in (1)for each of the 622 securities in the sample of 940 splits. We shall see later that there is strong evidence that the expected values of the residuals from (1)are non-zero in months close to the split. For these months the assumptions of he regression model concerning the disturbance term in (1) are not valid. Thus if these months were included in the sample, estimates of a and B would be subject to specification error, which could be very serious. We have attempted to avoid this source of specification error by excluding from the estimating samples those months for which the expected values of the 7 To check that our results do not arise from any special properties of the index Lt, we have also performed all tests using Standard and Poors Composite Price Index as the measure of market conditions; in all major respects the results agree 8 Cf. Markowitz [13, (96-101)1, Sharpe [17, 18]and Fama [4]. The logarithmic form of the model is appealing for two reasons. First, over the period covered by our data the distribution of the monthly values of loge Lt and loge Rit are fairly sym- metric, whereas the distributions of the relatives themselves skewed right. Sym- metry is desirable since models involving sy metrically distributed variables present fewer estimation problems than models involving variables with skewed distributions. B in 1), the sample residuals conform well to the assumptions of the simple linear regres- sion model Thus, the logarithmic form of the model appears to be well specified from a sta al point of view and has a natural economic interpretation (i. e, in terms of monthly rates of return with continuous compounding). Nevertheless, to check that our results do not depend critically on using logs, all tests have also been carried out using the simple regression of Rit on Lt. These results are in complete agree- ment with those presented in the text