The Adjustment of stock Prices to New Information OR。 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://inksistor.org/sici?sic0020-6598%028196902%02910%3a1%03c1%03ataospt%3e2.0.co%03b2-p International Economic Review is currently published by Economics Department of the University of Pennsylvania Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.htmlJstOr'sTermsandConditionsofUseprovidesinpartthatunlessyouhaveobtained 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 nt notice that appears on the screen or pri Each copy of any part of a JSTOR transmission must contain the same copyright notice that ap page of such transmission The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to journals and scholarly literature from around the world. The Archive is supported by libraries, scholar ies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the community take advantage of advances in technology. For more information regarding JSTOR, please contact support@jstor. org Sat oct2711:00272007
The Adjustment of Stock Prices to New Information 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%3A1%3C1%3ATAOSPT%3E2.0.CO%3B2-P International Economic Review is currently published by Economics Department of the University of Pennsylvania. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you 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 printed page of such transmission. The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Sat Oct 27 11:00:27 2007
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 ROLL1 1. INTRODUCTION a THERE IS an impressive body of empirical evidence which indicates that cessive price changes in individual common stod eks are ve rly inc endent. 2 Recent papers by Mandelbrot [11] and Samuelson[16] show rigor ously that independence of successive price changes is consistent with an "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 sual 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 kinds 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 stock split PLITS, 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 return 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 Manuseript received May 31, 1966, revised October 3, 1966. to Professors Lorie, Merton H. Miller, and Harry V. Roberts for many helpful tar ments and criticisms 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. s 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 a precise definition of"unusual " behavior of security returns will be provided
February, 1969 Vol, 10, No, 1 THE ADJUSTMENT OF STOCK PRICES TO NEW INFORMATION* BY EUGENEF. FAMA,LAWRENCEFISHER, MICHAELC. JENSENAND RICHARDROLL^ 1. INTRODUCTION THEREIS an impressive body of empirical evidence which indicates that successive price changes in individual common stocks are very nearly indeen dent.^ Recent papers by Mandelbrot [ll] and Samuelson [16] show rigorously that independence of successive price changes is colzsistent with an "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 independence of successive price changes. There has been very little actual testing of the speed of adjustment of prices to specijc kinds of new information. 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 stock split. 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 return on a split security in the months surrounding the split?3 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. 1 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 comments and criticisms. 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 speculative prices. a A precise definition of "unusual" behavior of security returns will be provided below
FAMA, FISHER. JENSEN AND ROLL in other more fundamental variables? 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 highes verage monthly rates of eturn on split shares occur in the few months mmediately preceding the split. This might appear to suggest that the split itself 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 the 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 luce this uncertainty, and a proposed split may be one source of such information In the past a large fraction of stock splits have been followed closely by dividend increases-and increases greater than those experienced at the same time by other securities in the market. In fact it is not unusual for the dividend change to be announced at the same time as the split. other studies(ef. Lintner [10] and Michaelsen [14]) have demonstrated that, once 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 There is another question concerning stock splits which th ider. That is, given that splitting is not costless, and since the only apparent resul s to multiply the number of shares per shareholder without increasing the share- holder's 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 stock split and with determining how market prices adjust to these factors rather than with explaining why firms split their shares
2 FAMA, FISHER, JENSEN AND ROLL in other more fundamental variables?' 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 rnatie 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 itself provides some impetus for increased returns. We shall present evidence, however, which suggests that such is not the case. The evidence supports the following reasoning: Although there has probably been a dramatic increase in earnings in the recent past, in the months immediately prior to the 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 information. In the past a large fraction of stock splits have been followed closely by dividend increases-and increases greater than those experienced at the same time by other securities in the market. In fact it is not unusual for the dividend change to be announced at the same time as the split. Other studies (cf. Lintner [lo] and Michaelsen [14]) have demonstrated that, once 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 management's There is another question concerning stock splits which this study does not consider. 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 shareholder's 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 [I].) 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 relatively 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 stock split and with determining how market prices adjust to these factors rather than with explaining why firms split their shares
ADJUSTMENT OF STOCK PRICES assessment of the firm' s 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 f the split will vanish. 5 3. SAMPLE AND METHODOLOGY a. The data. We define a"stock split" as an exchange of shares in which at least five shares are distributed for every four formerly outstanding. Thus this definition of splits includes all stock dividends of 25 per cent or greater We 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 split 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 33 year period, economic and hence general stock market condi- tions were far from static. Since we are interested in isolating whatever eatraordinary 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 Pit adjusted for capital changes in month t+1. For the method of adjustment see Fisher [5] 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 date). Rit=(Pit+ D/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 A1)]. It will suffice here to note that L is a com- s It is important to note that our hypothesis concerns the information content of dividend changes. There is nothing in our evidence policy per se affects the value of a firm. Indeed, the first suggested by Miller and Modigliani in [15,(430)] = from information effects, in a perfect capital market dividend polic the total market value of a firm 8 The basic data were contained in the master file of monthly dividends, and capital changes, collected and maintained by the center for Resea Security Prices graduate School of Business, University of Chicago). At the time this study was conducted, the file covered the period January, 1926 to December, 1960. For a description of the data see Fisher and Lorie [7]
ADJUSTMENT OF STOCK PRICES 3 assessment of the firm's 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 inforination effects of dividend changes are taken into account, the apparent price effects of the split will ~anish.~ 3. SAMPLE AND METHODOLOGY a. The data. We define a "stock split" as an exchange of shares in which at least five shares are distributed for every four formerly outstanding. Thus this definition of splits includes all stock dividends of 25 per cent or greater. We 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 split 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 E~change.~ b. Adjusting security returns for general market conditions. Of course, during this 33 year period, economic and hence general stock market conditions were far from static. Since we are interested in isolating whatever extraordinary 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 Pjt= price of the j-th stock at end of month t. Pj', = Pjt adjusted for capital changes in month t + 1. For the method of adjustment see Fisher [5]. Djt = cash dividends on the j-th security during month t (where the dividend is taken as of the ex-dividend data rather than the payment date). Rjt = (Pjt + ~j~)/Pf,~-l = price relative of the j-th security for month t. Lt = the link relative of Fisher's "Combination Investment Performance Index" [6, (table Al)]. It will suffice here to note that Lt is a com- 5 It is important to note that our hypothesis concerns the information content of dividend changes. There is nothing in our evidence which suggests that dividend policy per se affects the value of a firm. Indeed, the information hypothesis was first suggested by Miller and Modigliani in [15, (430)], where they show that, aside from information effects, in a perfect capital market dividend policy will not affect the total market value of a firm. 6 The basic data were contained in the master file of monthly prices, dividends, and capital changes, collected and maintained by the Center for Research in Security Prices (Graduate School of Business, University of Chicago). At the time this study was conducted, the file covered the period January, 1926 to December, 1960. For a description of the data see Fisher and Lorie [7]
FAMA, FISHER, JENSEN AND ROLL plicated average of the Rit for all securities that were on the n..Se. at the end of months t and t-1. Lt is the measure of "general market conditions"used 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: a g.Bt=a;+月;log+wit, ajt is a random disturbance term. It is assumed that wje satisheecurity assumptions of the linear regression model. That is,(a)uit has zero ex pectation and variance independent of t;(b the ujt are serially independent and (c) the distribution of u, is independent of log 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 lio 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 speci fication. Using the available time series on R3 and Lt, least squares has been used to estimate ay 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 the regression model concerning the disturbance term in (1) are not valid Thus if these months were included in the sample, estimates of a and S rould 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 Poor's Composite Price Index as the measure of market conditions; in all major respects the results agre completely with those reported below 8 Cf. Markowitz [13,(96-101) Sharpe [17, 18 and Fama The logarithmic form I is appea for two reasons. First, over the period covered by our ata the distribution of the monthly values of loge Le and loge rit are fairly sym metric, whereas the distributions of the relatives themselves are skewed right. Sym- metry is desirable since models involving symmetrically distributed variables present fewer estimation problems than models involving variables with skewed distributions. Second, we shall see below that when least squares is used to estimate a and a in ) 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- tistical point of view and has a natural economie 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
FAMA, FISHER, JENSEN AND ROLL plicated average of the Rjt for all securities that were on the N.Y.S.E. at the end of months t and t -1. Lt is the measure of "general market conditions" used in this st~dy.~ One form or another of the following simple model has often been suggested as a way of expressing the relationship between the monthly rates Of return provided by an individual security and general market condition^:^ (1) loge Rjt nj + $j loge Lt + ujt , where aj and Fj are parameters that can vary from security to security and ujt is a random disturbance term. It is assumed that ujt satisfies the usual assumptions of the linear regression model. That is, (a) ujt has zero expectation and variance independ.ent of t; (b) the ujt are serially independent; and (c) the distribution of uj is independent of log, 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 portfolio 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 Rjt and .Lt, least squares has been used to estimate nj and 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 the regression model concerning the disturbance term in (1)are not valid. Thus if these months were included in the sample, estimates of n and f 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 Poor's Composite Price Index as the measure of market conditions; in all major respects the results agree completely with those reported below. 8 Cf. Markowitz 113, (96-101)], Sharpe [la, 181 and Fama 141. 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 log, Lt and log, Rjt are fairly symmetric, whereas the distributions of the relatives themselves are skewed right. Symmetry is desirable since models involving symmetrically distributed variables present fewer estimation problems than models involving variables with skewed distributions. Second, we shall see below that when least squares is used to estimate a and P in (I), the sample residuals conform well to the assumptions of the simple linear regression model. Thus, the logarithmic form of the model appears to be well specified from a statistical 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 Rjt on Lt. These results are in complete agreement with those presented in the text