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 sug￾gested 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 ex￾pectation 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 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 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 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 P in (I), 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 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 agree￾ment with those presented in the text