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