ADJUSTMENT OF STOCK PRICES Mandelbrot [12])argues that distributions of returns are well approximate by the non-Gaussian (i.e. infinite variance) members of the stable Paretian family. If the stable non-Gaussian distributions also provide a good descrip- tion of the residuals in (1), then, at first glance, the least squares regression model would seem inappropriate Wise [19] has shown, however, that although least square estimates "efficient, "for most members of the stable Paretian family they provide estimates which are unbiased and consistent. Thus, given our large samples least squares regression is not completely inappropriate. In deference to the stable Paretian model, however, in measuring variability we rely primarily on the mean absolute deviation rather than the variance or the standard deviation. The mean absolute deviation is used since, for long-tailed distri butions, its sampling behavior is less erratic than that of the variance or the standard deviation! In sum we find that regressions of security returns on market returns over time are a satisfactory method for abstracting from the effects of gen eral market conditions on the monthly rates of return on individual secu rities. We must point out, however, that although (1)stands up fairly well to the assumptions of the linear regression model, it is certainly a gros over-simplified model of price formation; general market conditions alone do not determine the returns on an individual security. In (1)the effects of these"omitted variables"are impounded into the disturbance term u. In particular, if a stock split is associated with abnormal behavior in returns during months surrounding the split date, this behavior should be reflected in the estimated regression residuals of the security for these months. The re mainder of our analysis will concentrate on examining the behavior of the estimated residuals of split securities in the months surrounding the splits 3. "EFFECTS OF SPLITS ON RETURNS: EMPIRICAL RESULTS In this study we do not attempt to determine the effects of splits for in- dividual companies. Rather we are concerned with whether the process of splitting is in general associated with specific types of return behavior. To abstract from the eccentricities of specific cases we can rely on the simple process of averaging; we shall therefore concentrate attention on the behavior of cross-sectional averages of estimated regression residuals in the months b a. Some additional definitions. The procedure is as follows: For a given olit, define month 0 as the month in which the effective date of a split occurs. (Thus month 0 is not the same chronological date for all securities, and indeed some securities have been split more than once and hence have more than one month 0). 12 Month 1 is then defined as the month immediately Essentially, this is due to the fact that in computing the variance of a sample large deviations are weighted more heavily than in computing the mean absolute deviation, For empirical evidence concerning the reliability of the mean absolute deviation relative to the variance or standard deviation see Fama [3,(94-8) split more than onceADJUSTMENT OF STOCK PRICES 7 Mandelbrot [12]) argues that distributions of returns are well approximated by the non-Gaussian (i.e., infinite variance) members of the stable Paretian family. If the stable non-Gaussian distributions also provide a good descrip￾tion of the residuals in (I), then, at first glance, the least squares regression model would seem inappropriate. Wise [I91 has shown, however, that although least square estimates are not "efficient," for most members of the stable Paretian family they provide estimates which are unbiased and consistent. Thus, given our large samples, least squares regression is not completely inappropriate. In deference to the stable Paretian model, however, in measuring variability we rely primarily on the mean absolute deviation rather than the variance or the standard deviation. The mean absolute deviation is used since, for long-tailed distri￾butions, its sampling behavior is less erratic than that of the variance or the standard deviation1'. In sum we find that regressions of security returns on market returns over time are a satisfactory method for abstracting from the effects of gen￾era,l market conditions on the monthly rates of return on individual secu￾rities. We must point out, however, that although (1)stands up fair!y well to the assumptions of the linear regression model, it is certainly a grossly over-simplified model of price formation; general market conditions alone do not determine the returns on an individual security. In (1)the effects of these "omitted variables" are impounded into the disturbance term u. In particular, if a stock split is associated with abnormal behavior in returns during months surrounding the split date, this behavior should be reflected in the estimated regression residuals of the security for these months. The re￾mainder of our analysis will concentrate on examining the behavior of the estimated residuals of split securities in the months surrounding the splits. 3. "EFFECTS" OF SPLITS ON RETURNS: EMPIRICAL RESULTS In this study we do not attempt to determine the effects of splits for in￾dividual companies. Rather we are concerned with whether the process of splitting is in general associated with specific types of return behavior. To abstract from the eccentricities of specific cases we can rely on the simple process of averaging; we shall therefore concentrate attention on the behavior of cross-sectional averages of estimated regression residuals in the months surrounding split dates. a. Some additional definitions. The procedure is as follows: For a given split, define month 0 as the inonth in which the effective date of a split occurs. (Thus month 0 is not the same chronological date for all securities, and indeed some securities have been split more than once and hence have more than one month 0).12 Month 1is then defined as the month immediately " Essentially, this is due to the fact that in computing the variance of a sample, large deviations are weighted more heavily than in computing the mean absolute deviation. For empirical evidence concerning the reliability of the mean absolute deviation relative to the variance or standard deviation see Fama [3, (94-8)]. '2 About a third of the securities in the master file split. About a third of these split more than once