TABLE 2 RATIOS OF THE VARIANCE OF SMOOTHED FIRST DIF FERENCES TO THE VARIANCE OF UNSMOOTHED FIRST DIFFERENCES KENDALL'S STOCK PRICE INDEXES (Smoothing Performed by 21 Term Spencer Moving Average) Industry Group Ratios Banks and Discount Companies 0.16 Insurance Companies Investment Trusts 162 Cotton 210 7 Electric Light and Power 206 Iron and Steel Total Industrial Productive 212 Home Rails 138 Shipping 151 14 Stores and Catering 212 219 Breweries and Distilleries 17 Miscellaneous 221 T 218 19 Industrials (All Classes Combined) trend line, that is, if the trend line were a perfect fit, the variance ratio would be unity. If, on the other hand, all the serial corre lations of order greater than zero were identically zero, the ex pected values for a random walk, the variance ratio would be 0.143 the sum of the squares of the coefficients in the smoothing formula sible for Except for Series 3, the trend variance is not a much large proportion of the original variance of the first differences than would be expected in the case of a random walk. It must be con cluded that, with this exception, if trends exist in the first differ ences, they are very weak. All in all, Kendall's data do seem to confirm the random walk hypothesis. Further work by Osborne strengthens the random walk hypothesis from a different point of view. While Kendall 7 M. F. M. Osborne, Brownian Motion in the Stock Market, Opera tions Research, Vol, 7, No. 2, March-April 1959, pp. 145-173. See also comment and reply in Operations Research, Vol. 7, No. 6, November December 1959, pp. 806-811 13