của giá cổ phiếu thông thường, không có công bố sự ra đi thực tế từ bình thường là bằng chứng cho hay chống lại Mandelbrot là đủ để từ chối hypotheory Gaussian đã được trình bày. Một trong những sis của chúng tôi. Mục tiêu duy nhất là để xem nếu các mục tiêu chính ở đây | BEHAVIOR OF STOCK-MARKET PRICES 45 of common-stock prices no published evidence for or against Mandelbrot s theory has yet been presented. One of our main goals here will be to attempt to test Mandelbrot s hypothesis for the case of stock prices. c. THINGS TO COME Except for the concluding section the remainder of this paper will be concerned with reporting the results of extensive tests of the random walk model of stock price behavior. Sections III and IV will examine evidence on the shape of the distribution of price changes. Section III will be concerned with common statistical tools such as frequency distributions and normal probability graphs while Section IV will develop more direct tests of Mandelbrot s hypothesis that the characteristic exponent a for these distributions is less than 2. Section V of the paper tests the independence assumption of the random-walk model. Finally Section VI will contain a summary of previous results and a discussion of the implications of these results from various points of view. III. A First Look at the Empirical Distributions A. INTRODUCTION In this section a few simple techniques will be used to examine distributions of daily stock-price changes for individual securities. If Mandelbrot s hypothesis that the distributions are stable Paretian with characteristic exponents less than 2 is correct the most important feature of the distributions should be the length of their tails. That is the extreme tail areas should contain more relative frequency than would be expected if the distributions were normal. In this section no attempt will be made to decide whether the actual departures from normality are sufficient to reject the Gaussian hypothesis. The only goal will be to see if the departures are usually in the direction predicted by the Mandelbrot hypothesis. B. THE DATA The data that will be used throughout this paper consist of daily prices for each of the thirty stocks of the Dow-Jones Industrial The time periods
