NOTE ON THE VALIDITY OF THE RANDOM WALK FOR EUROPEAN STOCK PRICES

Abstract

The purpose of this note is to test whether European stock prices follow a random walk. A sample of 234 securities from 8 major European stock markets is used in this study. Some of the standard serial correlation tests which have been traditionally performed on the New York Stock Exchange are being applied to this body of data. The development of the random walk concept originated in some empirical findings that successive price variations were uncorrelated (Kendall [6], Osborne [10], etc.). It is now widely believed that the New York Stock Exchange is an efficient market and that U.S. security price behavior is quite consistent with a random walk concept. The most comprehensive work in this area is the study by Fama [4] on 30 Dow Jones Industrial stocks for a five-year period (1956-1961); for all differentiating intervals (from daily to monthly), the serial correlation coefficients were small and generally not significantly different from zero. However some authors (see Cheng and Deets [1], Jenning [5]) have recently suggested that a rebalancing strategy of portfolio investment will work better than a Buy and Hold strategy because of the existence of negative serial correlation of security prices. While this time dependence is only one of the arguments advanced in favor of the rebalancing strategy, it would certainly work in favor of the strategy. Reviewing the literature, it appears that Cootner [2], Moore [8], and Cheng and Deets [1] found a preponderance of negative signs for weekly changes, as did King [7] for monthly price relatives. Although Fama [4] reached the same conclusions for fourand nine-trading day changes, he found opposite results (i.e., positive serial correlation) for daily or sixteen-day returns. So did Kendall [6] for weekly returns. Few serious tests of the random walk have been performed on European data. This was probably due to the lack of systematic computerized data bases. In 1953 Kendall [6] did not find any evidence of systematic price patterns for British securities. However some evidence of positive serial correlation has been found more recently on the Dutch market (Theil and Leenders [11]) and the British Stock Exchange (e.g., Dryden [3]). The first goal of this note is to study the distribution of serial correlation coefficients of common stocks for each European market and draw comparison with the results found by Fama [4] on a comparable sample of American stocks. No important deviations from the random walk are found. Then the stationarity over time of serial correlation coefficients for individual securities