• 1

    The research described in this paper, performed in the Econometric Research Program at Princeton University, was supported by National Science Foundation Grant NSF-GS30. The computer facilities used are supported by National Science Foundation Grant NSF-GP579. This paper was originally presented at the Summer Meeting of the Econometric Society in Cleveland, Ohio, September 4-7, 1963. The authors would particularly like to acknowledge the helpful comments and criticisms of an earlier draft made by John W. Tukey.


A model of the form xt - xt-1= et

where xt is the price of a share at time t and et forms a sequence of independent random variates is postulated as a model of the price determining mechanism of stock markets.

The form of the distribution function of the et's is investigated. In opposition to suggestions that have been made in connection with other speculative price mechanisms it is found that the distribution function appears to be well approximated by a normal distribution. There is no evidence that the data treated are samples from a stable process with an infinite variance.

It is found that the model mentioned above, termed the random-walk model, provides a good explanation of the variation of stock market prices for daily observations of the price, and for the series formed by the price of every transaction taking place in the market. In the context of this model it is noted that it appears that the price determining mechanism continues to operate at a reduced ‘speed’ during times when the actual market is closed.

While it has been suggested that a correlation between the volume of shares transacted and the absolute value of the first differences of the price series should be expected, no such correlation was observed.

Two questions which the paper leaves open are the question of cross-sectional correlation between different shares, and the question of the possibility of information in moments of order greater than two.

In conclusion the following law is stated: ‘The price determining mechanism described in Section II (i. e. the random-walk indicated above) is the only mechanism which is consistent with the unrestrained pursuit of the profit motive by the participants in the market’.