Some observations on the random walk model

David Wilkie, United-Kingdom

The random walk or logarithmic Brownian motion model for share prices is now the standard one for many purposes, particularly option pricing, for which it is very useful. In this paper, however, we draw attention to many of the practical anomalies that can be seen with this model, in the short, medium and longer terms. In the short term we know that share prices move in discrete steps and are not available at all times. In the medium term we see that it is difficult for total return indices and share prices both to be uniform random walks, because dividend yields vary; that if share prices are lognormally distributed, share indices cannot be; that the CAPM is not consistent with lognormal distributions for both share prices and portfolio returns; and that the observed distribution of log share price changes is conspicuously fat-tailed, though the effect reduces with the time step. In the longer term we observe that share prices follow a similar track to many other related monetary indices, consumer prices, wages, company dividends and company earnings, with which they can be described as being cointegrated. The object of the paper is not to draw conclusions, but to stimulate discussion.
Date: 1 June - Time: 8:30 to 10:30 - Room: 251
Theme: 1.A. Stochastic dependence