The Stochastic Dependence of Security Price Changes and Transaction Volumes: Implications for the Mixture-of-Distributions Hypothesis

Abstract

A theory of financial markets based on a two-parameter portfolio model is shown to imply stochastic dependence between transaction volume and the change in the logarithm of security price from one transaction to the next. The change in the logarithm of price can therefore be viewed as following a mixture of distributions, with transaction volume as the mixing variable. For common stocks these distributions (of which the distribution of A log p is a mixture) appear to have a pronounced excess of frequency near the mean and a deficiency of outliers, relative to the normal. These findings are consistent with the hypothesis that stock price changes over fixed intervals of time follow mixtures of finitevariance distributions.