Cross-security tests of the mixture of distributions hypothesis

New cross-sectional tests of the Mixture of Distributions Hypothesis are presented. The tests assume that the distribution of the mixing variable (often interpreted as the daily rate of flow of information) is not identical for all securities. Cross-security differences in the mixing distribution cause cross-security differences in the joint distribution of returns and volume. The Hypothesis provides predictions about how these differences appear in the joint distribution. The predictions are confirmed in tests based on cross-security correlations among summary statistics that characterize shape and covariational attributes of the joint distribution of returns and volume. The results are consistent with the Mixture of Distributions Hypothesis.