THE RETURNS GENERATION PROCESS, RETURNS VARIANCE, AND THE EFFECT OF THINNESS IN SECURITIES MARKETS

The economic formulation of the returns generation process is further developed. Returns result from demand shifts which may stem from aggregate changes in the informational set that is available to all investors and/or from idiosyncratic tenders placed by some investors. These underlying stimuli are described by mutually independent compound Poisson processes. The model of the probability of security returns is consistent with the submartingale form of the efficient markets hypothesis. The returns generation model is used to obtain expressions for the expected value and variance of security returns, both for returns based on price quotations and for returns based on transaction prices. Expected quotations and transactions returns are shown to be equal. But a drift in the aggregate demand shift process causes the estimator of transaction returns variance to be greater than quotation returns variance, with the discrepancy directly related to thinness.