The Returns Generation Process, Returns Variance, and the Effect of Thinness in Securities Markets

Garman (1976). Further, our treatment of the returns generation process allows for upward drift in security prices, and thus is consistent with the submartingale model of efficient capital markets [see, e.g., Fama (1970)]. Our analysis does not focus upon incomplete equilibria, and thus is distinguished from Copeland's (1976) model of time-distributed price-volume adjustments under sequential arrival of information. The model of the returns generation process is used to obtain the expected value and variance of security returns. This is done first for returns based on bid/ask price quotations (which we call "quotation returns") and then for returns based on transaction prices (which we call "transaction returns"). Although we abstract from the bid-ask spread, a separate analysis of transaction returns is needed because demand shifts need not trigger transactions, and hence closing transaction prices, unlike closing quotes, need not reflect all current information. Our interest in the moments of returns distributions is focused primarily on variance,' and on the existence of a relationship between variance and the value of shares outstanding for individual securities. We consider the market value of shares outstanding for a security to be an (inverse) proxy measure of thinness in the