Volume, number of trades, and price adjustment process: Theory and empirical properties.

We develop a variant of the standard sequential trade model to discover the roles of both number of trades and trade size simultaneously. We demonstrate that the significance of the number of trades for the market maker's pricing depends on his prior probabilistic belief on the value of the underlying asset, the informedness of the market, and the elasticity of the informed traders' demand and supply schedules. We also show the economic situations where the number of trades rather than the trading volume sends a better signal to the market maker.;We implement empirical tests to see the implications of our theoretical model. We examine the relationships among the number of trades, the bid-ask spread, the past-price variability, the market informedness, and the firm size while the trading volume is held constant. The results indicate that the market maker generally raises the bid-ask spread when he experiences a relatively large number of transactions. There appears to be a persistent, positive effect of the number of trades on the market maker's setting of the bid-ask spread. We also find that past-price variability, market informedness, and firm size can effect the number of trades, but have a statistically insignificant effect on the bid-ask spread.;We further test whether the stock return has a positive relationship with the number of trades after considering the stochastic characteristics of its volatility. We examine whether the established time-series property of observed returns, AR(1) process, comes from the traders' strategic behavior rather than from simple measurement error in calculating returns. Our results show it to be plausible that this truly is the case.