The Demand for Brokers' Services: The Relation Between Security Trading Volume and Transaction Cost

In this paper a probability model with links to portfolio theory is constructed which, for any security, implies (1) that the expected number of transactions per unit time is a decreasing linear function of the ratio (r) of transaction cost to the security's price per share; and (2) that both the expected number of shares exchanged on any single transaction and the expected trading volume over any fixed time interval are decreasing -- but more complicated -- functions of r. The last function represents a demand function for brokers' services in the market for some security. Such functions are estimated for each of 20 common stocks, and it is found that volume is indeed measurably responsive to changes in transaction cost. The elasticity of the overall demand for brokers' services in the market for common stocks is estimated to be approximately -0.25.