Scope and Method of Study. This study develops a theory to explain the impacts of change in relative tick size on percentage transaction costs of different size trades. This theory assumes a profit maximizing objective function of liquidity suppliers. Solving the objective function we obtain a discrete empirical equilibrium percentage spread for a given size order with the limitation of minimum price change. Change in relative tick size will affect the discrete empirical equilibrium percentage spread, and also affect the percentage transaction costs measured by log price change. Our theory forecasts that the impacts of change in relative tick size on percentage transaction costs of small and large size trades are different. Moreover, this theory also indicates that the impacts of change in relative tick size on percentage transaction costs are related stock price and trading volume. To test our theory, this study uses intraday log price change to measure percentage transaction costs. Changes in percentage transaction costs surrounding stock splits and market wide tick size reductions form the basis for statistical tests of these hypotheses.

Findings and Conclusions. This study finds that stock split increases the percentage transaction costs of small size trades and tick size reduction decreases the percentage transaction costs of small size trades; moreover, stock split can decrease percentage transaction costs of large size trades and tick size reduction can increase percentage transaction costs of large size trades. In addition, This study finds that after NYSE 1997 tick size reduction, for extreme high price-low volume stocks, percentage transaction costs of all size trades increase; for extreme low price-high volume and low price-low volume stocks, percentage transaction costs of all size trades decrease; for extreme high price-high volume sample, the percentage transaction costs of small size trades decrease, and the percentage transaction costs of large size trades increase. The results of testing the empirical relationship between change in percentage transaction costs and change in relative tick size provide evidence to support our theory.