Microstructure Invariance in U.S. Stock Market Trades

This paper studies invariance relationships in tick-by-tick transaction data in the U.S. stock market. Over the 1993-2001 period, the estimated monthly regression coefficients of the log of trade arrival rate on the log of trading activity have an almost constant value of 0:666, strikingly close to the value of 2=3 predicted by the invariance hypothesis. Over the 2001-14 period, the estimated coefficients rise, and their average value is equal to 0:79, suggesting that the reduction in tick size in 2001 and the subsequent increase in algorithmic trading resulted in a more intense order shredding in more liquid stocks. The distributions of trade sizes, adjusted for differences in trading activity, resemble a log-normal before 2001; there is clearly visible truncation at the round-lot boundary and clustering of trades at even levels. These distributions change dramatically over the 2001-14 period with their means shifting downward. The invariance hypothesis explains about 88 percent of the cross-sectional variation in trade arrival rates and average trade sizes; additional explanatory variables include the invariance-implied measure of effective price volatility.