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