An Empirical Invariance of Stock Price and Related Problems

Abstract

We consider companies in S&P500 list which varies slightly each year. The intraday transactions data (trades and quotes) are downloaded from the Trade and Quote (TAQ) database in the Wharton Research Data Services. The returns are considered at five-minute and one-minute intervals for each year. For each stock the empirical distribution of the waiting time for a success, i.e. to hit the upper (lower) ten percentile of the returns, is considered. Most of the empirical distributions are close to each other across different stocks and different years under two comparison criteria, ROC area and Kolmogorov-Smirnov distance. This is an empirical invariance. The overlapping of the time points corresponding to successes for different stocks, the probability of the zero waiting time for a success, the outliers, empirical entropy, other percentiles are also considered.