On the Performance of the Tick Test

Abstract

In the present paper, we investigate the accuracy of the tick test from an analytical perspective by providing a closed formula for the performance of the prediction algorithm. This formula takes as inputs the spread of the traded asset, the volatility of the innovations, and the probability of news, among other parameters, and it outputs the percentage of times that the tick test will make correct predictions regarding the sign of a trade. Further analysis shows that by imposing restrictions on the underlying microstructure model, the formula for the tick test performance is related to simple statistics from a vector of trade price differences. This means that, without the need for quote data (or the real sign of the trades), the formula can assess the percentage of cases for which the tick test will make correct predictions. Using tick data for fifteen heavily traded stocks in the Brazilian equity market, we are able to compare the values from the analytical formula against the empirical performance of the tick test, showing that the formula is quite realistic in assessing the accuracy of the prediction algorithm.

Keywords: tick test, market microstructure, sign of a trade, PIN

JEL Classification: G1, C8