Measuring Price Discovery: The Variance Ratio, the R2 and the Weighted Price Contribution

Abstract:     
In this paper we analyze the statistical properties of three popular measures of price discovery used in empirical market micro structure research. We find that the variance ratio is a consistent estimator for the informativeness of trades or time periods if the price process follows a martingale. The R2 of unbiasedness regressions is consistent for all price processes, also if they exhibit autocorrelation or have a drift. However, the R2 is, like the variance ratio, biased for small samples. We find that weighted price contribution (WPC) is an unbiased estimator for driftless martingales. We characterize the bias of the WPC if the underlying process is autocorrelated and/or has a drift, and propose three WPC variants to adjust for these biases.

Keywords: market microstructure, price discovery, weighted price contribution

JEL Classifications: G14, C00, C13

Working Paper Series