Measuring price discovery: The variance ratio, the R2, and the weighted price contribution

We analyze the statistical properties of three price discovery measures: The variance ratio, the weighted price contribution (WPC), and the R2 of unbiasedness regressions. We find that, if the price process is a driftless martingale, only the WPC is an unbiased estimator for the return variance explained during a time interval. For autocorrelated processes with a drift, only the R2 of the unbiasedness regression is consistent, but it is biased for small samples.

► We analyze the statistical properties of three price discovery measures used in market microstructure research. ► If the price process is a driftless martingale, the variance ratio and the R2 of unbiasedness regressions are biased. ► Only the WPC is an unbiased estimator for driftless martingales. ► For autocorrelated processes with drifts, only the R2 is consistent, but biased for small samples.