A Comparison of the Results in Barber, Odean, and Zhu (2006) and Hvidkjaer (2006)

Barber, Odean and Zhu (BOZ, 2006) and Hvidkjaer (2006) construct portfolios based on the relative frequency of small buyer- and seller-initiated transactions on the NYSE, Amex and Nasdaq. Both studies find that stocks with small-trade selling pressures over the prior year outperform those with buying pressures. Hvidkjaer (2006) finds a similar pattern for one month returns using trading imbalances measured over the prior one month. By contrast, BOZ (2006) find the opposite pattern for one week returns using trading imbalances measured over the prior one week, namely that stocks with past smalltrade buying pressures outperform those with selling pressures. The short-term results are not necessarily contradictory, but certainly worthy of further scrutiny. The purpose of this note isto reconcile the two results. Using the imbalance measure in Hvidkjaer (2006) for the analysis at the one-week level, we find qualitatively identical results to those reported in BOZ (2006). However, the measure in Hvidkjaer (2006) produces a faster reversal from initially high to subsequent low returns for the buying pressure portfolio. We find that differences in small-trade volume between the measures in BOZ (2006) and Hvidkjaer explain this faster reversal. Once we control for small-trade volume, we find very similar results at the one-month level using the two measures.