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We document a directional asymmetry in the small stock concurrent and lagged response to large stock movements. When returns on large stocks are negative, the concurrent beta for small stocks is high, but the lagged beta is insignificant. When returns on large stocks are positive, small stocks have small concurrent betas and very significant lagged betas. That is, the cross-autocorrelation puzzle documented by Lo and MacKinlay (1990a) is associated with a slow response by some small stocks to good, but not to bad, common news. Time series portfolio tests and cross-sectional tests of the delay for individual securities suggest that existing explanations of the cross-autocorrelation puzzle based on data mismeasurement, minor market imperfections, or time-varying risk premiums fail to capture the directional asymmetry in the data.
McQueen et al. (Mon,) studied this question.