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This paper analyzes the Amihud (2002) measure of illiquidity and its role in asset pricing. It is shown first that the effect of illiquidity on asset pricing is clarified by using the turnover version of the Amihud measure and including firm size as a separate variable. When we decompose the Amihud measure into elements that correspond to positive (up) and negative (down) return days, we find that in general, only the down-day element commands a return premium. Further analysis of the up- and down-day elements using order flows shows that a sidedness variable, which captures the tendency for orders to cluster on the sell side on down days, is associated with a more significant return premium than the other components of the Amihud measure.
Brennan et al. (Mon,) studied this question.