A growing literature investigates the association between stock return variation and several aspects of information and governance structures, both in cross-country settings and cross-firm settings within the U.S. Several papers in this literature use idiosyncratic stock return volatility (s_e^2) as the measure of firm-specific return variation whereas others use return synchronicity, or R2. Although these two variables are economically equivalent, researchers interpret them differently depending on their assumptions about whether lower R2 (or higher s_e^2) captures firm-specific news or noise. We show that higher idiosyncratic volatility (or equivalently, lower R2) is associated with poorer information environments, measured as higher PIN scores, higher bid-ask spreads, greater price delay, greater levels of illiquidity, and more zero return days. In addition, we demonstrate, both analytically and empirically, that when the researcher is interested in assessing the association between R2 and some independent variable, he should control for (i) aggregate market return variation in cross-country settings; and (ii) firm-specific beta in cross-sectional settings.
Li, Bin, Shivaram Rajgopal, and Mohan Venkatachalam. "R2 and Idiosyncratic Risk Are Not Interchangeable." The Accounting Review 89, no. 6 (2014): 2261-2295.
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