R2 and Idiosyncratic Risk are not Interchangeable

Abstract

A growing literature investigates the association between firm-specific stock return variation (the dependent variable) and several aspects of firms’ information and governance structures. However, several papers in this literature use the variance of residual returns from a market model (sigma squared) as the measure of firm-specific return variation whereas others use return synchronicity, or R2. Although, at first blush, these two variables appear equivalent, we show that the specific dependent variable used, sigma squared or R2, can lead to contradictory inferences due to both econometric and economic considerations. Further tests suggest that, contrary to the traditional interpretation in the literature, lower R2 is associated with poorer information environments, measured as higher price delays, higher PIN scores, greater levels of illiquidity, more zero return days and higher bid-ask spreads.