R² and idiosyncratic risk are not interchangeable

A growing literature investigates the association between stock return variation and several aspects of information and governance structures, in both a crosscountry setting and a cross-firm setting within the U.S. Papers use either idiosyncratic stock return volatility (σ2e) or R2 as Interchangeable measures of firm-specific return variation but report inconsistent results. An important reason for the differing interpretations is the assumption about whether lower R2 (or higher σ2e) captures firm- specific news or noise. We document that higher σ2e(or equivalently, lower R2) resembles noise. In addition, we show, analytically and empirically, that different results obtain when using R2 or σ2e because the systematic risk inherent in the R2 metric is also correlated with the independent variable of interest. Therefore, we recommend that when assessing the association between R2 (or σ2e) and some independent variable, researchers (1) control for elements of systematic risk and (2) triangulate their findings with other measures of information environment.

Duke Scholars

Author Mohan Venkatachalam Fuqua School of Business