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