R2 and Idiosyncratic Risk Are Not Interchangeable

Abstract

A growing literature investigates the association between stock return variation and several aspects of information and governance structures, in both a cross-country setting and a cross-firm setting within the U.S. Papers use either idiosyncratic stock return volatility 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 ) captures firm-specific news or noise. We document that higher (or equivalently, lower R2) resembles noise. In addition, we show, analytically and empirically, that different results obtain when using R2 or 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 ) and some independent variable, researchers (1) control for elements of systematic risk and (2) triangulate their findings with other measures of information environment. Data Availability: The data in this study are available from commercial providers, e.g., WRDS, Compustat, CRSP, I/B/E/S.

Illiquidity and the Measurement of Stock Price Synchronicity

“…Returning to the question of whether low R 2 captures information or noise, the results suggest that measurement bias can make low R 2 appear to reflect more noise in prices-and therefore a weaker information environment (Kelly 2014;Li et al 2014)-when not controlling for the effect of illiquidity. Importantly, firm-specific information does manifest in lower R 2 , but stock illiquidity can mask such effects and reduce the R 2 metric's ability to measure firm-specific information in prices.…”

“…accounting data are from CRSP and COMPUSTAT Fundamentals Annual, respectively. For non-U.S. firms, market and accounting data are from COMPUSTAT Global Security Daily and COM-PUSTAT Global Fundamentals Annual, respectively (e.g., Li et al 2014), and we compute daily returns based on daily closing prices in local currency, adjusted for stock splits, dividends, and currency changes (e.g., the switch from domestic currency to Euros for EU firms). Following prior research using international security returns (e.g., Griffin et al 2010), we set to missing all daily returns (t and t − 1) that are greater than 200 percent and if R t−1 > 1 and (1 + R t−1 )(1 + R t ) − 1 < 0.2.…”

Financial Statement Comparability and Idiosyncratic Return Volatility

“…To alleviate the concern with potential estimation error associated with the IRV measure, we also control for systematic risk in our regression model following the suggestion of Li et al (). Regression results (untabulated) show systematic risk to be significantly and positively associated with IRV.…”

“…In particular, Teoh et al () show that stocks with a low R 2 incorporate less information about future fundamentals, and are more difficult for investors to analyze accurately. Moreover, Li et al () argue that, because R 2 is a relative (scaled) measure of IRV, similar inferences can be obtained using R 2 and as the dependent variables if, and only if, the correlation between the independent variable of interest and systematic risk (i.e., the scalar in R 2 ) is zero. Therefore, they suggest controlling for systematic risk in the empirical specification.…”

“…They contend that a lower R 2 implies that more firm‐specific information is incorporated into stock prices. However, recent studies clearly show that this measure does not reflect the extent to which firm‐specific information is accurately reflected in prices (Teoh et al ; Li et al ). In particular, Teoh et al () show that stocks with a low R 2 incorporate less information about future fundamentals, and are more difficult for investors to analyze accurately.…”