Expected stock returns, common idiosyncratic volatility and average idiosyncratic correlation

Motivated by Herskovic et al. (2016), we examine the role of the average idiosyncratic correlation (ICOR) in two types of markets: an emerging market and a developed market. Examining daily stock data from the Chinese stock market for the period 1995 to 2020 and from the US for the period 1926 to 2019, we adopt high-dimensional principal component analysis (PCA) and thresholding methods to re-estimate ICOR. We find that ICOR plays an important role in explaining the expected stock returns, as the common idiosyncratic volatility (CIV) does in Herskovic et al. (2016). ICOR has been neglected in the literature due to large estimation error in the idiosyncratic covariance matrix and our analysis provides evidence that ICOR is nonnegligible in both markets when we control for several common market factors. We show that the average idiosyncratic covariance, which is the numerator of ICOR, exhibits the same pattern as CIV. Furthermore, our regression analyses of expected stock returns in response to ICOR change in both markets show that, in contrast to the negative result for CIV, the stocks' high risk exposure to ICOR change comes with a higher risk premium, perhaps because of the synchronized but disproportionate changes in the monthly idiosyncratic covariance and idiosyncratic volatility.