On the Robustness of the Positive Relation between Expected Idiosyncratic Volatility and Expected Return

Abstract

My 2009 JFE paper ["Idiosyncratic Risk and the Cross-Section of Expected Stock Returns', Journal of Financial Economics, Vol. 91, pp. 24-37] documents a positive and statistically significant cross-sectional relation between expected idiosyncratic volatility (E(IVOL)) and expected stock return. A recent working paper titled "On the Relation between EGARCH Idiosyncratic Volatility and Expected Stock Returns" by Guo, Ferguson, and Kassa of University of Cincinnati suggests that the positive relation is driven by an in-sample approach to estimate E(IVOL). They fail to find a significant relation between return and their E(IVOL) estimated out of sample. I find that two estimation settings in their SAS code, one of which limits the maximum number of iterations and the other accepts estimates with a questionable convergence status, lead to potentially unreliable estimates and ultimately, the failure to find the positive relation between return and E(IVOL). Using more reliable settings, I re-estimate E(IVOL) strictly out of sample, and confirm a robust and significantly positive relation between return and E(IVOL), just as reported in my JFE paper.

Keywords: Idiosyncratic Volatility, Expected Idiosyncratic Volatility, EGARCH