1 The Relation Between Idiosyncratic Volatility and Expected Returns : A Statistical Artifact of Temporary Changes in Idiosyncratic Volatility

We document a systematic pattern of temporary increases in the estimated idiosyncratic volatility for the quintile of stocks with the highest estimated idiosyncratic volatility in a given month. A large portion of this temporary increase in the estimated idiosyncratic volatility is reversed in the subsequent month, which suggests the possibility of relatively large positive estimation errors. This temporary increase in the idiosyncratic volatility for the quintile of stocks with the highest estimated idiosyncratic volatility is associated with positive abnormal returns in the estimation month and negative abnormal returns in the subsequent month. Our evidence shows that these estimation errors or temporary changes in the estimated idiosyncratic volatility and the related positive and negative abnormal returns in the estimation and subsequent months, respectively, create a negative relation between the estimated idiosyncratic volatility and subsequent month returns documented in the prior literature (Ang et al. 2006). After controlling for the (negative) relation with the past month’s return, there is no significant relation between idiosyncratic volatility and subsequent month’s returns as predicted by traditional asset pricing models. Moreover, we find no significant relation between idiosyncratic volatility and subsequent returns for subsets of stocks that do not exhibit any significant changes in idiosyncratic volatility despite large differences in the levels of their idiosyncratic volatility. Overall, our results are consistent with the notion that there is no relation between the true underlying idiosyncratic volatility and expected returns, and that the previously documented negative relation between estimated idiosyncratic volatility and subsequent month’s returns is being driven by estimation errors (temporary one-month changes) in the estimated idiosyncratic volatility and the associated abnormal returns. ∗ Hongyan Li (email: hongyan@vt.edu, Tel: 540-231-4144) and Raman Kumar (email: rkumar@vt.edu, Tel: 540-2315700) are both from the Department of Finance, Pamplin College of Business, Virginia Tech. Blacksburg, VA, 24060. Hongyan Li acknowledges the support of 2015 Pamplin College of Business Summer Research Grant.