The Cross-Section of Volatility and Expected Returns: Then and Now

Abstract

We successfully replicate the main results of Ang, Hodrick, Xing, and Zhang (2006): Aggregate-volatility risk and idiosyncratic volatility (IV) are each priced in the cross-section of stock returns from 1963 to 2000. We also examine the pricing of volatility outside the original time period and under more recent asset-pricing models. With the exception of NASDAQ stocks, aggregate-volatility risk continues to be priced in the years following the Ang et al. (2006) sample period, and none of the more recent asset-pricing models we consider consistently accounts for the pricing of aggregate-volatility risk. The difference in abnormal returns between stocks with high and low IV decreases but remains significant out-of-sample. More recent asset-pricing models do not resolve the IV anomaly for the Ang et al. (2006) sample, but the four-factor model of Stambaugh and Yuan (2017) and the six-factor model of Barillas and Shanken (2018) resolve the anomaly out-of-sample and over the extended period of 1967 to 2016. Finally, both models eliminate the arbitrage asymmetry that Stambaugh, Yu, and Yuan (2015) propose as an explanation of the IV anomaly.

Keywords: Volatility risk, idiosyncratic risk, cross-section of returns, limits to arbitrage

JEL Classification: G11, G12, G14