This paper examines the pricing of volatility risk and idiosyncratic volatility in the cross-section of corporate bond returns for the period of 1994–2016. Results show that bonds with high volatility betas have low expected returns, and this negative relation appears in all segments of corporate bonds. Further, bonds with high idiosyncratic bond (stock) volatility have high (low) expected returns, and this relation strengthens as ratings decrease. Conventional risk factors and bond/issuer characteristics cannot account for these cross-sectional relations. There is evidence that the effect of idiosyncratic stock volatility on expected bond returns works through the channel of contemporaneous stock returns.

To attenuate an inherent errors-in-variables bias, portfolios are widely employed to test asset pricing models; but portfolios might mask relevant risk- or return-related features of individual stocks. We propose an instrumental variables approach that allows the use of individual stocks as test assets, yet delivers consistent estimates of ex post risk premiums. This estimator also yields well-specified tests in small samples. The market risk premium under the capital asset pricing model (CAPM) and the liquidity-adjusted CAPM, premiums on risk factors under the Fama–French three- and five-factor models, and the Hou et al. (2015) four-factor model are all insignificant after controlling for asset characteristics.