Expected Equity Returns Should Correlate with Idiosyncratic Risk Haug and Bruno
"Because levered equity is an option on the firm, variations in asset idiosyncratic risk (ivol) induces a negative relationship between equity ivol and expected returns. We show that the effect is caused by the nonlinear payoff of equity and the law of one price, and is present in all but risk-neutral economies. We test the cross-sectional predictions of our theory by contrasting the ivol-return relationship at the equity and asset levels. The ivol-return relationship is stronger for equity than for assets, and stronger for more levered firms---consistent with the theory. We test also the time-series implications of the theory. Time variation in asset ivol causes time variation in the option value of equity that translates into time varying risk factor loadings. Unconditional alpha subsequently becomes biased when asset ivol correlates with the market price of risk. We show empirically that a conditional CAPM that accounts for time variation in equity nonlinearity helps explain earlier findings that high-minus-low ivol-portfolios generate negative unconditional alpha."
"The implications of the analysis thus go beyond equity: One should expect to find correlation between ivol and expected returns for any derivative with non-trivial nonlinearities, be it real or financial. Ivol is thus truly a “characteristic” in asset pricing models that do not explicitly take nonlinearities into account, and is neither an “anomaly factor” nor a “priced risk factor.” Indeed, the absence of ivol-return correlation may indicate deviations from the law of one price."