Implied Volatility Spreads and Expected Market Returns

To save space, we present some of our …ndings in the Online Appendix. In Section I, we investigate the intertemporal relation between various skewness measures and expected market returns. In Section II, we orthogonalize the implied volatility spread measures with respect to the implied variance, realized variance, physical skewness and risk-neutral skewness measures. In Section III, we orthogonalize the implied volatility spread measures with respect to the implied variance and nonparametric value-at-risk measures to tease out the risk component of volatility spreads. In Section IV, we control for the non-normality of empirical return distributions by estimating the predictive regressions using a skewed fat-tailed density function in a maximum likelihood framework. In Section V, we address the issue of small-sample bias by utilizing the randomization and bootstrapping methods under the null hypothesis of no predictability. We also perform an alternative small-sample bias analysis by exploiting information about the autocorrelation structure of the volatility spread measures. In Section VI, rather than compounding market returns for di¤erent time periods, we use several lags of the volatility spread measures as independent variables. In Section VII, we use logarithmic excess market returns as dependent variables and control for squared volatility spreads to account for outliers and nonlinearities. In Section VIII, we include additional macroeconomic controls in our speci…cations.