Using options-implied variance, a forward-looking measure of conditional variance, we revisit the debate on the idiosyncratic risk-return relation. In both cross-sectional (for individual stocks) and time-series (for the market index) regressions, we find a negative relation between options-implied variance and future stock returns. Consistent with Miller’s (1977) divergence of opinion hypothesis, the negative relation gets stronger (1) for stocks with more stringent short-sale constraints or (2) when shorting stocks becomes more difficult. Moreover, the negative correlation of realized idiosyncratic variance or analyst forecast dispersion with future stock returns mainly reflects their close correlation with our conditional idiosyncratic variance measure.

Abstract A spurious positive relation between exponential generalized autoregressive conditional heteroskedasticity (EGARCH) estimates of expected month t idiosyncratic volatility and month t stock returns arises when the month t return is included in estimation of model parameters. We illustrate via simulations that this look-ahead bias is problematic for empirically observed degrees of stock return skewness and typical monthly return time series lengths. Moreover, the empirical idiosyncratic risk-return relation becomes negligible when expected month t idiosyncratic volatility is estimated using returns only up to month t − 1.