Idiosyncratic Risk and the Cross-Section of Realized Returns : Reconciling the Aggregate Returns’ Predictability Evidence

Whether idiosyncratic volatility has increased over time and whether it is a good predictor of future returns is a matter of active debate. We show formally through central limit arguments that there is a direct relationship between the dynamics of the cross-sectional variance of realized returns and the dynamics of average idiosyncratic variance. A key advantage of this measure is its observability at any frequency, while previous approaches have been limited to use monthly estimations. Another is that the concept extends naturally to cross-sectional higher-order moments. We confirm previous results obtained with other measures and provide new evidence on the time-series properties and predictive power of idiosyncratic risk on the market return that could not have been obtained with traditional measures. In particular, we find that the use of daily estimations and the introduction of robust proxies for higher-order moments induce a very substantial increase in the explanatory power of idiosyncratic risk on the average market portfolio return. Additionally, we provide some criteria for the choice of the weighting scheme used on the measure of idiosyncratic variance and find that taking a consistent weighting for the idiosyncratic variance measure and the market portfolio, leads to robust conclusions on the predictability exercise across different sample periods. This suggests that one important source of debate around the relationship between the market portfolio return and idiosyncratic volatility is precisely related to inconsistent choices on the weighting scheme