Expected idiosyncratic volatility

We use close to 80 million daily returns for more than 19,000 CRSP listed firms to establish the best forecasting model for realized idiosyncratic variances. Comparing forecasts from multiple models, we find that the popular martingale model performs worst. Using the root-mean-squared-error (RMSE) to judge model performance, ARMA(1,1) models perform the best for about 46 % of the firms in out-of-sample tests. The ARMA(1,1) model delivers an average RMSE that is statistically significantly lower than all alternative models, and also performs well when not the very best. Its forecasts reverse large, unexpected shocks to realized variances. When using this model to revisit the relation between idiosyncratic risk and returns (the IVOL puzzle), we fail to find a significant relation. The IVOL puzzle is closely connected to a very small set of observations where the martingale forecast over-predicts the future realized variance. These extreme observations are correlated with well-known firm characteristics associated with the IVOL puzzle such as poor liquidity as measured by high bid-ask spreads and the “MAX” effect.