Average skewness, which is the average of monthly skewness values across firms, performs well at predicting future market returns. This prediction still holds after controlling for the size or liquidity of the firms or for current business cycle conditions. Also, average skewness compares favorably with other economic and financial predictors of subsequent market returns. The asset allocation exercise based on predictive regressions also shows that average skewness generates superior performance.

This paper introduces a regime-switching combination approach to predict excess stock returns. The approach explicitly incorporates model uncertainty, regime uncertainty, and parameter uncertainty. The empirical findings reveal that the regime-switching combination forecasts of excess returns deliver consistent out-of-sample forecasting gains relative to the historical average and the Rapach et al. (2010) combination forecasts. The findings also reveal that two regimes are related to the business cycle. Based on the business cycle explanation of regimes, excess returns are found to be more predictable during economic contractions than during expansions. Finally, return forecasts are related to the real economy, thus providing insights on the economic sources of return predictability.

Pástor and Stambaugh (2012) find that from a forward-looking perspective, stocks are more volatile in the long run than they are in the short run. We demonstrate that when the nonnegative equity premium (NEP) condition is imposed on predictive regressions, stocks are in fact less volatile in the long run, even after taking estimation risk and uncertainties into account. The reason is that the NEP provides an additional parameter identification condition and prior information for future returns. Combined with the mean reversion of stock returns, this condition substantially reduces uncertainty on future returns and leads to lower long-run predictive variance.

In light of inconclusive evidence on the relation between market volatility and stock returns, this paper proposes a multi-factor volatility model and examines its impact on cross-sectional pricing. We also evaluate the out-of-sample performance and economic significance of multi-factor volatility. We find that conditional variances of the size and value dynamic factor earn significant and positive variance risk premia. In addition, multi-factor volatility can significantly improve the out-of-sample return predictability with a positive economic gain in asset allocation.