Multi-factor volatility and stock returns

•Volatility of dynamic factors helps to explain the cross section of expected stock returns.•The risk premium for volatility of the size and book-to-market factor is positive.•The model can better forecast stock returns.•The model brings significant economic values in asset allocation.

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.