  Based on intraday data for a large cross-section of individual stocks and
exchange traded funds, we show that short-term as well as long-term
fluctuations of realized market and average idiosyncratic higher moments risks
are priced in the cross-section of asset returns. Specifically, we find that
market and average idiosyncratic volatility and kurtosis are significantly
priced by investors mainly in the long-run even if controlled by market moments
and other factors, while skewness is mostly short-run phenomenon. A conditional
pricing model capturing the time-variation of moments confirms downward-sloping
term structure of skewness risk and upward-sloping term structure of kurtosis
risk, moreover the term structures connected to market skewness risk and
average idiosyncratic skewness risk exhibit different dymanics.
