Bond and stock returns have been observed in the literature to exhibit unconditional skewness and temporal persistence in conditional skewness. We demonstrate that observed persistence in conditional third central moments can be due to the spillover of conditional variance dynamics. The confounding of true skewness and a variance spillover effect is problematic for financial modeling. Using market data, we empirically demonstrate that a simple standardization approach removes the variance-induced skewness persistence. An important implication is that more parsimonious return and asset pricing models result if skewness persistence need not be modeled.