Volatility Shocks, Leverage Effects, and Time-Varying Conditional Skewness.

The article investigates the dynamics of conditional skewness in U.S. stock index returns using GARCH-X (generalized autoregressive conditional heteroskedasticity with exogenous variables) specifications that incorporate variance shocks derived from realized variances. It finds that conditional skewness is strongly influenced by these variance shocks and exhibits high persistence, with variance shocks acting as a common factor generating a substantial negative correlation between contemporaneous changes in conditional volatility and skewness. The study employs two flexible distributions—the Pearson Type IV and the Cubic Normal distributions—to model conditional skewness, highlighting the Cubic Normal distribution’s computational tractability and suitability for risk management applications. Empirical results based on daily, weekly, and monthly returns for major U.S. stock indexes (DJI, S&P 500, NASDAQ 100, Russell 2000) confirm the persistence of negative conditional skewness and its linkage to variance shocks, with implications for asset pricing, portfolio selection, and risk management. The article also addresses econometric challenges found in prior research, such as local optima and weak identification, demonstrating that the proposed GARCH-X approach using realized variances mitigates these issues.