This paper empirically compares the usefulness of information included in the volatility index (VIX) against several generalized autoregressive conditional heteroskedasticity (GARCH) models for predicting downside risk in the US stock market. Our main findings are as follows. First, using the univariate logit and quantile regression models, we reveal that the previous day's VIX and the forecast S&P 500 volatilities from GARCH, exponential GARCH (EGARCH), power GARCH (PGARCH), and threshold GARCH (TGARCH) models have statistically significant predictive power for large declines in the S&P 500. Second, direct comparisons with the multiple logit and quantile regression models demonstrate that the volatility forecasts from the EGARCH, PGARCH, and TGARCH models dominate the predictive power of the previous day's VIX; and we also clarify that the predictive power of volatility forecasts from the EGARCH and TGARCH models is much stronger. Third, our additional tests further suggest that the forecast VIX, the forecast volatility of VIX, and the forecast volatility of the first log differences of VIX cannot outperform the S&P 500 volatility forecasts from econometric models in predicting US stock market downside risk. Fourth, our vector-half (VECH), Baba-Engle-Kraft-Kroner (BEKK), dynamic conditional correlation (DCC), and asymmetric DCC (ADCC) multivariate GARCH (MGARCH)
PUBLIC INTEREST STATEMENTThis work empirically compares the usefulness of information included in the volatility index (VIX) with several GARCH-type econometric models for predicting downside risk in the US stock market. Our key findings are as follows. First, we reveal that the volatility forecasts from the EGARCH, PGARCH, and TGARCH models dominate the predictive power of the previous day's VIX, and that the predictive power of the volatility forecasts from the EGARCH and TGARCH models is much stronger. Second, around the US Lehman bankruptcy, there is almost perfect correlation across all three volatilities, the previous day's VIX and the EGARCH and TGARCH models' volatility forecasts, although ordinarily they are not always perfectly correlated. Our primary contribution is to clarify that econometric model volatility forecasts are superior in predicting the US stock market downside risk. We emphasize the importance of developing sophisticated econometric models and using econometric model volatility forecasts in practice. analyses demonstrate that the time-varying correlations between the previous day's VIX and the volatility forecasts from the EGARCH or TGARCH models are weaker than the correlations of volatility forecasts from the EGARCH and TGARCH models. Finally, our VECH-, BEKK-, DCC-, and ADCC-MGARCH analyses further clarify almost perfect correlations around the US Lehman Brothers bankruptcy across all three volatility series. The key contribution of this paper is that it clarifies the superiority of volatility forecasts using econometric models compared with VIX in predicting the US stock market downside risk. The primary implicat...
