Does the fear gauge predict downside risk more accurately than econometric models? Evidence from the US stock market

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) 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 implications of our results are the importance of developing effective technical models and the need to use econometric model volatility forecasts in practice.