Modelling the risk-return relation for the S&P 100: The role of VIX

A significantly positive risk-return relation for the S&P 100 market index is detected if the implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation. This result holds for 4 alternative GARCH specifications, irrespective of the conditional distribution, and regardless of whether the conditional mean equation includes a constant term. This finding is robust to sub-samples, and to using VIX innovations to control for dividend yield and trading volume effects. Monte Carlo evidence suggests that if VIX is not included, the risk-return relation is more likely to be negative or weak, in line with several previous studies. If VIX is included, the distribution of the risk-return parameter has more than 99% of its mass in the area of positive values. We conclude that VIX carries important forward-looking information which improves the precision of the conditional variance estimation and, subsequently, reveals a significantly positive relation. © 2011.