• conditional joint density;
  • GARCH models;
  • semi-nonparametric;
  • SPX;
  • VIX;
  • G17;
  • C01;
  • C02;
  • C14;
  • C15


We use the semi-nonparametric (SNP) model to study the relationship between the innovation of the Volatility Index (VIX) and the expected S&P 500 Index (SPX) returns. We estimate the one-step-ahead contemporaneous relation subject to leverage GARCH effect. Results agree with a body of newly established literature arguing non-linearity, and asymmetries. In addition, the risk-return behaviour depends on the signs as well as magnitudes of the perceived risk. We conclude that influence of fear or exuberance on the conditional market return is non-monotonic and hump-shaped. Very deep fear does not necessarily mean huge losses, instead, the loss may not be as bad as fears of normal levels. Results pass the robustness tests.