The Shape of the Risk Premium: Evidence from a Semiparametric Garch Model

Abstract

We examine the relationship between the risk premium on the S&P 500 index return and its conditional variance. We use the SMEGARCH - Semiparametric-Mean EGARCH - model in which the conditional variance process is EGARCH while the conditional mean is an arbitrary function of the conditional variance. For monthly S&P 500 excess returns, the relationship between the two moments that we uncover is nonlinear and nonmonotonic. Moreover, we find considerable persistence in the conditional variance as well as a leverage effect, as documented by others. Moreover, the shape of these relationships seems to be relatively stable over time.

Nous étudions la relation entre la prime de risque sur l'indice S&P 500 et sa variance conditionnelle. Nous utilisons le modèle SMEGARCH - Semiparametric-Mean EGARCH - selon lequel la variance conditionnelle suit un processus EGARCH, alors que la moyenne est une fonction arbitraire de la variance conditionnelle. Pour les rendements excédentaires mensuels sur l'indice S&P 500, la relation que nous trouvons est non linéaire et non monotone. De plus, nous trouvons beaucoup de persistance dans la variance conditionnelle ainsi qu'un effet de levier, tel que documenté par plusieurs autres auteurs.