Leverage Effect in Equity Markets Around the World

Abstract

Equity indices are known to exhibit an asymmetric leverage effect, meaning that negative returns have a greater impact on volatility than positive returns of the same magnitude. We reevaluate the presence of leverage effect in a large sample of 21 equity indices around the world. We utilize not only daily data, but also realized volatility calculated from high-frequency data. Using realized volatility as a benchmark allows us for a more precise comparison of volatility models. Moreover, we also study models based directly on realized volatility. We find that all the 21 equity indices analyzed exhibit the leverage effect. In order to investigate whether asymmetric models produce more accurate volatility forecasts than symmetric models, three pairs of volatility models are compared. Within each pair, two models are almost identical. The only difference is that one model allow for the leverage effect, whereas the other model is a restricted version, which does not allow for the leverage effect. We find that the volatility models that allow for the asymmetric leverage effect produce significantly more accurate forecasts than the symmetric volatility models.