  The leverage effect refers to the well-established relationship between
returns and volatility. When returns fall, volatility increases. We examine the
role of the leverage effect with regards to generating density forecasts of
equity returns using well-known observation and parameter-driven volatility
models. These models differ in their assumptions regarding: The parametric
specification, the evolution of the conditional volatility process and how the
leverage effect is accounted for. The ability of a model to generate accurate
density forecasts when the leverage effect is incorporated or not as well as a
comparison between different model-types is carried out using a large number of
financial time-series. We find that, models with the leverage effect generally
generate more accurate density forecasts compared to their no-leverage
counterparts. Moreover, we also find that our choice with regards to how to
model the leverage effect and the conditional log-volatility process is
important in generating accurate density forecasts
