The marginal distribution of financial time series such as returns is often negatively skewed. We investigate the relation between positive time-varying risk premia and the unconditional skewness of returns. We show that if the error distribution is symmetric, the negative unconditional asymmetry of returns should be the outcome of a negative correlation between their first two conditional moments. Following one of the implications of the intertemporal capital asset pricing model (ICAPM) of Merton (1973), there is a positive and linear relationship between risk and expected returns. Under a fully parametric EGARCH-in-Mean specification, we propose to use an asymmetric error distribution in order to match the unconditional asymmetry of asset returns. Value-at-Risk prediction of the largest stock market indices is performed as an application.
