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Portfolio selection and risk management are important problems that investors and portfolio managers face. The optimal portfolio construction, which assumes that investors are risk averse, see Markowitz (1952), is well known as a mean-variance analysis. The distributional characteristics of returns, like the unconditional skewness, are able to create new challenges in the classical portfolio theory of Markowitz. Apart from the mean and variance predictability, portfolio choice can be also made with skewness information. Such a perspective can create for investors the notion of skewness averse, as their financial decisions can be affected by properties of the return distribution.
The marginal distribution of financial time series such as returns is often negatively skewed. Asymmetries or nonlinearities in the conditional mean are important towards meeting the objection to generate skewed marginal distributions. This paper addresses the unconditional skewness of returns from the perspective of time-varying conditional first and second moments, together with the use of a more flexible conditional distribution for the returns.
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 an EGARCH-in-Mean specification, we propose to use an asymmetric error distribution in order to match the unconditional asymmetry of asset returns.
