Higher-Order Risk Preferences, Constant Relative Risk Aversion and the Optimal Portfolio Allocation

We derive the conditions for the optimal portfolio choice within a constant relative risk aversion type of utility function considering alternative probability distributions that are able to capture the asymmetric and leptokurtic features of asset returns. We illustrate the role — beyond risk aversion — played by higher-order moments in the optimal decision to form a portfolio of risky assets. In particular, we show that higher-order risk attitudes such as prudence and temperance associated with the third and fourth moments of the distribution define different optimal portfolios than those constrained under risk aversion