Higher moments such as Skewness and Kurtosis are not as explored as they should be.
These moments are crucial for managing portfolio risk. At least as important as volatility, if not more. Skewness relates to asymmetry risk and Kurtosis relates to tail risk.
Despite their great importance, those higher moments enjoy only a small portion of attention compared with their lower more friendly moments: the mean and the variance. In my opinion, one reason for this may be the impossibility of estimating those moments, estimating them accurately that is.
It is yet another situation where Curse of Dimensonality rears its enchanting head (and an idea for a post is born..).