The mean-variance model for portfolio optimization minimizes **portfolio risk** (covariance matrix), which is the *second* statistical moment of multivariate asset returns, and sometimes simultaneously maximizes **portfolio return**, which is the *first* statistical moment of asset returns. 

Is it possible to do asset allocation without any consideration to the moments of asset returns whatsoever? If so, what else is there to use? Do any theories and techniques exist that optimize investment portfolios *without* estimation of asset return moments? Do non-moment based portfolios perform well? 

(please not looking for the well-known heuristic methods either (equal weight, market cap weight, etc)