  Standard, PCA-based factor analysis suffers from a number of well known
problems due to the random nature of pairwise correlations of asset returns. We
analyse an alternative based on ICA, where factors are identified based on
their non-Gaussianity, instead of their variance. Generalizations of portfolio
construction to the ICA framework leads to two semi-optimal portfolio
construction methods: a fat-tailed portfolio, which maximises return per unit
of non-Gaussianity, and the hybrid portfolio, which asymptotically reduces
variance and non-Gaussianity in parallel. For fat-tailed portfolios, the
portfolio weights scale like performance to the power of $1/3$, as opposed to
linear scaling of Kelly portfolios; such portfolio construction significantly
reduces portfolio concentration, and the winner-takes-all problem inherent in
Kelly portfolios. For hybrid portfolios, the variance is diversified at the
same rate as Kelly PCA-based portfolios, but excess kurtosis is diversified
much faster than in Kelly, at the rate of $n^{-2}$ compared to Kelly
portfolios' $n^{-1}$ for increasing number of components $n$.
