Portfolio selection with parsimonious higher comoments estimation

Large investment universes are usually fatal to portfolio strategies optimizing higher moments because of computational and estimation issues resulting from the number of parameters involved. In this paper, we introduce a parsimonious method to estimate higher moments that consists of projecting asset returns onto a small set of maximally independent factors found via independent component analysis (ICA). In contrast to principal component analysis (PCA), we show that ICA resolves the curse of dimensionality affecting the comoment tensors of asset returns. The method is easy to implement, computationally efficient, and makes portfolio strategies optimizing higher moments appealing in large investment universes. Considering the value-at-risk as a risk measure, an investment universe of up to 500 stocks and adjusting for transaction costs, we show that our ICA approach leads to superior out-of-sample risk-adjusted performance compared with PCA, equally weighted, and minimum-variance portfolios.