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.

We introduce a method to determine the investor’s optimal portfolio size that maximizes the expected out-of-sample utility under parameter uncertainty. This portfolio size trades off between accessing investment opportunities and limiting the number of estimated parameters. Unlike sparse methods such as lasso, which exclude assets during the optimization step, our approach fixes the optimal number of assets before optimizing the portfolio weights, which improves robustness and provides greater flexibility in practical implementations. Empirically, our size-optimized portfolios outperform their counterparts applied to all available assets. Our methodology renders portfolio theory valuable even when the data-set dimension and sample size are comparable.