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It is well known that estimation issues severely impact the performances of investment strategies. This becomes even more problematic when accounting for higher moments as the number of parameters to be estimated quickly explodes with the number of assets. In this paper, we address this issue by relying on specific factor models. Although useful to reduce the dimension of the problem, principal component analysis (PCA) is only a partial solution. In particular, it does not break the exponential law that links the number of parameters to the moment order. This issue is tackled by using a new robust portfolio-selection technique that relies on independent component analysis (ICA). By linearly projecting the asset returns onto a small set of maximally independent factors, we obtain a sparse approximation of the comoment tensors of asset returns. This drastically de-creases the dimensionality of the problem and, as expected, leads to well-performing, robust and low-turnover investment strategies.
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Lassance, N., & Vrins, F. (2019). Robust portfolio selection using sparse estimation of comoment tensors (LFIN Working Paper 2020/03). https://hdl.handle.net/2078.5/268813